H∞ state‐feedback controller design for continuous‐time nonhomogeneous Markov jump systems

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.     

Rejection of persistent‐bounded disturbances in linear time‐delay systems by output‐feedback

In this paper, the problem of persistent‐bounded disturbance rejection of linear continuous‐time systems with time‐varying delays is investigated using the tools of invariant set analysis and Lyapunov‐function methodology. We derive less conservative sufficient conditions on robust attractor for time‐delay systems in terms of strict linear matrix inequalities (LMIs) to guarantee the desired ??₁‐performance. A robust output‐feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on two representative time‐delay examples. Copyright © 2009 John Wiley & Sons, Ltd.     

Rejection of persistent‐bounded disturbances in continuous time‐delay systems using observer‐based feedback

In this paper, the problem of persistent‐bounded disturbance rejection of linear continuous‐time systems with time‐varying delays is investigated using the tools of invariant set analysis and Lyapunov‐function methodology. We derive less conservative sufficient conditions on robust attractor for time‐delay systems in terms of strict linear matrix inequalities (LMIs) to guarantee the desired ??₁‐performance. A robust output‐feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on two representative time‐delay examples. Copyright © 2009 John Wiley & Sons, Ltd.     

Fixed‐structure controller design for polytopic systems via LMIs

In this paper, a new approach for fixed‐structure H₂ 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 H₂ 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 H₂ norm is established theoretically for both nominal and robust controller design. Copyright © 2014 John Wiley & Sons, Ltd.     

Constrained linear parameter‐varying control using approximate multiparametric programming

We develop an approximate multiparametric convex programming approach with its application to control constrained linear parameter‐varying systems. Recently, the application of the real‐time model predictive control (MPC) for various engineering systems has been significantly increased by using the multiparametric convex programming tool, known as explicit MPC approach. The main idea of explicit MPC is to move the major parts of the computations to offline phase and to provide an explicit piecewise affine solution of the constrained MPC problem, which is defined over a set of convex polyhedral partitions. In the proposed method, the idea of convex programming and partitioning is applied for linear parameter‐varying control systems. The feasible space of the time‐varying parameters is divided into simplices in which approximate solutions are calculated such that the approximation error is kept limited by solving sequences of linear programs. The approximate optimal solution within each simplex is obtained by linear interpolation of the optimal solutions in the simplex vertices, and then multiparametric programming tool is utilized to compute an explicit state feedback solution of linear quadratic optimal control problem for simplex vertices subject to state and input constraints. The proposed method is illustrated by a numerical example and the simulation results show the advantages of this approach.     

Real‐time scheduling of multiple uncertain receding horizon control systems

In this paper, a new scheduling approach is proposed that considers the effect of modeling uncertainty for multiple continuous time receding horizon control (RHC) systems. This is accomplished by combining a scheduling approach with results from the continuous time nonlinear systems theory. It is shown that using a rate monotonic priority assignment method combined with analytical bounds on the prediction error, the problem of scheduling multiple uncertain plants can be cast into an appropriate constrained optimization problem. The constraints guarantee that the processes will be schedulable. The optimization provides optimized performance and balanced resource allocation in the presence of uncertainty. The proposed method was applied to a real‐time simulation of RHC trajectory tracking for two hovercraft vehicles demonstrating the validity of the approach. Copyright © 2008 John Wiley & Sons, Ltd.     

A time‐varying coefficient‐based manipulability‐maximizing scheme for motion control of redundant robots subject to varying joint‐velocity limits

A time‐varying coefficient‐based manipulability‐maximizing (TVCMM) scheme subject to varying joint‐velocity limits (VJVL) is proposed and investigated in this paper for the optimal motion control of redundant robot manipulators (where a planar robot manipulator is specifically considered). In order to improve the manipulability during the end‐effector task execution, a manipulability‐maximizing index is considered into the scheme formulation. Besides, for the remedy of the nonzero initial/final joint‐velocity problem, a time‐varying coefficient is introduced and incorporated in the scheme, which is further reformulated as a quadratic program (QP) subject to equality and bound constraints. For guaranteeing the physical realizability of such a scheme, an efficient linear variational inequality‐based (LVI‐based) numerical algorithm is employed to solve such a QP, and an experiment based on a 6‐DOF manipulator is presented, of which the redundancy is on the horizontal plane. Simulative and experimental results validate the physical realization, effectiveness, and accuracy of the proposed QP‐based manipulability‐maximizing scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Improved reachable set estimation of discrete‐time systems with time‐varying delay

This paper is concerned with the problem of reachable set estimation of discrete‐time systems with time‐varying delay and bounded disturbance. By applying the improved reciprocally convex combination approach to bound the forward difference of the double summation and triple summation, respectively, a less conservative reachable set estimation condition is developed in matrix inequalities. Based on the criterion, a less conservative stability criterion is obtained as a by‐product. Numerical examples are presented to validate the effectiveness of the obtained results.     

Robust satisfactory fault‐tolerant control of continuous‐time interval systems with time‐varying state and input delays

With the performance constraints on exponential stability, H_∞ norm of disturbance attenuation and upper bound of quadratic cost performance, the satisfactory and passive fault‐tolerant control problem is investigated for a class of interval systems with time‐varying input and state delays in the case of possible actuator faults. The bounded‐varying dynamics of actuator faults is described by interval matrix, which is more general and can be dealt with by the interval system theory. The delay‐dependent satisfactory fault‐tolerant controller design is developed based on multi‐objective optimization strategy. The results are derived in the forms of linear matrix inequalities, which is convenient to be solved in practice. Simulative example is presented to illustrate the effectiveness and necessity of the proposed fault‐tolerant control strategy. Copyright © 2011 John Wiley & Sons, Ltd.     

Reliable control for interval time‐varying delay systems subjected to actuator saturation and stochastic failure

This paper is devoted to the problem of reliable control for interval time‐varying delay systems subjected to actuator saturation and stochastic failure. A new practical actuator fault model is proposed by assuming that the actuator fault obeys a certain probabilistic distribution. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. Delay distribution and fault distribution‐dependent estimations of the domain of attraction are obtained by using the LMI techniques and an optimization method, such that the mean‐square stability of the systems can be guaranteed for given H_∞ performance index γ. Two illustrative examples are exploited to show the effectiveness of the proposed design procedures. Copyright © 2011 John Wiley & Sons, Ltd.     

A new result for closed‐loop poles region of LQ‐optimal discrete‐time systems

This paper deals with a new result for pole location of linear quadratic (LQ) optimal discrete‐time systems. In this paper a new region in which the closed‐loop eigenvalues of an LQ‐optimal discrete time system are located is determined. It has been shown that this region is bounded by four lines parallel to the real and imaginary axes, creating a square region. This region is symmetric with respect to the real axis of z‐plane, but not with respect to the imaginary axis. Inequality constraints, which bound the closed‐loop eigenvalues in a discrete‐time LQ‐optimal system, are also presented via two theorems. These theorems cover all systems except the ones where A is singular and H is positive semidefinite at the same time. The result is also extended to the problem of the prescribed degree of stability for LQ optimal discrete‐time systems. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust ℋ︁2 static output feedback design starting from a parameter‐dependent state feedback controller for time‐invariant discrete‐time polytopic systems

This paper investigates the problem of computing robust ??₂ static output feedback controllers for discrete‐time uncertain linear systems with time‐invariant parameters lying in polytopic domains. A two stages design procedure based on linear matrix inequalities is proposed as the main contribution. First, a parameter‐dependent state feedback controller is synthesized and the resulting gains are used as an input condition for the second stage, which designs the desired robust static output feedback controller with an ??₂ guaranteed cost. The conditions are based on parameter‐dependent Lyapunov functions and, differently from most of existing approaches, can also cope with uncertainties in the output control matrix. Numerical examples, including a mass–spring system, illustrate the advantages of the proposed procedure when compared with other methods available in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Further results on H ∞ control for discrete‐time uncertain singular systems with interval time‐varying delays in state and input

This paper investigates the state feedback robust H _∞ control problem of a class of discrete‐time singular systems with norm‐bounded uncertainties and interval time‐varying delays in state and input. A new bounded real lemma for discrete‐time singular systems with a pair of time‐varying interval state delays is first investigated. Mathematical comparisons of the new bounded real lemma and two existing ones are presented. Then, on the basis of the bounded real lemma proposed here, a sufficient condition in the form of nonlinear matrix inequality, such that the considered state feedback robust H _∞ control problem is solvable, is given. In order to solve the nonlinear matrix inequality, a cone complementarity linearization algorithm is offered. Several numerical examples are presented to show the applicability of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Estimation and synthesis of reachable set for discrete‐time periodic systems

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

Robust H∞ performance analysis for uncertain discrete‐time singular systems with time‐varying delays

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.     

A suboptimal learning control scheme for non‐linear systems with time‐varying parametric uncertainties

In this paper, learning control is integrated with non‐linear optimal control to enhance control performance of a class of non‐linear systems with time‐varying parametric uncertainties. A suboptimal control strategy based on a control Lyapunov function (CLF) and Sontag's formula provides suboptimal performance as well as stability along the time horizon for the nominal part of the non‐linear dynamic system. The proposed learning mechanism learns the unknown time‐varying parametric uncertainties so as to eliminate uncertain effects. System information both in time horizon and learning repetition horizon are incorporated in a composite energy function (CEF). The proposed control scheme achieves asymptotic convergence along the learning repetition horizon and boundedness and pointwise convergence of the tracking error (perfect tracking performance) along the time horizon. Copyright © 2001 John Wiley & Sons, Ltd.     

Reachable set estimation for neutral Markovian jump systems with mode‐dependent time‐varying delays

This study, under zero initial condition, aims to characterize the reachable set bound for a class of neutral Markovian jump systems (NMJSs) with interval time‐varying delays and bounded disturbances. To begin with, the time‐delays are considered to be mode‐dependent while delay mode and system mode are different. By utilizing free‐weighting matrix method and reciprocally convex combination technique, an ellipsoid‐like bound is characterized for the concerned NMJS with completely known transition probabilities. Based on the provided analytical framework, the case of same delay mode and system mode is also handled. Then, benefitting from a group of free‐connection weighting matrices, the reachable set estimation issue is tackled for the NMJS involving mode‐independent time‐varying delays and partially known transition probabilities. The theoretical analysis is confirmed by numerical simulations.     

Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H_∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.