Stochastic optimal control problems in which two-dimensional diffusion processes are controlled until they enter a given set are solved explicitly. When symmetry can be used, exact solutions are obtained. The same arguments are valid for one-dimensional processes. In the general case, it is shown how to obtain good approximate solutions. Various examples are presented.

Riderless bicycles are typically nonholonomic, underactuated, and nonminimum-phase systems. The instability and complex dynamic coupling make the trajectory generation and tracking of the bicycles more challenging. In this paper, we consider both the trajectory generation and position tracking of a riderless bicycle. To achieve smooth motion performances, the desired planar trajectory of the contact point of the bicycle's rear wheel is constructed using a parameterized polynomial curve that can connect two given endpoints with associated tangent angles. The optimal parameters of the polynomial curve are obtained by minimizing the maximum of the roll angle's quasistatic trajectory of the bicycle, and this problem is solved by the particle swarm optimization algorithm. Then, position tracking of the desired planar trajectory with balance is converted into an optimization problem subject to the dynamic constraints. The cost function is designed as the combination of the position errors and the roll acceleration of the bicycle, in order to achieve an accurate tracking performance and to prevent the bicycle from falling down. This optimization problem is solved by the Gauss pseudospectral method. Simulation results are presented to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

Nonlinear model predictive control (NMPC) allows one to explicitly treat nonlinear dynamics and constraints. To apply NMPC in real time on embedded hardware, online algorithms as well as efficient code implementations are crucial. A tutorial-style approach is adopted in this article to present such algorithmic ideas and to show how they can efficiently be implemented based on the ACADO Toolkit from MATLAB (MathWorks, Natick, MA, USA). Using its code generation tool, one can export tailored Runge–Kutta methods—explicit and implicit ones—with efficient propagation of their sensitivities. The article summarizes recent research results on autogenerated integrators for NMPC and shows how they allow to formulate and solve practically relevant problems in only a few tens of microseconds. Several common NMPC formulations can be treated by these methods, including those with stiff ordinary differential equations, fully implicit differential algebraic equations, linear input and output models, and continuous output independent of the integration grid. One of the new algorithmic contributions is an efficient implementation of infinite horizon closed-loop costing. As a guiding example, a full swing-up of an inverted pendulum is considered. Copyright © 2014 John Wiley & Sons, Ltd.

This article presents a distributed model predictive control methodology to manage energy resources for a set of consumer subsystems. The objective of the controller is to optimally distribute the allowable energy to the subsystems. The proposed methodology yields a distributed solution that converges to the optimum that would be obtained by a centralized controller. This optimal performance is achieved by expressing the problem in terms of slack variables and the global coupling constraint as a set of local subsystem constraints, thereby favoring the application of distributed model predictive control. Hardware-in-the-loop experiments with an air-conditioning thermal solar plant are performed to show the good performance of the proposed distributed controller. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the attitude of a ground vehicle travelling in cornering is controlled using a variable stiffness semi-active suspension control. The main goal of the variable stiffness semi-active suspension controller is to track as close as possible the performance of the full-active suspension control. The work is subdivided into two main parts. At first, making use of optimal control theory, the full-active suspension control of the full car is designed in various ways, depending on the choices of the state's variables. Afterwards, the variable stiffness control algorithm is derived based on the variable damping semi-active control concept, except that the variable damping is now replaced by the variable stiffness mechanism. Simulation results using various types of manoeuvre show that, when external body forces are applied to the vehicle, the variable stiffness control tracks the performance of the full-active control for high damping and stiffness coefficient, and for mild damping and stiffness coefficient, the performance of the variable stiffness control follows that of the skyhook controller. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, a fractional linear control system, containing Caputo derivative, with an integral performance index is studied. First, the existence and uniqueness of a solution to the mentioned control system is obtained. The main result is a theorem on the existence of optimal solutions to considered optimal control problems. Moreover, in order to find these solutions, the necessary optimality conditions (Pontryagin maximum principle) are derived. Our considerations consist of two parts: first, we consider starting a problem with zero initial condition and, next, with nonzero initial condition. All results are obtained by using results of such a type for equivalent fractional optimal control problem containing a Riemann–Liouville derivative. Copyright © 2014 John Wiley & Sons, Ltd.

The operation of urban traffic networks with distributed model predictive control (DMPC) can be more flexible than centralized strategies because DMPC allows for graceful expansion of the control infrastructure, localized reconfiguration, and tolerance to faulty operation. Yet, computational performance is less efficient than with centralized model predictive control (MPC) because of the added complexity brought about by distribution schemes. To assess the trade-off between flexibility and performance, in this paper we assess the tolerance to failure and performance of DMPC in contrast with centralized control. The problem of concern is the signal setting of green time in a representative traffic network modeled in a commercial microscopic traffic simulator. A software tool is developed for implementing and simulating the DMPC framework in tandem with the simulator. Comparisons of DMPC with MPC and a baseline feedback control strategy that does not use constrained optimization show that DMPC can achieve performance gains with respect to the baseline case and enhance tolerance to failure. Computations for DMPC are less efficient than with centralized MPC; nevertheless, the time taken by DMPC is well below the required for field use. Although the true distributed deployment of DMPC requires special hardware, its implementation in a central cluster can be made without loss of operational flexibility. Copyright © 2014 John Wiley & Sons, Ltd.

This paper develops a new optimal linear quadratic observer-based tracker with input constraint for the linear unknown system with a direct transmission term from input to measured output. The off-line observer/Kalman filter identification method is used to determine the linear sampled-data model with a direct feed-through term. On the basis of this model, a high-gain optimal linear quadratic analog observer-based tracker is proposed, so that it can effectively induce a high quality performance on the state estimation and the trajectory tracking design. Besides, the prediction-based digital redesign method is utilized to obtain a relatively low-gain and implementable observer and digital tracker from the theoretically well-designed high-gain analog observer and tracker for the linear system with a direct transmission term from input to output. To reduce the magnitude of control input, which is caused by the high-gain property to fit the requirement of the input constraint, the modified linear quadratic analog tracker is proposed. Thus, the control input can be compressed effectively without losing the original high performance of tracking much. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the problem of sliding mode control for a class of systems with unmatched parametric uncertainties and external perturbations is considered. LMI technique and polytopic models are used in the design of the switching surface. To achieve some performance requirements and good robustness, in the sliding mode, the *H*_{∞} norm and the pole clustering method are investigated. Based on the unit vector control approach, a robust control is developed, then, to direct and maintain the system states onto the sliding manifold in finite time. Finally, the validity of the proposed design strategy is demonstrated through the simulation of the quarter-car suspension system. Copyright © 2014 John Wiley & Sons, Ltd.

This paper proposes a robust algorithm for time-optimal rigid spacecraft reorientation trajectory generation. Based on the Pontryagin's maximum principle, the first-order necessary optimality conditions are derived. These optimality conditions are numerically satisfied by adopting a pseudospectral method integrated homotopic approach to solve the associated shooting functions. First, the energy-optimal reorientation solution is obtained using the Radau pseudospectral method, which has a spectral convergence speed and can give a precise estimation of the initial costates used to start the homotopic approach. Then, a modified homotopy scheme is given to deform the associated energy-optimal solution to the desired time-optimal solution continuously. Finally, for the inertially symmetric spacecraft reorientation problem, the newly found time-optimal solutions are presented. The performance of the algorithm is illustrated by simulating a general asymmetric rigid spacecraft time-optimal reorientation problem. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, a fault reconstruction scheme for a class of discrete-time descriptor linear parameter-varying systems is investigated. A discrete-time polytopic descriptor linear parameter-varying system subject to external disturbances and actuator faults is first established; then, using *H*_{∞} techniques and regional pole constraints, a novel polytopic unknown-input proportional-integral observer is constructed to simultaneously reconstruct system states and actuator faults. Existence conditions for the new polytopic unknown-input proportional-integral observer are explicitly derived. The stability and convergence of the presented observer are proved through Lyapunov theory and linear matrix inequalities. Using a slack-matrix-variable technique, less conservative results for observer design are obtained. At last, an illustrative example is simulated to verify the effectiveness of the proposed fault reconstruction approach. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the finite-horizon near optimal adaptive regulation of linear discrete-time systems with unknown system dynamics is presented in a forward-in-time manner by using adaptive dynamic programming and Q-learning. An adaptive estimator (AE) is introduced to relax the requirement of system dynamics, and it is tuned by using Q-learning. The time-varying solution to the Bellman equation in adaptive dynamic programming is handled by utilizing a time-dependent basis function, while the terminal constraint is incorporated as part of the update law of the AE. The Kalman gain is obtained by using the AE parameters, while the control input is calculated by using AE and the system state vector. Next, to relax the need for state availability, an adaptive observer is proposed so that the linear quadratic regulator design uses the reconstructed states and outputs. For the time-invariant linear discrete-time systems, the closed-loop dynamics becomes non-autonomous and involved but verified by using standard Lyapunov and geometric sequence theory. Effectiveness of the proposed approach is verified by using simulation results. The proposed linear quadratic regulator design for the uncertain linear system requires an initial admissible control input and yields a forward-in-time and online solution without needing value and/or policy iterations. Copyright © 2014 John Wiley & Sons, Ltd.

The global control of large-scale production machines composed of interacting subsystems is a challenging problem due to the intrinsic presence of high coupling, constraints, nonlinearity, and communication limitations. In this work, a pragmatic approach to distributed nonlinear model predictive control (DNMPC) is presented with guaranteed decrease in cost. Furthermore, in order to tackle time-varying process dynamics, a learning algorithm is developed, thereby improving the performance of the global control. The proposed control framework is experimentally validated on a hydrostatic drivetrain, which exhibits nonlinear dynamics, strongly interacting subsystems. The experimental results indicate that good tracking performance and disturbance rejection can be obtained by the proposed DNMPC. Copyright © 2014 John Wiley & Sons, Ltd.

We consider the control of a large-scale system composed of state-coupled linear subsystems that can be added or removed offline. In this paper, we present plug-and-play (PnP) design methods based on model predictive control, meaning that (i) the design of a local controller requires information from parent subsystems only, (ii) the plugging in/out of a subsystem triggers at most the redesign of controllers associated to subsystems coupled to it, and (iii) plug-in/out operations are automatically denied if they compromise the stability of the overall system or constraint satisfaction. We advance previously proposed PnP decentralized control schemes by introducing a distributed control architecture that exploits communication between coupled subsystems. New controllers embody coupling attenuation terms that make PnP design applicable even when existing synthesis method are not. The main features of our approach are illustrated considering the PnP design of controllers for regulating the frequency of multiple generators in power networks. Copyright © 2014 John Wiley & Sons, Ltd.

This paper exposes a methodology to solve state and input constrained optimal control problems for nonlinear systems. In the presented ‘interior penalty’ approach, constraints are penalized in a way that guarantees the strict interiority of the approaching solutions. This property allows one to invoke simple (without constraints) stationarity conditions to characterize the unknowns. A constructive choice for the penalty functions is exhibited. The property of interiority is established, and practical guidelines for implementation are given. A numerical benchmark example is given for illustration. © 2014 The Authors. Optimal Control Applications and Methods published by John Wiley & Sons, Ltd.

This work presents a control approach to deal with plants formed by several interconnected subprocesses and where the interconnection between subprocesses can change during the plant operation. The change from one operation mode to another, where each operation mode is defined by a discrete variable set, implies a change in the process behaviour that must be counteracted by the control system. In this work, a practical hybrid model predictive control is proposed to take the behaviour changes related to the hybrid nature of the process into account. The proposed control algorithm is based on the adaptation of several well-known control strategies that have been successfully applied in the industrial field. A solar thermal system (composed of a solar thermal flat collector field, one or more accumulation tanks connected in series and a gas heater) is used to show the resulting control strategy through detailed simulations. Copyright © 2014 John Wiley & Sons, Ltd.

The paper presents a review of active set (AS) algorithms that have been deployed for implementation of fast model predictive control (MPC). The main purpose of the survey is to identify the dominant features of the algorithms that contribute to fast execution of online MPC and to study their influence on the speed. The simulation study is conducted on two benchmark examples where the algorithms are analyzed in the number of iterations and in the workload per iteration. The obtained results suggest directions for potential improvement in the speed of existing AS algorithms. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, a new approach for fixed-structure *H*_{2} controller design in terms of solutions to a set of linear matrix inequalities are given. Both discrete-time and continuous-time SISO time-invariant systems are considered. Then the results are extended to systems with polytopic uncertainty. The presented methods are based on an inner convex approximation of the non-convex set of fixed-structure *H*_{2} controllers. The designed procedures are initialized either with a stable polynomial or with a stabilizing controller. An iterative procedure for robust controller design is given that converges to a suboptimal solution. The monotonic decreasing of the upper bound on the *H*_{2} norm is established theoretically for both nominal and robust controller design. Copyright © 2014 John Wiley & Sons, Ltd.

In this study, the guaranteed cost control of discrete time uncertain system with both state and input delays is considered. Sufficient conditions for the existence of a memoryless state feedback guaranteed cost control law are given in the bilinear matrix inequality form, which needs much less auxiliary matrix variables and storage space. Furthermore, the design of guaranteed cost controller is reformulated as an optimization problem with a linear objective function, bilinear, and linear matrix inequalities constraints. A nonlinear semi-definite optimization solver—PENLAB is used as a solution technique. A numerical example is given to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

The paper studies the problem of mixed *H*_{2}/*H*_{∞} control for a class of nonlinear discrete-time networked control systems. By using the indicator function method, random network-induced delays and stochastic packet dropouts are taken into account in a unified framework in the designed mixed *H*_{2}/*H*_{∞} controller. In the presences of random transmission delays, stochastic packet dropouts and all admissible disturbances, the resulting closed-loop system is stochastically stable in mean square and attains the prescribed *H*_{2} and *H*_{∞} performances. The designed mixed *H*_{2}/*H*_{∞} controller can be obtained by solving a set of feasible linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the developed method. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, an adaptive dynamic surface control approach is presented for the longitudinal motion of an air-breathing hypersonic vehicle. Fully tuned radial basis function neural network that regulates weights, width, and center of Gaussian function simultaneously is developed to estimate aerodynamic uncertainties and atmospheric disturbances. The nonlinear control law is subsequently designed by dynamic surface control approach for the vehicle model converted into strict block feedback form by input–output linearization method. Simulation results show that the velocity can be successfully tracked over a large range from Mach 11 to Mach 12 and an altitude range from 26 to 30 km. The presented approach has perfect ability of restraining unknown and time-varying nonlinear dynamics during flight. Copyright © 2014 John Wiley & Sons, Ltd.

This paper considers the problem of robust *H**∞* performance analysis for uncertain discrete-time singular systems with time-varying delays. Firstly, a delay-dependent stability criterion under the *H**∞* performance index for the systems is given based on constructing a generalized Lyapunov–Krasovskii function and introducing a new difference inequality. Then, a sufficient condition ensuing the system to be regular, causal as well as stable for all admissible uncertainties is proposed in terms of a set of strict linear matrix inequalities (LMIs). Finally, we provide examples to show the reduced conservatism and effectiveness of the proposed conditions. Copyright © 2014 John Wiley & Sons, Ltd.

This paper focuses on cooperative distributed model predictive control (MPC) of wind farms, where the farms respond to active power control commands issued by the transmission system operator. A distributed MPC scheme is proposed, which aims at satisfying the requirements imposed by the grid code while minimizing the farm-wide mechanical structure fatigue. The distributed MPC control law is defined by a global finite-horizon optimal control problem, which is solved at every time step by distributed optimization. The computational approach is completely distributed, that is, every turbine evaluates its own globally optimal input by considering local measurements and communicating to neighboring turbines only. Two MPC versions are compared, in the first of which the farm-wide power output constraint is implemented as a hard constraint, whereas in the second, it is implemented as a soft constraint. As for distributed optimization methods, the alternating direction method of multipliers as well as a dual decomposition scheme based on fast gradient updates are compared. The performance of the proposed distributed MPC controller, as well as the performance of the distributed optimization methods used for its operation, are compared in the simulation on four exemplary scenarios. The results of the simulations imply that the use of cooperative distributed MPC in wind farms is viable both from a performance and from a computational viewpoint. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with the time optimal control problem governed by the internal controlled Cahn–Hilliard equation. We prove the existence of optimal controls. Moreover, we give necessary optimality conditions for an optimal control of our original problem by using the one of the approximate problems. Copyright © 2014 John Wiley & Sons, Ltd.

We consider the problem of synthesizing simple explicit model predictive control feedback laws that provide closed-loop stability and recursive satisfaction of state and input constraints. The approach is based on replacing a complex optimal feedback law by a simpler controller whose parameters are tuned, off-line, to minimize the reduction of the performance. The tuning consists of two steps. In the first step, we devise a simpler polyhedral partition by solving a parametric optimization problem. In the second step, we then optimize parameters of local affine feedbacks by minimizing the integrated squared error between the original controller and its simpler counterpart. We show that such a problem can be formulated as a convex optimization problem. Moreover, we illustrate that conditions of closed-loop stability and recursive satisfaction of constraints can be included as a set of linear constraints. Efficiency of the method is demonstrated on two examples. Copyright © 2014 John Wiley & Sons, Ltd.

Realization of causal current output-based optimal full/reduced-order observer and tracker for the linear sampled-data system with a direct transmission term from input to output is proposed in this paper. First, a high-gain optimal linear quadratic analog tracker based on the reduced-order observer is proposed for the system model with a direct transmission term from input to output, so that it can effectively induce a high quality performance on state estimation and trajectory tracking design theoretically. Then, the prediction-based digital redesign method enables it to make the digitally controlled system to track the desired trajectory closely. However, there induces a causal problem on the realization of current output-based optimal full/reduced-order observer and tracker for the sampled-data system with a direct transmission term form input to measured output. To overcome this problem, a realization of the causal observer-based sampled-data tracker is newly proposed in this paper. An illustrative example is presented to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with finite-time control and *L*_{1}-gain analysis of positive switched systems. First, by using the multiple linear copositive Lyapunov functions approach, a sufficient condition for the finite-time stability of autonomous systems under consideration is established. Second, the finite-time boundedness with a weighted *L*_{1}-gain performance of autonomous systems with uncertain disturbances is addressed. Furthermore, state-feedback controllers guaranteeing the finite-time stability and the finite-time boundedness of non-autonomous systems are constructed, respectively. Finally, an illustrative example is given to show the validity of the present design. Copyright © 2014 John Wiley & Sons, Ltd.

This paper describes autonomous racing of RC race cars based on mathematical optimization. Using a dynamical model of the vehicle, control inputs are computed by receding horizon based controllers, where the objective is to maximize progress on the track subject to the requirement of staying on the track and avoiding opponents. Two different control formulations are presented. The first controller employs a two-level structure, consisting of a path planner and a nonlinear model predictive controller (NMPC) for tracking. The second controller combines both tasks in one nonlinear optimization problem (NLP) following the ideas of contouring control. Linear time varying models obtained by linearization are used to build local approximations of the control NLPs in the form of convex quadratic programs (QPs) at each sampling time. The resulting QPs have a typical MPC structure and can be solved in the range of milliseconds by recent structure exploiting solvers, which is key to the real-time feasibility of the overall control scheme. Obstacle avoidance is incorporated by means of a high-level corridor planner based on dynamic programming, which generates convex constraints for the controllers according to the current position of opponents and the track layout. The control performance is investigated experimentally using 1:43 scale RC race cars, driven at speeds of more than 3 m/s and in operating regions with saturated rear tire forces (drifting). The algorithms run at 50 Hz sampling rate on embedded computing platforms, demonstrating the real-time feasibility and high performance of optimization-based approaches for autonomous racing. Copyright © 2014 John Wiley & Sons, Ltd.

Impulse control problems, in which a continuously evolving state is modified by discrete control actions, have applications in epidemiology, medicine, and ecology. In this paper, we present a simple method for solving impulse control problems for systems of differential equations. In particular, we show how impulse control problems can be reformulated and solved as discrete optimal control problems. The method is illustrated with two examples. Published 2014. This article has been contributed to by US Government employees and their work is in the public domain in the USA.

This paper is concerned with the robust stability problem for uncertain discrete-time systems with interval time-varying delays and randomly occurring parameter uncertainties. By construction of a suitable Lyapunov–Krasovskii functional and utilization of new zero equalities with delay-partitioning approach, improved delay-dependent criteria for the robust stability of the systems are derived in terms of linear matrix inequalities for guaranteeing the asymptotic stability of the concerned systems. The effectiveness and reduction of conservatism of the derived results are demonstrated by three numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.

In this work, we study the coupling of a culture of microalgae limited by light and an anaerobic digester in a two-tank bioreactor. The model for the reactor combines a periodic day-night light for the culture of microalgae and a classical chemostat model for the digester. We first prove the existence and attraction of periodic solutions of this problem for a 1 day period. Then, we study the optimal control problem of optimizing the production of methane in the digester during a certain timeframe, the control on the system being the dilution rate (the input flow of microalgae in the digester). We apply Pontryagin's Maximum Principle in order to characterize optimal controls, including the computation of singular controls. We present numerical simulations by direct and indirect methods for different light models and compare the optimal 1-day periodic solution to the optimal strategy over larger timeframes. Finally, we also investigate the dependence of the optimal cost with respect to the volume ratio of the two tanks. Copyright © 2014 John Wiley & Sons, Ltd.

We analyze a class of linear-quadratic optimal control problems with an additional *L*^{1}-control cost depending on a parameter *β*. To deal with this nonsmooth problem, we use an augmentation approach known from linear programming in which the number of control variables is doubled. It is shown that if the optimal control for a given is bang-zero-bang and the switching function has a stable structure, the solutions are Lipschitz continuous functions of the parameter *β*. We also show that in this case the optimal controls for *β*^{ * } and a with | *β* − *β*^{ * } | sufficiently small coincide except on a set of measure . Finally, we use the augmentation approach to derive error estimates for Euler discretizations. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we propose a model predictive control scheme for discrete-time linear invariant systems based on inexact numerical optimization algorithms. We assume that the solution of the associated quadratic program produced by some numerical algorithm is possibly neither optimal nor feasible, but the algorithm is able to provide estimates on primal suboptimality and primal feasibility violation. By adaptively tightening the complicating constraints, we can ensure the primal feasibility of the approximate solutions generated by the algorithm. We derive a control strategy that has the following properties: the constraints on the states and inputs are satisfied, asymptotic stability of the closed-loop system is guaranteed, and the number of iterations needed for a desired level of suboptimality can be determined. The proposed method is illustrated using a simulated longitudinal flight control problem. Copyright © 2014 John Wiley & Sons, Ltd.

Competition glider flying is a game of stochastic optimization, in which mathematics and quantitative strategies have historically played an important role. We address the problem of uncertain future atmospheric conditions by constructing a nonlinear Hamilton–Jacobi–Bellman equation for the optimal speed to fly, with a free boundary describing the climb/cruise decision. We consider two different forms of knowledge about future atmospheric conditions, the first in which the pilot has complete foreknowledge and the second in which the state of the atmosphere is a Markov process discovered by flying through it. We compute an accurate numerical solution by designing a robust monotone finite difference method. The results obtained are of direct applicability for glider flight. Copyright © 2014 John Wiley & Sons, Ltd.

A study of optimal impulsive Moon-to-Earth trajectories is presented in a planar circular restricted three-body framework. Two-dimensional return trajectories from circular lunar orbits are considered, and the optimization criterion is the total velocity change. The optimal conditions are provided by the optimal control theory. The boundary value problem that arises from the application of the theory of optimal control is solved using a procedure based on Newton's method. Motivated by the difficulty of obtaining convergence, the search for the initial adjoints is carried out by means of two different techniques: homotopic approach and adjoint control transformation. Numerical results demonstrate that both initial adjoints estimation methods are effective and efficient to find the optimal solution and allow exploring the fundamental tradeoff between the time of flight and required Δ*V*. Copyright © 2014 John Wiley & Sons, Ltd.

This paper proposes three near-optimal (to a desired degree) deterministic charge and discharge policies for the maximization of profit in a grid-connected storage system. The changing price of electricity is assumed to be known in advance. Three near-optimal algorithms are developed for the following three versions of this optimization problem: (1) The system has supercapacitor type storage, controlled in continuous time. (2) The system has supercapacitor or battery type storage, and it is controlled in discrete time (i.e., it must give constant power during each sampling period). A battery type storage model takes into account the diffusion of charges. (3) The system has battery type storage, controlled in continuous time. We give algorithms for the approximate solution of these problems using dynamic programming, and we compare the resulting optimal charge/discharge policies. We have proved that in case 1 a bang off bang type policy is optimal. This new result allows the use of more efficient optimal control algorithms in case 1. We discuss the advantages of using a battery model and give simulation and experimental results. Copyright © 2014 John Wiley & Sons, Ltd.

The Hydrosol pilot plant was installed in the small solar power systems solar tower at CIEMAT-Plataforma Solar de Almería (PSA), Spain, for producing solar hydrogen from water using a ferrite-based redox technology. It consists of two reactors where hydrogen and oxygen production cycles are alternated for quasi-continuous hydrogen production. In the first step (water splitting), an exothermic reaction takes place at an operating temperature of 800℃. The second step (thermal reduction) is an endothermic reaction, which requires an operating temperature of 1200℃. Recently, an adaptive control strategy for controlling these operating temperatures in the solar hydrogen reactor has been proposed and implemented, using the number of heliostats focused as the control signal. The algorithm chooses which heliostats have to be focused estimating the concentrated solar power contribution of each heliostat. Then, the heliostats are focused, starting from those which provide lower power. This paper is based on this control strategy, but considering a new algorithm to choose the heliostats. Using the concentrated solar power contributions, a knapsack problem is defined to obtain a local optimal solution, which provides a set of heliostats that minimizes the error between the setpoint and the reactor concentrated solar power. In order to evaluate the performance of this method, simulation and experimental results are shown and discussed. Copyright © 2014 John Wiley & Sons, Ltd.

A field programmable gate array (FPGA) based model predictive controller for two phases of spacecraft rendezvous is presented. Linear time-varying prediction models are used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of the longer range manoeuvres, whilst a fixed and receding prediction horizon is used for fine-grained tracking at close range. The resulting constrained optimisation problems are solved using a primal–dual interior point algorithm. The majority of the computational demand is in solving a system of simultaneous linear equations at each iteration of this algorithm. To accelerate these operations, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze soft-core processor on the FPGA, on which the remainder of the system is implemented. Certain logic that can be hard-coded for fixed sized problems is implemented to be configurable online, in order to accommodate the varying problem sizes associated with the variable prediction horizon. The system is demonstrated in closed-loop by linking the FPGA with a simulation of the spacecraft dynamics running in Simulink on a PC, using Ethernet. Timing comparisons indicate that the custom implementation is substantially faster than pure embedded software-based interior point methods running on the same MicroBlaze and could be competitive with a pure custom hardware implementation.Copyright © 2014 John Wiley & Sons, Ltd.

A key objective in the European Union climate and energy package for 2020 is the reduction of energy consumption. Buildings are responsible for more that one third of global energy consumption, where heating, ventilation, and air conditioning systems account for more than half of it. In extreme climates, the existing passive measures of bioclimatic buildings are not enough at time to maintain a suitable users’ thermal comfort. However, this thermal comfort must be reached reducing the energy spent by the heating, ventilation, and air conditioning system of the building. Control systems, and more specifically model predictive control, are a suitable way to find a trade-off between users’ thermal comfort and energy saving. Simulation tools are essential for the efficient and automated testing and validation of these control strategies. This paper presents a simulation tool of an office room from a bioclimatic building, namely, the CDdI-CIESOL-ARFRISOL building, to test advanced control strategies against a simulation model, to evaluate them, in terms of users comfort and energy consumption, and to validate them, considering the real room itself. Details about the simulation tool are given, together with the evaluation of its goodness through a real test using a nonlinear model predictive control in an office room of that building. Copyright © 2014 John Wiley & Sons, Ltd.

This paper discusses a new approximation method for operators that are solution to an operational Riccati equation. The latter is derived from the theory of optimal control of linear problems posed in Hilbert spaces. The approximation is based on the functional calculus of self-adjoint operators and the Cauchy formula. Under a number of assumptions, the approximation is suitable for implementation on a semi-decentralized computing architecture in view of real-time control. Our method is particularly applicable to problems in optimal control of systems governed by partial differential equations with distributed observation and control. Some relatively academic applications are presented for illustration. More realistic examples relating to microsystem arrays have already been published. Copyright © 2014 John Wiley & Sons, Ltd.

A mesh refinement method is described for solving a continuous-time optimal control problem using collocation at Legendre–Gauss–Radau points. The method allows for changes in both the number of mesh intervals and the degree of the approximating polynomial within a mesh interval. First, a relative error estimate is derived based on the difference between the Lagrange polynomial approximation of the state and a Legendre–Gauss–Radau quadrature integration of the dynamics within a mesh interval. The derived relative error estimate is then used to decide if the degree of the approximating polynomial within a mesh should be increased or if the mesh interval should be divided into subintervals. The degree of the approximating polynomial within a mesh interval is increased if the polynomial degree estimated by the method remains below a maximum allowable degree. Otherwise, the mesh interval is divided into subintervals. The process of refining the mesh is repeated until a specified relative error tolerance is met. Three examples highlight various features of the method and show that the approach is more computationally efficient and produces significantly smaller mesh sizes for a given accuracy tolerance when compared with fixed-order methods. Copyright © 2014 John Wiley & Sons, Ltd.

Two methods are presented for approximating the costate of optimal control problems in integral form using orthogonal collocation at Legendre–Gauss (LG) and Legendre–Gauss–Radau (LGR) points. It is shown that the derivative of the costate of the continuous-time optimal control problem is equal to the negative of the costate of the integral form of the continuous-time optimal control problem. Using this continuous-time relationship between the differential and integral costate, it is shown that the discrete approximations of the differential costate using LG and LGR collocation are related to the corresponding discrete approximations of the integral costate via integration matrices. The approach developed in this paper provides a way to approximate the costate of the original optimal control problem using the Lagrange multipliers of the integral form of the LG and LGR collocation methods. The methods are demonstrated on two examples where it is shown that both the differential and integral costate converge exponentially as a function of the number of LG or LGR points. Copyright © 2014 John Wiley & Sons, Ltd.

This article describes the application of optimal control to a solar furnace that is used to perform temperature stress cycling tests in material samples. This process is characterized by having nonlinearities that depend on the sample properties and relate the temperature of the sample with the solar energy fluctuations and the position of the furnace shutter. An optimal control problem with fix terminal time and free terminal state and control constraints is addressed in continuous time domain. The solution is approximated using discretized state and costate equations and applied to the furnace according to a receding horizon strategy. The performance of the overall system is evaluated from computer simulations which show that the controller is able to tolerate, up to some degree, the presence of parameter uncertainty. Copyright © 2014 John Wiley & Sons, Ltd.

Modern computational power and efficient direct collocation techniques are decreasing the solution time required for the optimal control problem, making real-time optimal control (RTOC) feasible for modern systems. Current trends in the literature indicate that many authors are applying RTOC with a recursive open-loop structure, relying on a high recursion rate for implicit state feedback to counter disturbances and other unmodeled effects without explicit closed-loop control. The limitations of using rapid, instantaneous optimal solutions are demonstrated analytically and through application to a surface-to-air missile avoidance control system. Two methods are proposed for control structure implementation when using RTOC to take advantage of error integration through either classical feedback or disturbance estimation. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

By choosing the optimal steering history of a spacecraft, it is possible to maximize the mass delivered from a park orbit to a mission orbit. A low‒thrust orbit transfer that models coasts when passing through the Earth's shadow can be formulated as a large‒scale optimal control problem with many distinct phases. This paper presents a technique that constructs an initial guess using a receding horizon algorithm. A series of large‒scale multiphase optimal control problems are then solved to refine the phase structure of the problem. The final optimal solution incorporates high fidelity physics and mesh refinement techniques within a large sparse nonlinear programming approach.

The problem of fault detection for networked control systems with respect to packet dropouts is investigated in this paper based on average dwell time method. For the cases that there may be sensor stuck failure and packet dropouts, the networked control systems are modeled as discrete time switched systems. Subsequently, a novel fault detection scheme, which is valid to detect the failures with small magnitudes even the outage ones, is proposed by making the generated residuals sensitive to servo inputs in faulty cases and robust against it in normal case. By utilizing the average dwell time method, new sufficient conditions, which include some existing results, for characterizing the sensitivity performance and the attenuation performance are presented in terms of linear matrix inequalities. Meanwhile, the relation between the packet dropout rate and the system performance is established. Finally, an application of a linearized aircraft is given to demonstrate the effectiveness of the proposed results. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we consider a linear quadratic regulator control problem for spacecraft rendezvous in an elliptical orbit. A new spacecraft rendezvous model is established. On the basis of this model, a linear quadratic regulator control problem is formulated. A parametric Lyapunov differential equation approach is used to design a state feedback controller such that the resulting closed-loop system is asymptotically stable, and the performance index is minimized. By an appropriate choice of the value of a parameter, an approximate state feedback controller is obtained from a solution to the periodic Lyapunov differential equation, where the periodic Lyapunov differential equation is solved on the basis of a new numerical algorithm. The spacecraft rendezvous mission under the controller obtained will be accomplished successfully. Several illustrative examples are provided to show the effectiveness of the proposed control design method. Copyright © 2014 John Wiley & Sons, Ltd.

The field of preview control has attracted many researchers for its applications in guidance of autonomous vehicles, robotics, and process control, as this field is well suited for use in design of systems that have reference signals known *a priori*. The paper presents the efforts of various researchers in the field of preview control. The literature available in this field, since 1966, is categorized based on *formulation*, *method domain*, *solution approach*, and *objective*. The preview control problem is formulated and solved using classical time-domain optimal control design tools for under water vehicle model. The key observation obtained from the discussions shows the enormous scope of work available in the field of preview control. Copyright © 2014 John Wiley & Sons, Ltd.

The robust reliable guaranteed cost control for Takagi–Sugeno fuzzy systems with interval time-varying delay is considered in this paper. Some free weighting matrices and non-negative terms are provided to improve the conservativeness of our main results. An LMI optimization approach is applied to solve the problems of robust reliable guaranteed cost control and minimization of cost function. Copyright © 2014 John Wiley & Sons, Ltd.

Nonlinear model predictive control (NMPC) depends on performing a constrained nonlinear optimization, based on predictions of future system behavior, during a sampling interval to determine the control action to be applied to the system during the next time step. The difficulty in designing an optimization procedure to solve a constrained NMPC problem is due to the finite time horizon to which the predictive model is evaluated, the state and control actuator constraints, and sampling interval length. The resulting objective function, which is to be optimized is typically not differentiable. Although there are many commercial, shareware, and open-source optimization packages available that can perform a nonlinear constrained optimization for most cases, there are NMPC implementations requiring embedded code or that must meet stringent timing requirements that preclude the use of off-the-shelf packages. In cases where the predictive model is known, such as aerodynamic or hydrodynamic systems, a direct-search optimization algorithm can perform well enough in a real-time environment. Direct search algorithms are simple to implement and can be made more efficient by applying differential geometric techniques to the search methodology. The typical smoothness of the equations of motion for vehicular systems allows the objective function's stationarities to be handled in a straight-forward way. Copyright © 2013 John Wiley & Sons, Ltd.

The issues of stability analysis of a class of continuous uncertain switched singular time-delay systems consisting of discrete and distributed delays is investigated in this paper. Based on the LMIs, constructing the new extended Lyapunov-like Krasovskii functional, and the average dwell-time approach, delay-dependent sufficient conditions are derived to check the stability of such systems. By solving the corresponding LMIs, the average dwell-time and switching signal condition are obtained. This paper also highlights the relationship between the average dwell-time of the switched singular time-delay system, exponential rate of differential, and algebraic states. Two numerical examples show the effectiveness of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.

This paper is devoted to the study of an optimal control problem for a fed-batch bioreactor with one species and one substrate. Our objective is to obtain an optimal feedback control, steering the system in minimal time to a given target defined by conditions on the substrate concentration and the volume of the reactor. The novelty in this work is that a mortality rate for the biomass and hydrolysis of dead biomass are included in the model. The optimal synthesis (optimal feeding strategy) has been obtained by Moreno (1999) when both mortality and hydrolysis are considered negligible. Whenever the model includes these effects, the total mass of the system is no longer conserved, and it is not possible to reduce the dimension of the system. Thanks to the Pontryagin maximum principle and the Hamilton–Jacobi equation, we overcome this difficulty and provide an optimal synthesis of the problem in the impulsive framework. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, a stochastic optimal control problem is investigated in which the system is governed by a stochastic functional differential equation. In the framework of functional Itô calculus, we build the dynamic programming principle and the related path-dependent Hamilton–Jacobi–Bellman equation. We prove that the value function is the viscosity solution of the path-dependent Hamilton–Jacobi–Bellman equation. Copyright © 2013 John Wiley & Sons, Ltd.

An optimal control problem for a mathematical model of tumour–immune dynamics under the influence of chemotherapy is considered. The toxicity effect of the chemotherapeutic agent on both tumour and immunocompetent cells is taken into account. A standard linear pharmacokinetic equation for the chemotherapeutic agent is added to the system. The aim is to find an optimal strategy of treatment to minimize the tumour volume while keeping the immune response not lower than a fixed permissible level as far as possible. Sufficient conditions for the existence of not more than one switching and not more than two switchings without singular regimes are obtained. The surfaces in the extended phase space, on which the last switching appears, are constructed analytically.Copyright © 2013 John Wiley & Sons, Ltd.

This paper is concerned with the design of mixed *H*_{2} ∕ *H*_{ ∞ } controllers for discrete-time delay systems and networked control systems. The controllers are obtained by solving a constrained optimization problem. Those constraints are suitably transformed into linear matrix inequalities, in such a way that the problem is solved using available algorithms. The stability is ensured resorting to the Lyapunov–Krasovskii theory. Additionally, the paper investigates an asynchronous event-based sampling policy that allows a reduction of the bandwidth usage and the energy consumption. The relation between the boundedness of the stability region and the threshold that triggers the events is studied. The robustness and performance of the proposed technique is showed by numerical simulations. Copyright © 2013 John Wiley & Sons, Ltd.

This paper considers a collection of agents performing a shared task making use of relative information communicated over an information network. The designed suboptimal controllers are state feedback and static output feedback, which are guaranteed to provide a certain level of performance in terms of a linear quadratic regulator (LQR) cost. Because of the convexity of the LQR performance region, the suboptimal LQR control problem with state feedback is reduced to the solution of two inequalities, with the minimum and maximum eigenvalues of the Laplacian matrix as the coefficients. The advantage of the method is that the LQR control problem of network multi-agent systems can be converted into the LQR control of a set of single-agent systems, and the structure constraint on the feedback gain matrix can be eliminated. It can be shown that the size of the LQR control problem will not increase according to the number of the node in the fairly general framework. The method can be extended to the synthesis of the static output feedback, which is derived from the weighting matrices in LQR. Through some coordinate transformation and the augmentation of the output matrix, the LQR synthesis is provided on the basis of the output measurements of the adjacent agents. Numerical examples are presented to illustrate the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, a class of networked control systems with output feedback control and *H*_{ ∞ } performance is discussed. It considers packet dropouts in both measurement (S/C) and actuation (C/A) channels. Markovian chain principle is used in modeling the packet dropouts in S/C and C/A channels. The time scale adopted in these two independent homogeneous Markov chain is linear with the physical time. The model also takes into consideration the late arriving packets. The effect of interaction between packet dropouts in both channels on the stability of system, when the networks of both (S/C) and (C/A) channels overlap is also examined. Sufficient condition for the existence of *H*_{ ∞ } output feedback controller is presented and it is shown that it is dependent on the upper bounds of the number of consecutive packet dropouts. The developed stability analysis and control scheme is also investigated with partially known transition probability matrices. Finally, a numerical example has been given to show the effectiveness of developed method. Copyright © 2013 John Wiley & Sons, Ltd.

The neoclassical model of economic growth is used to model the economic growth of a HIV-infected community with efforts in controlling the epidemic. An optimal control model with pure-state constraints is formulated and investigated. It is found that reduction of prevalence for the disease and economic growth agrees in a positive sense in the communities with high rate of population growth and low income. Moreover, the same control strategy will decrease the prevalence even if the capital is not growing for the case of high income communities. However, a disease control strategy with economic growth as its objective will not result in decrease in prevalence if the rate of population growth of the community is very low. Therefore, if the rate of the population growth of a community is nearly the replacement level, then the utility function for the selection of disease control strategies should not be an economic benefit. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we study the stability conditions and stabilization problem of Takagi-Sugeno systems under the discrete-time framework. By introducing slack matrices, we obtain extended stability condition in an LMI form. Both parallel distributed compensation (PDC) control law, and non-PDC control law are studied. Finally, we give an example to compare our results with other methods. Copyright © 2013 John Wiley & Sons, Ltd.

This paper investigates the problem of delay-dependent dynamic output feedback control for a class of discrete-time Markovian jump linear systems (MJLSs). The systems under consideration are subject to time-varying delay and defective mode information. The defective transition probabilities comprise of three types: exactly known, uncertain, and unknown. By employing a two-term approximation for the time-varying delay, the original MJLSs can be equivalently converted into a feedback interconnection form, which contains a forward subsystem with constant time-delays and a feedback one with norm-bounded uncertainties. Then, based on the scaled small-gain theorem, the problem is therefore recast as an control problem in the face of uncertainties via an input–output framework. It is shown that the explicit expressions of the desired controller gains can be characterized in terms of strict linear matrix inequalities via some linearization techniques. Simulation studies are performed to illustrate the effectiveness and less conservatism of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, the robust exponential synchronization problem for a class of neutral complex networks with discrete and distributed time-varying delays is investigated. Some delay-dependent synchronization criteria are derived by using the descriptor model transformation method; the stability condition of error dynamical networks based on the Lyapunov–Krasovskii functional is obtained via linear matrix inequality (LMI) formulation. Finally, numerical examples are presented to show the effectiveness of the proposed theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

Controlling several and possibly independent moving agents in order to reach global goals is a tedious task that has applications in many engineering fields such as robotics or computer animation. Together, the different agents form a whole called swarm, which may display interesting collective behaviors. When the agents are driven by their own dynamics, controlling this swarm is known as the particle swarm control problem. In that context, several strategies, based on the control of individuals using simple rules, exist. This paper defends a new and original method based on a centralized approach. More precisely, we propose a framework to control several particles with constraints either expressed on a per-particle basis, or expressed as a function of their environment. We refer to these two categories as respectively *Lagrangian* or *Eulerian* constraints. The contributions of the paper are the following: (i) we show how to use optimal control recipes to express an optimization process over a large state space including the dynamic information of the particles; and (ii) the relation between the Lagrangian state space and Eulerian values is conveniently expressed with graph operators that make it possible to conduct all the mathematical operations required by the control process. We show the effectiveness of our approach on classical and more original particle swarm control problems. Copyright © 2013 John Wiley & Sons, Ltd.

By constructing a complete metric space and a compact set of admissible control functions, this paper investigates the existence and stability of solutions of optimal control problems with respect to the right-hand side functions. On the basis of set-valued mapping theory, by introducing the notion of essential solutions for optimal control problems, some sufficient and necessary criteria guaranteeing the existence and stability of solutions are established. New derived criteria show that the optimal control problems whose solutions are all essential form a dense residual set, and so every optimal control problem can be closely approximated arbitrarily by an essential optimal control problem. The example shows that not all optimal control problems are stable. However, our main result shows that, in the sense of Baire category, most of the optimal control problems are stable. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, a control design approach is presented, which uses human data in the development of bipedal robotic control techniques for multiple locomotion behaviors. Insight into the fundamental behaviors of human locomotion is obtained through the examination of experimental human data for walking on flat ground, upstairs, and downstairs. Specifically, it is shown that certain outputs of the human, independent of locomotion terrain, can be characterized by a single function, termed the *extended canonical human function*. Through feedback linearization, human-inspired locomotion controllers are leveraged to drive the outputs of the simulated robot, via the extended canonical human function, to the outputs from human locomotion. An optimization problem, subject to the constraints of *partial hybrid zero dynamics*, is presented that yields parameters of these controllers that provide the best fit to human data while ensuring stability of the controlled bipedal robot. The resulting behaviors are stable walking on flat ground, upstairs, and downstairs—these three locomotion modes are termed ‘motion primitives’. A second optimization is presented, which yields controllers that evolve the robot from one motion primitive to another—these modes of locomotion are termed ‘motion transitions’. A directed graph consisting these motion primitives and motion transitions has been constructed for the stable motion planning of bipedal locomotion. A final simulation is given, which shows the controlled evolution of a robotic biped as it transitions through each mode of locomotion over a pyramidal staircase. Copyright © 2013 John Wiley & Sons, Ltd.