The primal-dual comparative statics method of Samuelson (1965) and Silberberg (1974) is extended to cover the class of non-autonomous, finite horizon differential games in which a locally differentiable open-loop Nash equilibrium exists. In doing so, not only is a one-line proof of an envelope theorem provided but also the heretofore unknown intrinrsic comparative dynamics of open-loop Nash equilibria are uncovered. The intrinsic comparative dynamics are shown to be contained in a symmetric and negative semidefinite matrix that is subject to constraint. The results are applied to a canonical differential game in capital theory, and the resulting comparative dynamics are given an economic interpretation. Copyright © 2016 John Wiley & Sons, Ltd.

There is no standard framework for solving optimization problems for systems described by agent-based models (ABMs). We present a method for constructing individual-level controls that steer the population-level dynamics of an ABM towards a desired state. Our method uses a system of partial differential equations (PDEs) with control functions to approximate the dynamics of the ABM with control. An optimal control problem is formulated in terms of the PDE model to mimic the optimization goal of the ABM. Mathematical theory is used to derive optimal controls for the PDE model, which are numerically approximated and transformed for use in the ABM.

We use the Sugarscape ABM, a prototype ABM that includes agent and environmental heterogeneity and accumulation of agent resources over time. We present a PDE model that approximates well the spatial, temporal, and resource dynamics of the Sugarscape ABM. In both models, control represents taxation of agent wealth with the goal to maximize total taxes collected while minimizing the impact of taxation on the population over a finite time. Solutions to the optimal control problem yield taxation rates specific to an agent's location and current wealth. The use of optimal controls (generated by the PDE model) within the ABM performed better than other controls we evaluated, even though some error was introduced between the ABM and PDE models. Our results demonstrate the feasibility of using a PDE to approximate an ABM for control purposes and illustrate challenges that can arise in applying this technique to sophisticated ABMs. Copyright © 2016 John Wiley & Sons, Ltd.

A novel method is presented to solve the nonzero-sum multi-player Nash differential game. It combines the use of the variation and Legendre pseudo-spectral methods. By the variation method, the original game is converted into a regular optimal control problem, avoiding the need to solve the associated Hamilton–Jacobi equation. Then the latter problem is converted into a common nonlinear programming problem via the Legendre pseudo-spectral method, by which the saddle-point for the original game can be achieved accurately. As an illustration, the air combat between two pursuers and an evader is formulated as a nonzero-sum differential game. The simulation results show that numerical solutions can converge to the saddle-points from different initial conditions, which demonstrates the feasibility and validity of the proposed method. Because the solution process requires little computational time, this method will allow for the development of a real time air combat control strategy. In addition, the simulations show that if the initial states of the two pursuers are fixed, there is an optimal initial heading angle for the evader to delay the interception time most effectively. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the observer-based *H*_{∞} controller design problem for nonlinear networked control systems with random communication delays. Firstly, the dynamic observer-based control scheme is modelled, where the control input of the observer is different from the control input of the plant. Then, a less conservative delay-dependent *H*_{∞} stabilization criterion is derived by using an improved Lyapunov function. And the proof of stabilization criterion is completed in terms of four cases when the time delays in two communication channels are constant or time-varying, respectively. The derived stabilization criterion is formulated in the form of a non-convex matrix inequality, which can be solved by an optimal cone complementary linearization iteration algorithm to obtain the minimum disturbance attenuation level. Finally, several numerical examples and an illustrative example are provided to clarify the effectiveness and merits of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

In this study, a deterministic optimal control problem is investigated in which the system is governed by an ordinary differential equation with a general cost functional. In the framework of Fréchet derivatives, we establish the maximum principle with the Hamilton systems for this optimal control problem. Copyright © 2016 John Wiley & Sons, Ltd.

We present a novel distributed primal-dual active-set method for model predictive control. The primal-dual active-set method is used for solving model predictive control problems for large-scale systems with quadratic cost, linear dynamics, additive disturbance, and box constraints. The proposed algorithm is compared with dual decomposition and an alternating direction method of multipliers. Theoretical and experimental results show the effectiveness of the proposed approach for large-scale systems with communication delays. The application to building control systems is thoroughly investigated. Copyright © 2016 John Wiley & Sons, Ltd.

This paper deals with the problem of robust *H*_{∞} control for linear switched systems with time-varying delay and dead-zone inputs. First, a new state-dependent switching law is proposed for the switched system with stable and unstable subsystems. Based on the proposed switching law and using the scaled small gain theorem, a more general stability criterion for the switched delay systems is established. Second, an adaptive memory controller is proposed for the switched system with dead-zone inputs. With the help of a two-term approximation of the time-varying delay, the proposed memory controller only depends on the bounds of the time-varying delay. Sufficient conditions on the existence of the desired controller are formulated in terms of linear matrix inequalities. Three examples are provided to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.

Detection and isolation of actuator and sensor faults in presence of disturbance for a class of linear networked control systems is considered, while unknown network-induced delay is taken into account. The network-induced delay effect is modeled by time-varying polytopic uncertainties. Using eigen-structure assignment approach, a fault detection filter is designed to decouple the fault and plant disturbance, while minimizing the effect of the induced delays in the network, using *H*_{∞} and *H*_{−} index theories and benefiting from the free parameters in the eigen-structure assignment approach. If the full disturbance de-coupling is not feasible, another filter is designed to achieve partial de-coupling and maximum robustness against the disturbance and network-induced delay, while sensitivity to the fault is optimized. The actuator fault and disturbance vectors are augmented to define a new disturbance vector for isolation of the sensor and actuator faults. Numerical simulations are performed to evaluate the feasibility and applicability of the proposed approach.

An efficient robust reliability method for non-fragile robust control design of dynamic system with bounded parametric uncertainties is presented systematically, in which the uncertainties existing in the controlled plant and controller realization are taken into account simultaneously in an integrated framework. Reliability-based design optimization of non-fragile robust control for parametric uncertain systems is carried out by optimizing the *H*_{2} and *H*_{∞} performances of the closed-loop system, with the constraints on robust reliabilities. The non-fragile robust controller obtained by the presented method may possess a coordinated optimum performance satisfying the precondition that the system is robustly reliable with respect to the uncertainties existing in controlled plant and controller. Moreover, the robustness bounds of uncertain parameters can be provided. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. It is demonstrated by a numerical example that the presented method is effective and feasible.

In this paper, distributed model predictive control (MPC) problems are considered for input-saturated polytopic uncertain systems by a saturation-dependent Lyapunov function approach. The actuator saturation is processed by the transformation into the linear convex combination form. By the decomposition of the control input, distributed MPC controllers are designed in parallel for each subsystems. The Lyapunov Function we select is saturation dependent, which is less conservative than the general Lyapunov Function approach. An invariant set condition is provided and min–max distributed MPC is proposed based on the invariant set. The robust distributed MPC controllers are determined by solving a linear matrix inequality (LMI) optimization problem. To reduce the conservatism, we present a robust distributed MPC algorithm, which is not only saturation dependent but also parameter dependent. A Jacobi iterative algorithm is developed to coordinate the distributed MPC controllers. A simulation example with multi-subsystem is carried out to demonstrate the effectiveness of the proposed distributed MPC algorithms.

In this paper, a novel identifier–actor–critic optimal control scheme is developed for discrete-time affine nonlinear systems with uncertainties. In contrast to traditional adaptive dynamic programming methodology, which requires at least partial knowledge of the system dynamics, a neural-network identifier is employed to learn the unknown control coefficient matrix working together with actor–critic-based scheme to solve the optimal control online. The critic network learns the approximate value function at each step. The actor network attempts to improve the current policy based on the approximate value function. The weights of all neural networks are updated at each sampling instant. Lyapunov theory is utilized to prove the stability of closed-loop system. It shows that system states and neural network weights are uniformly ultimately bounded. Finally, simulations are provided to illustrate the effectiveness of the developed method. Copyright © 2016 John Wiley & Sons, Ltd.

A distributed multi-agent convex optimization problem over a network with time-varying connectivity is considered, where the agents are to collectively minimize a sum of nonsmooth but Lipschitz continuous functions subject to a convex constraint set. Based on Gaussian smoothing of the objective functions, a distributed projective random gradient-free algorithm is considered for the constrained optimization problem, where each agent performs a local averaging operation, takes the one-sided or two-sided randomized gradient approximates instead of the subgradients to minimize its own objective function, and projects on the constraint set. The bounds on the limiting performance of the algorithm in mean are obtained, and it is proven that there is mean consensus between agents for diminishing step sizes. It is showed that with appropriately selected step sizes, the agent estimates generated by the algorithm converge to the same stationary point of the smoothed version of the problem with probability 1. Therefore, with sufficient small smoothing parameters, we obtain the result of consensus and convergence of the agent estimates to an optimal solution with probability 1. A numerical example is provided to justify the theoretical analysis. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the optimal linear quadratic regulation problem for discrete-time systems with state and control dependent noises and multiple delays in the input. We show that the problem admits a unique solution if and only if a sequence of matrices, which are determined by coupled difference equations developed in this paper, are positive definite. Under this condition, the optimal feedback controller and the optimal cost are presented via some coupled difference equations. Our approach is based on the stochastic maximum principle. The key technique is to establish relations between the costate and the state. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents a solution of the optimal control problem for a class of pseudo Euler-Lagrange systems and proposes a systematic approach to find a Lyapunov function for stability analysis and controller synthesis for such systems. There are three main contributions of the paper. First, a systematic procedure is proposed and proved to construct a Lyapunov function for pseudo Euler-Lagrange system directly from the mathematical structure of the differential equations, without the need to determine any kinetic or potential energy of the system first. Second, control methodologies for pseudo Euler-Lagrange systems are also developed. In particular, an optimal controller is found for the case of second order dynamics yielding the same structure for the closed-loop Lyapunov function as the one derived from the systematic procedure outlined as the first contribution. Finally, the optimal control methodology is extended to systems with order higher than two for a class of triangular systems. The method proposed here works for any mathematical model in the class of pseudo Euler-Lagrange systems and is therefore not restricted to models of physical systems. Several examples illustrate the application of the novel approach, including mass-spring-damper systems and Van der Pol oscillators. Copyright © 2016 John Wiley & Sons, Ltd.

Optimal trajectory and muscle forces of a human-like musculoskeletal arm are predicted for planar point-to-point movements using optimal control theory. The central nervous system (CNS) is modeled as an optimal controller that performs a reaching motion to final states via minimization of an objective function. For the CNS strategy, a cubic function of muscles stresses is considered as an appropriate objective function that minimizes muscles fatigue. A two-DOF nonlinear musculoskeletal planar arm model with four states and six muscle actuators is used for the evaluation of the proposed optimal strategy. The nonlinear variational formulation of the corresponding optimal control problem is developed and solved using the method of variation of extremals. The initial and (desired) final states (position and velocity) are used as input kinematic information, while the problem constraints include the motion range of each joint, maximum allowable muscle tension, and stability requirements. The resulting optimal trajectories are compared with experimental data as well as those corresponding to recent researches on model predictions of human arm movements. It is demonstrated that the proposed optimal control strategy using minimum fatigue criterion is more realistic in prediction of motion trajectories in comparison with previous work that has utilized minimum joints' torque criterion. Accordingly, minimization of muscles fatigue is an effective biomechanical criterion for the CNS in prediction of point-to-point human arm motions. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents a new approach to trajectory optimization for nonlinear systems. The method exploits homotopy between a linear system and a nonlinear system and neighboring extremal optimal control, in combination with few iterations of a convergent optimizer at each step, to iteratively update the trajectory as the homotopy parameter changes. To illustrate the proposed method, a numerical example of a three-dimensional orbit transfer problem for a spacecraft is presented. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents a physiological model of glucose–insulin (GI) interaction and design of a Continuous-time Model Predictive Controller (CMPC) to regulate the blood glucose (BG) level in Type I diabetes mellitus (TIDM) patients. For the designing of the CMPC, a nonlinear physiological model of TIDM patient is linearized as a ninth-order state-space model with an implanted insulin delivery device. A novel control approach based on Continuous-time Model Predictive technique is proposed for the BG regulation with rejection of periodic or random meal and exercise disturbances in the process. To justify its efficacy a comparative analysis with Linear Quadratic Gaussian (LQG) control, and recently published control techniques like Proportional-Integral-Derivative (PID), Linear Quadratic Regulator with Loop Transfer Recovery (LQR/LTR) and H-infinity has been established. The efficiency of the controller with respect to accuracy and robustness has been verified via simulation. The proposed controller performances are assessed in terms of ability to track a *normoglycaemic* set point of 81 mg/dl (4.5 mmol/l) in the presence of Gaussian and stochastic noise. Copyright © 2016 John Wiley & Sons, Ltd.

An optimal portfolio problem with one risk-free asset and two jump-diffusion risky assets is studied in this paper, where the two risky asset price processes are correlated through a common shock. Under the criterion of maximizing the mean-variance utility of the terminal wealth with state dependent risk aversion, we formulate the time-inconsistent problem within a game theoretic framework and look for subgame perfect Nash equilibrium strategy. Based on the technique of stochastic control theory and the corresponding extended Hamilton–Jacobi–Bellman equation, the closed-form expressions of the optimal equilibrium strategy and value function are derived. Furthermore, we find that the optimal strategy, that is, the amount of money invested into the risky asset, is proportional to current wealth. Finally, some numerical examples are presented to show the impact of model parameters on the optimal results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper studies small unmanned aerial vehicle dynamic soaring for conserving onboard energy to extend flight endurance performance. A novel dynamic soaring path planning approach is proposed using the Dubins path. It enjoys a significant improvement in computational efficiency. In addition, a custom-built trajectory tracking controller is developed for a nonlinear unmanned aerial vehicle dynamics model to verify the implementation of the proposed path planning approach. Extensive numerical simulations are conducted to demonstrate the effectiveness of the proposed design and development. Copyright © 2016 John Wiley & Sons, Ltd.

In this study, we investigate the optimal control of a class of singularly perturbed linear stochastic systems with Markovian jumping parameters. After establishing an asymptotic structure for the stabilizing solution of the coupled stochastic algebraic Riccati equations, a parameter-independent composite controller is derived. Furthermore, the cost degradation in a reduced-order controller is discussed. Thus, the exactness of the proposed approximate control is discussed for the first time. As an additional important contribution, a numerical algorithm for solving the coupled stochastic algebraic Riccati equations is proposed, and the feature of the resulting higher-order controller is shown. Finally, a simple example is presented to demonstrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, optimal control of a general nonlinear multi-strain tuberculosis (TB) model that incorporates three strains drug-sensitive, emerging multi-drug resistant and extensively drug-resistant is presented. The general multi-strain TB model is introduced as a fractional order multi-strain TB model. The fractional derivatives are described in the Caputo sense. An optimal control problem is formulated and studied theoretically using the Pontryagin maximum principle. Four controls variables are proposed to minimize the cost of interventions. Two simple-numerical methods are used to study the nonlinear fractional optimal control problem. The methods are the iterative optimal control method and the generalized Euler method. Comparative studies are implemented, and it is found that the iterative optimal control method is better than the generalized Euler method. Copyright © 2016 John Wiley & Sons, Ltd.

This paper focuses on the full-order state estimation problem for continuous-time Markovian jumping systems with time delay and incomplete transition probabilities. Based on the Lyapunov stability theory, an extended Wirtinger's inequality is used to value the upper bound of integral term by considering the relationship among time delay, its upper, and their difference. At the same time, an extended vector inequality is applied to deal with the accompanying fractions that contain the information of time delay. As a result, an improved stability criterion is derived, and a full-order state estimates design method is proposed. Finally, two examples are provided to illustrate the merits of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Design methods are proposed for static and fixed-order dynamic output feedback controllers for discrete-time Luré systems with sector-bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear matrix inequalities, which are nonconvex. By using convex relaxation methods, controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs) and iterative LMIs, which are associated with semidefinite programs. The proposed design methods are developed from stability conditions using parameter-dependent Lyapunov functions, and existing iterative numerical methods are adapted to solve certain classes of nonconvex optimization problems for controller design. Several numerical examples are provided to illustrate and verify the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.

Model Predictive and linear quadratic Gaussian controllers are designed for a 5MW variable-speed pitch-regulated wind turbine for three operating points – below rated wind speed, just above rated wind speed, and above rated wind speed. The controllers are designed based on two different linear dynamic models (at each operating point) of the same wind turbine to study the effect of utilising different control design models (i.e. the model used for designing a model-based controller) on the control performance. The performance of the LQG controller is enhanced by improving the robustness, achieved by replacing the Kalman filter with a modified Luenberger observer, whose gain is obtained to minimise the effect of uncertainty and disturbance. Copyright © 2016 John Wiley & Sons, Ltd.

The investigation of a reaction–diffusion system with new nonlinear reactions kinetics to model the fermentation of wine is presented. The reactive part extends existing ordinary differential models by taking into account oxygen availability and ethanol toxicity. The presence of spatial diffusion and the inclusion of a heat equation allow geometrical and thermal effects in the model. Existence, uniqueness, and regularity of solutions to this system of reaction–diffusion partial differential equations are discussed. A boundary optimal control problem is formulated with the purpose of steering an ideal fermentation process. This optimal control problem is theoretically investigated and numerically solved in the adjoint method framework. The existence of an optimal control is proved, and its solution is characterized by means of the corresponding optimality system. To solve this system, an implicit–explicit splitting approach is considered, and a Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization scheme is implemented. Results of numerical experiments demonstrate the validity of the fermentation model and of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.

This paper investigates the classical time-optimal rest-to-rest three-axis reorientation of the inertially symmetric rigid spacecraft. First-order necessary optimality conditions are derived from the Pontryagin's maximum principle. Then, control structures (i.e., switching times and control torques) for the time-optimal solution with five, six, and seven switches are given. For any five-switch, six-switch, or seven-switch time-optimal solution, a finite number of control structures exist, and relations among the control structures and their associated time-optimal solutions are analytically derived. By utilizing the control structure, efficient numerical optimization algorithm based on multiple-interval Radau pseudospectral method is proposed. Numerical results show that, after rounding to integer, five-switch and six-switch time-optimal solutions exist for rotation angles on the interval [1,180] deg, and s es on the interval [1,72] deg. Finally, time-optimal solutions for typical rotation angles are given to illustrate and validate the new findings. Copyright © 2016 John Wiley & Sons, Ltd.

This paper studies the problem of *H*_{∞} state-feedback controller design for continuous-time nonhomogeneous Markov jump systems. The time-varying transition rate matrix in continuous-time domain is considered to lie in a convex bounded domain of polytopic type. By constructing a parameter-dependent Lyapunov function and fully considering the information about the rate of change of time-varying parameters, a new sufficient condition on the existence of an *H*_{∞} state-feedback controller is provided in the form of a parameter-dependent matrix inequality. Moreover, based on the structure characteristics of Lyapunov matrix and transition matrix, the parameter-dependent matrix inequality is converted into a finite set of linear matrix inequalities, which can be readily solved. Two numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

The radial basis function (RBF) network and autoregressive exogenous (ARX) model are combined to form the structure of the RBF-ARX model. The RBF-ARX model can describe the global nonlinear dynamic process of the object, and its function coefficients are approximated by data-driven method. The structured nonlinear parameters optimization method (SNPOM) is generally used to optimize model parameters, but this method is very complicated and hard to be mastered by engineers. However, genetic algorithm (GA) is simple and widely used. So the thought of GA optimizing RBF-ARX is generated, called GA-ARX-RBF, and applied to nonlinear dynamic flatness control system. In this article, the recursive least squares method to optimize linear weights of RBF is also used to improve the SNPOM, which reduces the complexity and storage capacity of data processing. Meanwhile, GA to optimize all the parameters of the RBF-ARX model replaces SNPOM completely. A GA-RBF-ARX modeling and optimizing method is proposed. In order to prove the efficiency of GA-RBF-ARX, it is applied into flatness control system, which has the characters of nonlinear, multivariable, and multi-disturbance. The flatness recognition model and flatness predictive model are established. A predictive controller based on GA-RBF-ARX is designed for 900HC reversible cold rolling mill. The simulation results demonstrate that the flatness control system based on GA-RBF-ARX is effective and has a better precision. The method is easily mastered by engineers and helps to promote the practical value of RBF-ARX. Copyright © 2016 John Wiley & Sons, Ltd.

The mechatronic elevator system driven by a permanent magnet synchronous motor is modeled using mechanical and electrical equations. In addition, the dimensionless forms are derived for practicable movements. This paper proposes and demonstrates the reference model of a minimum-input absolute electrical energy control scheme based on the Hamiltonian function. Furthermore, a model reference adaptive control scheme based on the Lyapunov function is proposed for tracking the reference model to achieve a robust control performance, thus combining the minimum-energy reference model of the minimum-input absolute electrical energy control and the robust control offered by the model reference adaptive control. The proposed model reference adaptive minimum-energy control yields robust minimum-energy control performance. Subsequently, the experimental parameters of the elevator system were identified through self-learning particle swarm optimization. The experimental results demonstrate the robust minimum-energy control performance of the proposed model reference adaptive minimum-energy control. Copyright © 2016 John Wiley & Sons, Ltd.

We study optimal control problems for linear systems with prescribed initial and terminal states. We analyze the exact penalization of the terminal constraints. We show that for systems that are exactly controllable, the norm-minimal exact control can be computed as the solution of an optimization problem without terminal constraint but with a nonsmooth penalization of the end conditions in the objective function, if the penalty parameter is sufficiently large. We describe the application of the method for hyperbolic and parabolic systems of partial differential equations, considering the wave and heat equations as particular examples. Copyright © 2016 John Wiley & Sons, Ltd.

Our work is devoted to an optimal control problem for two-dimensional parabolic partial differential equations(PDEs) and its application in engineering sciences. An adjoint problem approach is used for analysis of the Fréchet gradient of the cost functional, and we prove the gradient is Lipschitz continuous. An improved conjugate gradient method is proposed to solve this problem. Based on Lipschitz continuity of the gradient, the convergence analysis of the conjugate gradient algorithm we proposed is studied. Results of some computational experiments obtained by the conjugate gradient algorithm are illustrated. The results show that the improved conjugate gradient algorithm is effective. Copyright © 2016 John Wiley & Sons, Ltd.

The finite-horizon linear quadratic regulation problem is considered in this paper for the discrete-time singular systems with multiplicative noises and time delay in the input. Firstly, the extremum principle is discussed, and a stationary condition is derived for the singular stochastic system. Then, based on the relationships established between the state and the costate variables, the stationary condition is also shown to be a sufficient criterion assuring the existence of the solution for the stochastic control problem. The optimal controller is designed as a linear function of the current state and the past inputs information, which can be recursively calculated by effective algorithms. With the designed optimal controllers, the explicit expression is also derived for the minimal value of the performance index. One numerical example is provided in the end of the paper to illustrate the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we deal with the problem of time-optimal trajectory planning and feedforward controls for robotic manipulators along predetermined geometric paths. We propose a convex relaxation to generate time-optimal trajectories and feedforward controls that are dynamically feasible with respect to the complete nonlinear dynamic model, considering both Coulomb friction and viscous friction. Even though the effects of viscous friction for time-optimal motions become rather significant due to the required large speeds, in previous formulations, viscous friction was ignored. We present a strategic formulation that turns out non-convex because of the consideration of viscous friction, which nonetheless leads naturally to a convex relaxation of the referred non-convex problem. In order to numerically solve the proposed formulation, a discretization scheme is also developed. Importantly, for all the numerical instances presented in the paper, focusing on applying the algorithm results to a six-axis industrial manipulator, the proposed convex relaxation solves exactly the original non-convex problem. Through simulations and experimental studies on the resulting tracking errors, torque commands, and accelerometer readings for the six-axis manipulator, we emphasize the importance of penalizing a measure of total jerk and of imposing acceleration constraints at the initial and final transitions of the trajectory. Copyright © 2016 John Wiley & Sons, Ltd.

This paper proposes less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation. The transition rates associated with the transition probabilities are expressed in terms of three properties, which do not require the lower and upper bounds of the transition rates, differently from other approaches in the literature. The resulting conditions are converted into the second-order matrix polynomial of the unknown transition rates. The polynomial can be represented as quadratic form of vectorized identity matrices scaled by one and the unknown transition rates. And then, the LMI conditions are obtained from the quadratic form. Also, an optimization problem is formulated to find the largest estimate of the domain of attraction in mean square sense of the closed-loop systems. Finally, two numerical examples are provided to illustrate the effectiveness of the derived stabilization conditions. Copyright © 2016 John Wiley & Sons, Ltd.

This paper addresses an issue on reduced-order observer-based robust fault estimation and fault-tolerant control for a class of uncertain nonlinear discrete-time systems. By introducing a nonsingular coordinate transformation, a new nonlinear reduced-order fault estimation observer (RFEO) is proposed with a wide application range in order to achieve an accurate estimation of both states and faults. Next, an improved algorithm is given to obtain the optimal estimation by using a novel iterative linear matrix inequality technique. Furthermore, an RFEO-based output feedback fault-tolerant controller, which is independent of the RFEO, can maintain the stability and performance of the faulty system. Simulation results of an aircraft application show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

The bang-bang type optimal control problems arising from time-optimal or fuel-optimal trajectory planning in aerospace engineering are computationally intractable. This paper suggests a hybrid computational framework that utilizes differential flatness and mapped Chebyshev pseudospectral method to generate a related but smooth trajectory, from which the original non-smooth solutions are achieved continuously by the analytic homotopic algorithm. The flatness allows for transcribing the original problem into an integration-free flat outputs optimization problem with reduced number of decision variables. Chebyshev pseudospectral method is applied to parameterizing the flat outputs, and the numerical accuracy for the derivatives of flat outputs at collocation nodes, which are readily computed using differentiation matrices, is greatly enhanced by conformal map and barycentric rational interpolation techniques. Based on the obtained smooth trajectory, the analytic homotopic approach constructs an auxiliary optimal control problem whose costates are simply zero, avoiding the estimation of initial costates. The hybrid framework successfully addresses the difficulties of pseudospectral method and homotopic approach when they are applied separately. Numerical simulations of time-optimal trajectory planning for spacecraft relative motion and attitude maneuver are presented, validating the performance of the hybrid computational framework. Copyright © 2016 John Wiley & Sons, Ltd.

The problem of *H _{∞}* output tracking control over networked control systems (NCSs) with communication limits and environmental disturbances is studied in this paper. A wide range of time-varying stochastic problem arising in networked tracking control system is reduced to a standard convex optimization problem involving linear matrix inequalities (LMIs). The closed-loop hybrid NCS is modeled as a Markov jump linear system in which random time delays and packet dropouts are described as two stochastic Markov chains. Gridding approach is introduced to guarantee the finite value of the sequences of transmission delays from sensor to actuator. Sufficient conditions for the stochastic stabilization of the hybrid NCS tracking system are derived by the LMI-based approach through the computation of the optimal

The reduced-order model of the optimal control problem governed by Burgers equation is derived using the proper orthogonal decomposition (POD) method. The reduced-order solution depending on parameters, which are different from the nominal values, may not be accurate if the POD basis functions depending on the nominal values are used to derive the reduced-order model. It is known that Burgers equation is sensitive to the perturbations in the diffusion term, so we use the sensitivity information to improve the robustness of the POD solution by generating two new bases: extrapolated and expanded POD basis. We compare these different bases in terms of accuracy, robustness, and computational time. Copyright © 2015 John Wiley & Sons, Ltd.

This paper studies the static output feedback stabilization problems. An improved path-following method is proposed for continuous-time systems as well as for discrete-time systems. The method has two advantages. Firstly, by virtue of a new linearization approach, the related bilinear matrix inequalities ensuring the stabilization of the systems are expanded and linearized around some points. The initialization methods for both systems are built. Then a wide range perturbation step is added to help the method escape from local optimum. The effectiveness and merits of the proposed method are shown through several examples. Copyright © 2015 John Wiley & Sons, Ltd.

For periodic gait optimization problem of the bipedal walking robot, a class of global and feasible sequential quadratic programming algorithm (FSQPA) is proposed based on discrete mechanics and optimal control. The optimal controls and trajectories are solved by the modified FSQPA. The algorithm can rapidly converge to a stable gait cycle by selecting an appropriate initial gait; otherwise, the algorithm only needs one step correction that generates a stable gait cycle. Under appropriate conditions, we provide a rigorous proof of global convergence and well-defined properties for the FSQPA. Numerical results show that the algorithm is feasible and effective. Meanwhile, it reveals the movement mechanism in the process of bipedal dynamic walking, which is the velocity oscillations. Furthermore, we overcome the oscillatory behavior via the FSQPA, which makes the bipedal robot walk efficiently and stably on even terrain. The main result is illustrated on a hybrid model of a compass-like robot through simulations and is utilized to achieve bipedal locomotion via FSQPA. To demonstrate the effectiveness of the high-dimensional bipedal robot systems, we will conduct numerical simulations on the model of RABBIT with nonlinear, hybrid, and underactuated dynamics. Numerical simulation results show that the FSQPA is feasible and effective. Copyright © 2015 John Wiley & Sons, Ltd.

It is nontrivial to control a dynamic system that is switched consistently with a completely unknown switched modes. This problem is further complicated if the system is subject to stochastic disturbance. This paper studies the linear quadratic optimal control problem of linear continuous systems with stochastic disturbance and unknown switched process. By integrating one-step adaptive estimator with optimal control theory, a linear quadratic optimal stabilization controller based on sampled feedback is developed for systems that are continuous in nature yet switched consistently with unknown modes. It is shown that with the proposed control scheme, both parameter estimate error and system stabilization error are ensured to be bounded, and the existence of the upper bound is explicitly confirmed. The results compliment and extend the existing works on digital feedback control of switched linear continuous systems with unknown switched processes and stochastic disturbances. Copyright © 2015 John Wiley & Sons, Ltd.

This paper addresses the problems of simultaneous actuator and sensor fault estimation for a class of descriptor linear parameter varying systems. By extending the sensor fault as an auxiliary state, the original system can be transformed into a descriptor one. Then, by the using of *H*_{∞} optimization technique, a reduced-order observer is developed with a new defining variable. The proposed approach is based on the parameterizations of the obtained algebraic constraints from the error equation. By using the designed reduced-order observer and super twisting algorithm, the actuator fault can be reconstructed via a polytopic algebraic method. Finally, a simulation example of electric network is given to illustrate the validation of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

This paper studies target-reaching problems for systems controlled by multiple agents in which every agent implements control based on the choice selected independently from a private choice set. The agents' choices jointly determine the system target to be reached, and all the possible choice combinations define a set of targets to be reached. Without exchanging choice information among the agents, the existence of a set of control laws to realize all the targets in a given target set is a nontrivial question. For linear systems, the necessary and sufficient condition is shown hinged on a *compatibility condition* on the target set. Under the compatible condition, coordinated optimal control laws are derived such that any target in the target set can be achieved. Copyright © 2015 John Wiley & Sons, Ltd.

Recent technology breakthroughs towards a fully automated artificial pancreas give rise to the need of new monitoring tools aiming at increasing both reliability and performance of a closed-loop glycemic regulator. Based on error grid analysis, an insightful monitoring tool is proposed to assess if a given closed-loop implementation respects its specification of an optimally performing glycemic regulator under uncertainty. The optimal behavior specification is obtained using linearly solvable Markov decision processes, whereby the Bellman optimality equation is made linear through an exponential transformation that allows obtaining the optimal control policy in an explicit form. The specification for the desired glucose dynamics is learned using Gaussian processes for state transitions in an optimally performing artificial pancreas. By means of the proposed grid, the specification is *vis-à-vis* compared with glucose sensor readings so that any significant deviation from the expected closed-loop performance under abnormal or faulty scenarios can be detected. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a novel NN-based optimal adaptive consensus-based formation control scheme over finite horizon is presented for networked mobile robots or agents in the presence of uncertain robot/agent dynamics. The uncertain robot formation dynamics are approximated online by using an NN-based identifier and a suitable weight tuning law. In addition, a novel time-varying value function is derived by using the augmented error vector, which consists of the regulation and consensus-based formation errors of each robot. By using the value function approximation and the identified dynamics, the near optimal control input over finite horizon is derived. This finite horizon optimal control leads to a time-varying value function, which becomes the solution of the Hamilton–Jacobi–Bellman equation, and control input is approximated by a second NN with time-varying activation function. A novel weight update law for the NN value function is developed to tune the value function, satisfy the terminal constraint, and relax an initial admissible controller requirement. The Lyapunov stability method is utilized to demonstrate the consensus of the overall formation. Finally, simulation results are given to verify theoretical claims. Copyright © 2015 John Wiley & Sons, Ltd.

We consider a continuous-time positive bilinear control system, which is a bilinear control system with Metzler matrices. The positive orthant is an invariant set of such a system, and the corresponding transition matrix is entrywise nonnegative for all time. Motivated by the stability analysis of positive linear switched systems under arbitrary switching laws, we define a control as optimal if it maximizes the spectral radius of the transition matrix at a given final time. We derive high-order necessary conditions for optimality for both singular and bang–bang controls. Our approach is based on combining results on the second-order derivative of a simple eigenvalue with the generalized Legendre-Clebsch condition and the Agrachev–Gamkrelidze second-order optimality condition. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is devoted to general optimal control problems (OCPs) associated with a family of nonlinear continuous-time switched systems in the presence of some specific control constraints. The stepwise (fixed-level type) control restrictions we consider constitute a common class of admissible controls in many real-world engineering systems. Moreover, these control restrictions can also be interpreted as a result of a quantization procedure appglied to the inputs of a conventional dynamic system. We study control systems with a priori given time-driven switching mechanism in the presence of a quadratic cost functional. Our aim is to develop a practically implementable control algorithm that makes it possible to calculate approximating solutions for the class of OCPs under consideration. The paper presents a newly elaborated linear quadratic-type optimal control scheme and also contains illustrative numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, the control system of a permanent-magnet synchronous machine wind turbine generator connected to the grid is studied. A set of wind speed time series is used to model the rapidly changing wind speed component as a stochastic process. Several control laws, including the nonlinear stochastic optimal controller, are developed, and their efficiency is examined comparatively and under various conditions. Also, the effect of parameter uncertainty to the system efficiency is shown through simulations. The results show that the system efficiency increase obtained by the use of sophisticated control techniques, although not dramatic, is not negligible. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we investigate an optimal control problem in which the objective is to decelerate a simplified vehicle model, subject to input constraints, from a given initial velocity down to zero by minimizing a quadratic cost functional. The problem is of interest because, although it involves apparently simple drift-less dynamics, a minimizing trajectory does not exist over the admissible input trajectories. This problem is motivated by a minimum-time problem for a fairly complex car vehicle model on a race track. Numerical computations run on the car trajectory optimization problem provide evidence of convergence issues and of an apparently unmotivated ripple in the steer angle. Characterizing this ripple behavior is important to fully understand and exploit minimizing vehicle trajectories. We are able to isolate the key features of this chattering behavior in a very simple dynamics/objective setting. We show that the cost functional has an infimum, but an admissible minimizing input trajectory does not exist. We also show that the infimum can be arbitrarily approximated by bang-bang inputs with a sufficiently large number of switches. We reproduce this phenomenon in numerical computations and characterize it by means of non-existence of admissible minimizing trajectories. Copyright © 2015 John Wiley & Sons, Ltd.

We are interested in the mathematical modeling and control of electric power lines. The electric transmission lines under consideration are modeled as directed graph where the evolution of voltage, and current is described by a linear 2 × 2 system of hyperbolic balance laws. Open and closed loop control concepts are investigated for control actions at nodal points in the network. Theoretical and numerical results are presented and compared for different scenarios. Copyright © 2015 John Wiley & Sons, Ltd.

This paper proposes a new design method of *H*_{∞} filtering for nonlinear large-scale systems with interconnected time-varying delays. The interaction terms with interval time-varying delays are bounded by nonlinear bounding functions including all states of the subsystems. A stable linear filter is designed to ensure that the filtering error system is exponentially stable with a prescribed convergence rate. By constructing a set of improved Lyapunov functions and using generalized Jensen inequality, new delay-dependent conditions for designing *H*_{∞} filter are obtained in terms of linear matrix inequalities. Finally, an example is provided to illustrate the effectiveness of the proposed result. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the optimal guaranteed cost synchronization problem for a class of coupled neural networks with Markovian jump parameters and mode-dependent mixed time-delay. The coupled neural networks contained *N*-identical delayed neural nodes and *M* switch modes from one mode to another according to a Markovian chaining with known transition probability. All the coupled networks' parameters covering the coupled matrix and discrete and distributed time-delay also depend on the Markovian jump mode. The associated optimal guaranteed cost function is a quadratic function; the activation function is supposed to satisfy sector-bounded condition. By employing a new Lyapunov–Krasovskii functional and some analytic skills, the sufficiency conditions of guaranteed cost synchronization are derived to ensure that coupling neural network is asymptotically synchronized for related cost function in mean square. The exported sufficient condition is closely contacted with the distributed time-delay, the mode transition probability, the discrete-time delay, and the coupled structure of networks. The achieved conditions are given in the light of LMI that can be usefully solved by using the semi-definite program scheme. Moreover, an LMI-based approach to export the guaranteed cost synchronization controller is formulated to minimize the optimal guaranteed cost for closed-loop dynamical networks. Numerical simulations are developed to further display the efficiency of the achieved theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a combined feedback/feedforward design methodology is proposed for fractional systems in order to cope with model uncertainty and to minimize performance degradation. Based on a fractional commensurate uncertain model, a parametric robust controller is first designed. Then, a parametric command signal for the unity feedback loop is designed. Finally, an optimal set of tuning parameters is found by solving a constrained min–max optimization problem in order to minimize the worst-case settling time. Simulation results show the effectiveness of the methodology. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the problems of reachable set estimation and synthesis for discrete-time periodic systems under bounded peak disturbances. For the reachable set estimation problem, the lifting approach and the pseudo-periodic Lyapunov function approach are utilized to determine the bounding ellipsoids for the reachable set. By using the lifting approach, the periodic system is transformed into several time-invariant systems; then, the bounding ellipsoids are determined through the transformed time-invariant systems. By applying the pseudo-periodic Lyapunov function approach, the bounding ellipsoids are determined through the original periodic system directly. Genetic algorithm is adopted in the pseudo-periodic Lyapunov function approach to search for the optimal value of the decision variables. Moreover, based on the reachable set estimation results, state-feedback controllers are designed for manipulating the reachable set. Finally, numerical examples are presented to verify the effectiveness of the theoretical findings. Copyright © 2015 John Wiley & Sons, Ltd.

Every therapy that fights against cancer aims to reduce the tumor volume as far as possible. However, the price of low tumor volume has to be paid twice: as financial cost and also as side effect cost. In this article, we present qualitative correlation between the steady-state tumor volume and inhibitor serum concentration based on the tumor growth model. Assuming standard state feedback, we present qualitative correlation between the steady-state tumor volume and the parameters of the controller. In case of using an observer, we specify the steady-state tumor volume and the expression for determining the steady-state error of the state observer. We apply a limit for the state feedback to guarantee the stability of the closed-loop system and the positivity of the control signal. The controller parameters depend on the applied operation point where the nonlinear system was linearized. We have investigated the effect of the operation point via simulations, and we present a quantitative theory for choosing the effective operating point. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, the observer-based *H*_{∞} control problem for uncertain singular time-delay systems with actuator saturation is concerned. First, a delay-dependent linear matrix inequality (LMI) condition is obtained which, guarantees that the uncertain singular time-delay systems with actuator saturation are regular, impulse free, and asymptotically stable with *H*_{∞} performance condition. Then, with this condition, the estimation of stability region and the design method of observer-based *H*_{∞} controller are given by solving LMIs and convex optimization problem. Finally, some numerical examples are provided to demonstrate the merit of the obtained results. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we consider a multitime multiobjective fractional variational problem of minimizing a vector of quotients of path-independent curvilinear integral functionals subject to certain partial differential equations and inequations. Using the so-called parametric approach, we establish necessary and sufficient optimality conditions for the considered class of multitime multiobjective fractional variational problems under both (*F*,*ρ*)-convexity and generalized (*F*,*ρ*)-convexity. Further, the parametric multiobjective variational dual problem is formulated for the considered multitime multiobjective fractional variational problem, and several duality results are established under (generalized) (*F*,*ρ*)-convexity. Copyright © 2015 John Wiley & Sons, Ltd.

No abstract is available for this article.

]]>In this article, two adaptive model predictive controllers (AMPC) are applied to regulate the blood glucose in type 1 diabetic patients. The first controller is constructed based on a linear model, while the second one is designed by using a nonlinear Hammerstein model. The adaptive version of these control schemes is considered to make them more robust against model mismatches and external disturbances. The least squares method with forgetting factor is used to update the model parameters. For simulation study, two well-known mathematical models namely, Puckett and Hovorka which describe the dynamical behavior of patient's body have been selected. The performances and robustness of the proposed controllers are tested for regulating the blood glucose of diabetic patients in presences of model mismatches and measurement noises. Simulation results indicate that the non-linear model predictive controller (NMPC) outperforms the linear one. To improve the performance of the NMPC in rejecting the meal disturbances, two different feedforward control strategies have been considered. Simulation results indicate that the combined adaptive NMPC with feedforward controller has a better performance over the other considered control schemes. Copyright © 2015 John Wiley & Sons, Ltd.

In the paper, we study an optimal control problem connected with a fractional Roesser model described by partial Riemann–Liouville derivatives. A theorem on the existence optimal solutions and the maximum principle for such problem with nonhomogeneous boundary conditions are proved. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, automatic generation control (AGC) of a two-area multi-source power system interconnected via alternating current/direct current (AC/DC) parallel links under restructured power environment is proposed. Each area is equipped with multipower generating sources such as thermal and hydro/gas. To execute the different market contracts in restructured power system, the optimal regulators are designed and implemented using optimal control theory. It is observed that the system dynamic results effectively satisfy the AGC requirements in restructured power system, as well as the system dynamic performance is improved by using AC/DC parallel links in comparison with that obtained with AC link as an area interconnection between the control areas. Furthermore, the eigenvalue study is performed to examine the system stability with and without AC/DC parallel links. Finally, the effectiveness of the optimal regulators is checked for the system under study with physical constraints like time delay, boiler dynamics, generation rate constraints, and governor dead band nonlinearity and variations in system parameters from the nominal values. It is shown that the optimal regulators optimized for linear system are robust enough and work well in the proposed realistic AGC system incorporating physical constraints and wide variations in parameters. Copyright © 2015 John Wiley & Sons, Ltd.

The paper deals with the problem of robust *H*_{∞} control for stochastic time-delayed Markovian switching systems under partly known transition rates and actuator saturation via anti-windup design. The problem we address is the design of anti-windup compensators, which guarantee that the resulting closed-loop system is robustly stochastically stable with *H*_{∞} performance. By employing local sector conditions and an appropriate Lyapunov–Krasovskii function, sufficient conditions for solving the problem are derived in the form of linear matrix inequalities. Finally, numerical examples are given to demonstrate the validity of the main results. Copyright © 2015 John Wiley & Sons, Ltd.

The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic differential equations with Poisson jumps in Hilbert spaces. First, we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using the successive approximation approach. The results are formulated and proved by using the fractional calculus, solution operator, and stochastic analysis techniques. The existence of optimal control pairs of system governed by fractional neutral stochastic differential equations with Poisson jumps is also presented. An example is given to illustrate the theory. Copyright © 2015 John Wiley & Sons, Ltd.

A stochastic Lotka–Volterra predator–prey system driven by both Brownian motion and Poisson counting measure is modeled and studied in this paper. A new ergodic method is proposed to solve the classical optimal harvesting problem. Equivalency between time averaged yield function and sustained yield function is proved by this new approach. The optimal harvesting strategy and the corresponding maximum yield with respect to stationary probability density are obtained. Several examples are taken to show that results in this paper are new even in the deterministic case. The method proposed in this paper can avoid trouble of solving the corresponding partial differential equations, and it can be extended to a more general high-dimensional case or some other stochastic system. Copyright © 2015 John Wiley & Sons, Ltd.

Fractional calculus is the field of mathematical analysis that deals with the investigation and applications of integrals, derivatives of arbitrary order. The strength of derivatives of non-integer order is their ability to describe real situations more adequately than integer order derivatives, especially when the problem has memory or hereditary properties. This paper is mainly concerned with the square-mean almost automorphic mild solutions to a class of fractional neutral stochastic integro-differential equations with infinite delay driven by Poisson jumps. The existence of square-mean almost automorphic mild solutions of the previous fractional dynamical system is proved by using the method of successive approximation. The results are formulated and proved by using the fractional calculus, solution operator, and stochastic analysis techniques. Further, the existence of optimal control of the proposed problem is also presented. An example is provided to illustrate the developed theory. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a composite Chebyshev finite difference method to numerically solve nonlinear optimal control problems with multiple time delays. The proposed discretization scheme is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev Gauss–Lobatto points. Our approach is an extension and also a modification of the Chebyshev finite difference scheme. A direct approach is used to transform the delayed optimal control problem into a nonlinear programming problem whose solution is much more easier than the original one. Some useful error bounds are established. In addition, the convergence of the method is discussed. A wide variety of numerical experiments are investigated to show the usefulness and effectiveness of the proposed discretization procedure. The method has a simple structure and can be implemented without too much effort. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a real-time MPC-based tracking strategy for linear systems subject to time-varying constraints. The framework is quite general because the time-varying constraints can apply both to the state and to the input. To handle the problem, a polytopic invariant set computed off-line is homogeneously dilated or contracted on-line to fit the polytopic time-varying constraints. The invariant set is used as an admissible terminal constraint set so that it guarantees stability and convergence in the tracking task. The on-line cost of the homothetic invariant set computation is low enough to cope with systems subject to stringent real-time constraints. Copyright © 2015 John Wiley & Sons, Ltd.

In this work, the feasibility of applying a Sliding Mode Predictive Controller (SMPC) to improve greenhouse inside air temperature control is addressed in terms of energy consumption, disturbance handling and set point tracking accuracy. Major research issues addressed concern the SMPC robustness study in greenhouse control, as well as to evaluate if the levels of performance and energy consumptions are acceptable when compared with the traditional generalized predictive controller. Besides the external disturbances related to weather conditions throughout the considered period, such as solar radiation and temperature variations, internal effects of irrigation system and external air flow entering the greenhouse must be taken into account. Simulations based on real data, carried out for a period of 4months, suggest that the strategy herein described not only appropriately rejects these disturbances, but also keeps the manipulated variables (heating and cooling) within feasible practical limits, with low levels of energy consumption, motivating its refinement for real application. SMPC results are presented and compared with the ones obtained with the generalized predictive controller. Both controllers are subject to actuator constraints and employ the Quadratic Programming for optimization. Copyright © 2015 John Wiley & Sons, Ltd.

The main contribution of this paper is to identify explicit classes of locally controllable second-order systems and optimization functionals for which optimal control problems can be solved analytically, assuming that a differentiable optimal cost-to-go function exists for such control problems. An additional contribution of the paper is to obtain a Lyapunov function for the same classes of systems. The paper addresses the Lie point symmetries of the Hamilton–Jacobi–Bellman (HJB) equation for optimal control of second-order nonlinear control systems that are affine in a single input and for which the cost is quadratic in the input. It is shown that if there exists a dilation symmetry of the HJB equation for optimal control problems in this class, this symmetry can be used to obtain a solution. It is concluded that when the cost on the state preserves the dilation symmetry, solving the optimal control problem is reduced to finding the solution to a first-order ordinary differential equation. For some cases where the cost on the state breaks the dilation symmetry, the paper also presents an alternative method to find analytical solutions of the HJB equation corresponding to additive control inputs. The relevance of the proposed methodologies is illustrated in several examples for which analytical solutions are found, including the Van der Pol oscillator and mass–spring systems. Furthermore, it is proved that in the well-known case of a linear quadratic regulator, the quadratic cost is precisely the cost that preserves the dilation symmetry of the equation. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we focus on a class of a two-dimensional optimal control problem with quadratic performance index (cost function). We are going to solve the problem via the Ritz method. The method is based upon the Legendre polynomial basis. The key point of the Ritz method is that it provides greater flexibility in the initial and non-local boundary conditions. By using this method, the given two-dimensional continuous-time quadratic optimal control problem is reduced to the problem of solving a system of algebraic equations. We extensively discuss the convergence of the method and finally present our numerical findings and demonstrate the efficiency and applicability of the numerical scheme by considering three examples. Copyright © 2015 John Wiley & Sons, Ltd.

This paper extends the existing proximate time-optimal servomechanism control methodology to the more typical second-order servo systems with a damping element. A parameterized design of expanded proximate time-optimal servomechanism control law with a speed-dependent linear region is presented for rapid and smooth set-point tracking using a bounded input signal. The control scheme uses the time-optimal bang-bang control law to accomplish maximum acceleration or braking whenever appropriate and then smoothly switches into a linear control law to achieve a bumpless settling. The closed-loop stability is analyzed, and then the control scheme is applied to the position–velocity control loop in a permanent magnet synchronous motor servo system for set-point position regulation. Numerical simulation has been conducted, followed by experimental verification based on a TMS320F2812 digital signal controller board. The results confirm that the servo system can track a wide range of target references with superior transient performance and steady-state accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

Unemployment is continuously increasing worldwide because of enormous increase in population. This paper attempts to propose an optimal control policy for a deterministic unemployment model. The model considers three states, namely, unemployment, employment, and newly created vacancies. Factors like retirement and death of employed persons, termination from job, and so forth are also included in the model. The optimal control analysis for proposed unemployment model is performed using Pontryagin's maximum principle. The conditions for optimal control of the unemployment problem with effective use of implemented policies to provide employment to unemployed persons and to create new vacancies are derived and analyzed. Copyright © 2015 John Wiley & Sons, Ltd.

The paper presents a constraint transformation approach for nonlinear model predictive control (MPC) subject to a class of state and control constraints. The approach uses a two-stage transformation technique to incorporate the constraints into a new unconstrained MPC formulation with new variables. As part of the stability analysis, the relationship of the new unconstrained MPC scheme to an interior penalty formulation in the original variables is discussed. The approach is combined with an unconstrained gradient method that allows for computing the single MPC iterations in a real-time manner. The applicability of the approach, for example, to fast mechatronic systems, is demonstrated by numerical as well as experimental results. Copyright © 2015 John Wiley & Sons, Ltd.