This note is concerned with the linear estimation problems for discrete-time systems where the measurements are subject to random time delay and packet dropout. Different from most of previous works, the time-stamping is assumed to be unavailable in this paper. In this case, the estimation problems for such systems are very difficult because the information of the received measurements is not exactly known in most cases. To overcome the difficulty caused by the random delay and unavailability of time-stamping, a new observation is introduced by the summation of all the measurements received in the same time. Then, the random time delay measurement system is converted into a constant-delay measurement system with multiplicative noises where the noise is binary distributed random variables with known distributions. Finally, the linear optimal estimator is derived by using the transformation of auto-regressive moving average model to state-space model and the standard Kalman filtering. The convergence and stability of the filter are also analyzed. A simulation example is given to show the effectiveness of the proposed estimator. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents an approach to solve a singular quadratic optimization problem for linear time varying systems based on the *so-called* integral high-order sliding mode control. The plant which is time varying is affected for some bounded disturbances, and the criterion to minimize is degenerated, in the sense that the weighting matrix can possess any rank. It is shown the natural connection between the order of singularity of the time varying quadratic criterion, which is connected to the rank of the cost matrix and the order of the sliding mode. An integral high-order sliding mode is proposed to control the behavior of the transit phase before arriving toward the corresponding higher order singular time varying optimal manifold in prescribed time. The transformation to the phase-variable form for the Linear Time Variant Systems (LTVS) becomes the key step to solve the problem, and the proposed solution provides the insensitivity of trajectory w.r.t. matched bounded uncertainties. Such a design is applied to a probe landing problem to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

This paper aims to stabilize hybrid stochastic differential equations with norm-bounded uncertainties by feedback controls based on the discrete-time observations of both state and mode. The control structure appears only in the drift part (the deterministic part) of a stochastic differential equations, and the controlled system will be robustly exponentially stable in mean square. Our stabilization criteria are in terms of linear matrix inequalities whence the feedback controls can be designed more easily in practice. An example is given to illustrate the effectiveness of our results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper reconsiders existence of worst-case Nash equilibria in noncooperative multi-player differential games, this, within an open-loop information structure. We show that these equilibria can be obtained by determining the open-loop Nash equilibria of an associated differential game with an additional initial state constraint. For the special case of linear-quadratic differential games, we derive both necessary and sufficient conditions for solvability of the finite planning horizon problem. In particular, we demonstrate that, unlike in the standard linear-quadratic differential game setting, uniqueness of equilibria may fail to hold. A both necessary and sufficient condition under which there is a unique equilibrium is provided. A sufficient existence condition for a unique equilibrium is derived in terms of a Riccati differential equation. Consequences for control policies are demonstrated in a simple debt stabilization game. © 2016 The Authors. *Optimal Control Applications and Methods* published by John Wiley & Sons, Ltd.

In this paper, we study a partially observed linear quadratic optimal control problem derived by stochastic differential delay equations. Combining backward separation method with stochastic filtering, we obtain optimal feedback regulators in some special cases. Some filtering results for anticipated backward stochastic differential equations are also developed by expressing the solutions of the anticipated backward stochastic differential equations as some Itô's processes. Copyright © 2016 John Wiley & Sons, Ltd.

In this work, we propose a feedback control law that enforces capture of a moving target by a slower pursuer in finite time. It is well known that if this problem is cast as a pursuit-evasion differential game, then the moving target can always avoid capture by taking advantage of its speed superiority, provided that both the target and the pursuer are employing feedback strategies in the sense of Isaacs. Thus, in order to have a well-posed pursuit problem, additional assumptions are required so that the pursuer can enforce capture of the faster target in finite time provided that it emanates from a set of ‘favorable’ initial positions, which constitute its *winning set*. In particular, we assume that the target's velocity either is constant and perfectly known to the pursuer (perfect information case) or can be decomposed into a dominant component, which is constant and known to the pursuer, and a second component that is uncertain and unknown to the pursuer (imperfect information case). It turns out that in both cases, the winning sets of the pursuer are pointed convex cones which have a common apex and a common axis of symmetry but different opening angles. We subsequently propose continuous feedback laws that enforce finite-time capture while the pursuer never exits its winning set before capture takes place, for both cases. Copyright © 2016 John Wiley & Sons, Ltd.

This paper explores the optimal control of quantum state transfer in a two-dimensional quantum system by a sequence of non-selective projection measurements. We show that for a given initial state, one can always find the corresponding projection operator that can effectively drive the given initial state to any arbitrary target pure state. An external control field is proposed to compensate the effect of the free evolution of system. Numerical simulations and characteristics analysis are given in three cases: without considering free evolution, considering free evolution, and with the action of external control field. The simulating experimental results show that the optimal measurement control is more effective by using proposed external control field. Copyright © 2016 John Wiley & Sons, Ltd.

This paper investigates fuel-optimal impulsive reconfiguration of formation-flying satellites near circular reference orbit. First, the general reconfiguration is transformed into reconfiguration that should be accomplished during multiple orbital periods of the chief. Then, based on the primer vector analysis, multiple-impulse fuel-optimal analytical solutions for the transformed reconfiguration are derived. It is shown that multiple-impulse fuel-optimal analytical solutions appear conjugated and the corresponding reconfiguration trajectories are symmetric about the chief. Furthermore, for fuel-optimal analytical solution with three or more impulses, the associated impulse magnitudes may have many combinations, which would yield different reconfiguration trajectories but with the same fuel cost. Finally, numerical examples for three typical formation reconfiguration maneuvers, including resizing, reorientation, and reassignment, are given to illustrate and validate the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper proposes an integrated actuator and sensor active fault-tolerant model predictive control scheme. In this scheme, fault detection is implemented by using a set-valued observer, fault isolation (FI) is performed by set manipulations, and fault-tolerant control is carried out through the design of a robust model predictive control law. In this paper, a set-valued observer is used to passively complete the fault detection task, while FI is actively performed by making use of the constraint-handling capability of robust model predictive control. The set-valued observer is chosen to implement fault detection and isolation (FDI) because of its simple mathematical structure that is not affected by the type of faults such as sensor, actuator, and system-structural faults. This means that only one set-valued observer is needed to monitor all considered actuator and sensor statuses (health and fault) and to carry out the fault detection and isolation task instead of using a bank of observers (each observer matching a health/fault status). Furthermore, in the proposed scheme, the advantage of robust model predictive control is that it can effectively deal with system constraints, disturbances, and noises and allow to implement an active FI strategy, which can improve FI sensitivity when compared with the passive FI methods. Finally, a case study based on the well-known two-tank system is used to illustrate the effectiveness of the proposed fault-tolerant model predictive control scheme. Copyright © 2016 John Wiley & Sons, Ltd.

The paper deals with the problem of delay-dependent output feedback *L*_{1} control for positive Markovian jump systems with mode-dependent time-varying delays and partly known transition rates. First, by constructing an appropriate co-positive type Lyapunov function, sufficient conditions for stochastic stability and *L*_{1}-gain performance of the open-loop system are developed. Then, an effective method is proposed to construct the output feedback controller. These sufficient criteria are derived in the form of linear programming. A key point of this paper is to extend the special requirement of completely known transition rates to more general form that covers completely known and completely unknown transition rates as two special cases. Finally, a numerical example is given to illustrate the validity of the main results. Copyright © 2016 John Wiley & Sons, Ltd.

Control Performance Assessment (CPA) and tuning of PID controllers are studied in this paper. We propose a framework for systematic analysis of the tradeoff between the structural complexity of the controller and its performance. As the measure of the controller performance, an LQG based index is used. The problem is augmented with an additional term which forces sparsity on the complexity of a decentralized PID controller. The desired complexity is controlled via a weighting parameter which determines the cost of each additional element (i.e., P, I, and D terms). The result is a decentralized multivariable PID controller in which the complexity of each loop controller is optimized such that the desired LQG Performance Index is achieved with the lowest controller complexity. For larger multivariable systems, this will translate into a substantially reduced set of controller parameters. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical example of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Problems within the important class of reaction-diffusion systems may be optimized with these tools. © 2016 The Authors. Optimal Control Applications and Methods published by John Wiley & Sons, Ltd.

This paper provides necessary conditions of optimality, in the form of a maximum principle, for optimal control problems of switching systems. Dynamics of the constituent processes take the form of stochastic differential equations with control terms in the drift and diffusion coefficients. The restrictions on the transitions or switches between operating modes are described by the collection of functional equalities. The main result is proved via an approximation functional and Ekeland's variational principle. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the problem of guaranteed cost control for switched linear parameter-varying (LPV) systems. A parameter and state-dependent switching law with dwell time is designed. The guaranteed cost control problem for switched LPV systems is still solvable even though this problem for each subsystem is unsolvable. First, a sufficient condition ensuring the solvability of the guaranteed cost control problem for switched LPV systems is presented via multiple parameter-dependent Lyapunov functions. Then, the parameter-dependent controller is designed, such that the closed-loop system is asymptotically stable with the guaranteed cost index. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an aero-engine. Copyright © 2016 John Wiley & Sons, Ltd.

An improved control vector parameterization (CVP) method is proposed to solve optimal control problems with inequality path constraints by introducing the *l _{1}* exact penalty function and a novel smoothing technique. Both the state and control variables are allowed to appear explicitly in the inequality path constraints simultaneously. By applying the penalty function and smoothing technique, all the inequality path constraints are firstly reformulated as non-differentiable penalty terms and incorporated into the objective function. Then, the penalty terms are smoothed by using a novel smooth function, leading to a smooth optimal control problem with no inequality path constraints. With discretizing the control space, a corresponding nonlinear programming (NLP) problem is derived, and error between the NLP problem and the original problem is discussed. Results reveal that if the smoothing parameter is sufficiently small, the solution of the NLP problem is approximately equal to the original problem, which shows the convergence of the proposed method. After clarifying some theories of the proposed approach, a concomitant numerical algorithm is put forward with furnishing the updating rules of both the penalty parameter and smoothing parameter. Simulation examples verify the advantages of the proposed method for tackling nonlinear optimal control problems with different inequality path constraints. Copyright © 2016 John Wiley & Sons, Ltd.

We study control of the angular-velocity actuated nonholonomic unicycle, via a simple, bounded extremum seeking controller which is robust to external disturbances and measurement noise. The vehicle performs source seeking despite not having any position information about itself or the source, able only to sense a noise corrupted scalar value whose extremum coincides with the unknown source location. In order to control the angular velocity, rather than the angular heading directly, a controller is developed such that the closed loop system exhibits multiple time scales and requires an analysis approach expanding the previous work of Kurzweil, Jarnik, Sussmann, and Liu, utilizing weak limits. We provide analytic proof of stability and demonstrate how this simple scheme can be extended to include position-independent source seeking, tracking, and collision avoidance of groups on autonomous vehicles in GPS-denied environments, based only on a measure of distance to an obstacle, which is an especially important feature for an autonomous agent. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we investigate the *H*_{∞} control problem for a class of switched nonlinear systems based on passivity. The solvability conditions of the *H*_{∞} control problem are obtained by designing a state-dependent switching law and state feedback controller of each subsystem. In addition, if all subsystems are not passive, we make a partition of the state space and design controllers for subsystems such that each subsystem has the passivity property on the associated region, and then obtain solvability conditions of the *H*_{∞} control problem. An example is provided to demonstrate the effectiveness of the proposed design method. Copyright © 2016 John Wiley & Sons, Ltd.

This paper concerns with the jump linear quadratic Gaussian problem for a class of nonhomogeneous Markov jump linear systems (MJLSs) in the presence of process and observation noise. By assuming that mode transition rate matrices (MTRMs) are piecewise homogeneous whose variation is subjected to a high-level Markov process, two Markov processes are proposed to model the characteristics of nonhomogeneous MJLSs: the variation of system mode is governed by a low-level Markov process, while the variation of MTRM is governed by a high-level one. Based on this model, a mode-MTRM-based optimal filter is firstly given where filter gain can be obtained via coupled Riccati equations. Secondly, we extend the separation principle of the linear quadratic problem to the nonhomogeneous MJLSs case. An optimal controller is then designed to minimize the quadratic system cost. Finally, a potential application in solar boiler system is given to illustrate the developed theoretical methods. Copyright © 2016 John Wiley & Sons, Ltd.

This paper deals with the problem of finite frequency full-order filter design for discrete-time and continuous-time linear systems, with polytopic uncertainties. Based on the generalized Kalman–Yakubovich–Popov lemma and a parameter-dependent Lyapunov function, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we introduce a large number of slack variables by applying Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed performance. This leads to performance improvement and reduction of conservatism in the solution. It is shown later that the robust filter gains can be obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.

Control of drinking water networks is an arduous task, given their size and the presence of uncertainty in water demand. It is necessary to impose different constraints for ensuring a reliable water supply in the most economic and safe ways. To cope with uncertainty in system disturbances due to the stochastic water demand/consumption and optimize operational costs, this paper proposes three stochastic model predictive control (MPC) approaches, namely, chance-constrained MPC, tree-based MPC, and multiple-scenario MPC. A comparative assessment of these approaches is performed when they are applied to real case studies, specifically, a sector and an aggregate version of the Barcelona drinking water network in Spain. Copyright © 2016 John Wiley & Sons, Ltd.

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.

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.

No abstract is available for this article.

]]>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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.