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.

A key factor to success in implementations of real time optimal control, such as receding horizon control (RHC), is making efficient use of computational resources. The main trade-off is then between efficiency and accuracy of each RHC iteration, and the resulting overall optimality properties of the concatenated iterations, that is, how closely this represents a solution to the underlying infinite time optimal control problem (OCP). Both these issues can be addressed by adapting the RHC solution strategy to the expected form of the solution. Using gradual dense–sparse (GDS) node distributions in direct transcription formulations of the finite time OCP solved in each RHC iteration is a way of adapting the node distribution of this OCP to the fact that it is actually part of an RHC scheme. We have previously argued that this is reasonable, because the near future plan must be implemented now, but the far future plan can and will be revised later. In this paper, we investigate RHC applications where the asymptotic qualitative behavior of the OCP solution can be analyzed in advance. For some classes of systems, explicit exponential convergence rates of the solutions can be computed. We establish such convergence rates for a class of control affine nonlinear systems with a locally quadratic cost and propose to use versions of GDS node distributions for such systems because they will (eventually) be better adapted to the form of the solution. The advantages of the GDS approach in such settings is illustrated with simulations. Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents a feedback controller designing approach for a large class of finite-time optimal control problems. This approach involves a piecewise truncated variational iteration method (PTVIM) for solving the nonlinear Hamilton–Jacobi–Bellman equation. By using the finite iterations of PTVIM, an analytic approximate solution for value function and suboptimal feedback control law is obtained. Some illustrative examples are employed to demonstrate the accuracy and efficiency of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we introduce a new analytic technique for a class of nonlinear optimal control problems and present a theorem of convergence of the method. In this scheme, first, the original optimal control problem is transformed into a nonlinear two-point boundary value problem via the Pontryagin's maximum principle, and then, we apply a new method for solving two-point boundary value problem. The proposed modification is made by introducing He's polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for using in these problems. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, an algebraic rule for tuning the integer realizations of fractional-order *PI* controllers is developed, with an integral square error performance index, which outperforms that of an optimal ordinary PI controller. To this end, the *PI*^{λ} control structure is used in conjunction with a third-order integer approximating filter to provide a three parameter fixed-structure extension of the ordinary PI controller. Next, the extra degree of freedom in setting the order of integration *λ* is leveraged to introduce a steepest descent direction in the extended controller parameter space. It is then stated that shifting the parameters of an ordinary PI controller along the proposed descent direction will result in a fractional-based three parameter controller with a performance index, which is superior to that of the original PI controller. The stability of the controller parameters derived in this manner is then analyzed, and examples and simulation results are offered to verify the theoretical expectations and analyses. Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents a novel computational approach to generate the suboptimal solutions for a class of nonlinear optimal control problems (OCP's) with a quadratic performance index. Our method is based on the one-dimensional differential transform method (DTM) and new polynomials that are called DT's polynomials. This method simplifies the difficulties and massive computational work for calculating the differential transform of nonlinear function. The convergence of proposed method are discussed in detail. This method consists of a new modified version of the DTM together with a shooting method such as procedure, for solving the extreme conditions obtained from the Pontryagin's maximum principle. The results reveal that the proposed methods are very effective and simple. Comparisons are made between new DTM generated results, results from literature, and MATLAB bvp4c generated results, and good agreement is observed. Copyright © 2013 John Wiley & Sons, Ltd.

We propose a linearized formulation for min–max control problems with separated dynamics. First, we investigate the existence of the value function and saddle points for semicontinuous costs. Second, we obtain dual formulations and dynamic programming principles. Copyright © 2013 John Wiley & Sons, Ltd.

Minimal-control-energy strategies are substantiated and illustrated for linear-quadratic problems with penalized endpoints and no state-trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite-dimensional set of admissible control trajectories to the finite-dimensional Euclidean space of initial conditions. An efficient real-time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure-upper-bounded brake, flexible-endpoint setting. Copyright © 2013 John Wiley & Sons, Ltd.