Mixed H2/H∞ robust model predictive control with saturated inputs

In this paper, we investigate the mixed H₂/H_∞ robust model predictive control (RMPC) for polytopic uncertain systems, which refers to the infinite horizon optimal guaranteed cost control (OGCC). To fully use the capability of actuators, we adopt a saturating feedback control law as the control strategy of RMPC. As the saturating feedback control law can be effectively represented by the convex hull of a group of auxiliary linear feedback laws, the auxiliary feedback laws allow us to design the actual feedback control law without consideration of the input constraints directly to achieve the improved performance. Moreover, we suggest the relative weights on the actual and auxiliary feedback laws to the RMPC, which in turn improves the closed-loop system performance. Furthermore, an off-line design of the proposed RMPC is also developed to make it more practical. Numerical studies demonstrate the effectiveness of the proposed algorithm.     

Robust H∞ control of uncertain stochastic Markovian jump systems with mixed time-varying delays

In this paper, robust H_∞ control for a class of uncertain stochastic Markovian jump systems (SMJSs) with interval and distributed time-varying delays is investigated. The jumping parameters are modelled as a continuous-time, finite-state Markov chain. By employing the Lyapunov-Krasovskii functional and stochastic analysis theory, some novel sufficient conditions in terms of linear matrix inequalities are derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method comparing with some existing results.     

Stabilisation and H∞ control of neutral stochastic delay Markovian jump systems

This paper investigates the exponential stabilisation and H_∞ control problem of neutral stochastic delay Markovian jump systems. First, a delay feedback controller is designed to stabilise the neutral stochastic delay Markovian jump system in the drift part. Second, sufficient conditions for the existence of feedback controller are proposed to ensure that the resulting closed-loop system is exponentially stable in mean square and satisfies a prescribed H_∞ performance level. Finally, numerical examples are provided to show the effectiveness of the proposed design methods.     

A geometric approach to H∞ control of nonlinear Markovian jump systems

This paper first discusses the H_∞ control problem for a class of general nonlinear Markovian jump systems from the viewpoint of geometric control theory. Following with the updating of the Markovian jump mode, the appropriate diffeomorphism can be adopted to transform the system into special structures, which establishes the basis for the geometric control of nonlinear Markovian jump systems. Through discussing the strongly minimum-phase property or the strongly γ-dissipativity of the zero-output dynamics, the H_∞ control can be designed directly without solving the traditional coupled Hamilton–Jacobi inequalities. A numerical example is presented to illustrate the effectiveness of our results.     

Delay-dependent robust H ∞ control for uncertain fuzzy Markovian jump systems

This paper is concerned with the problem of delay-dependent robust H _∞ control for uncertain fuzzy Markovian jump systems with time delays. The purpose is to design a mode-dependent state-feedback fuzzy controller such that the closed-loop system is robustly stochastically stable and satisfies an H _∞ performance level. By introducing slack matrix variables, a delay-dependent sufficient condition for the solvability of the problem is proposed in terms of linear matrix inequalities. An illustrative example is finally given to show the applicability and effectiveness of the proposed method. Recommended by Editorial Board member Young Soo Suh under the direction of Editor Jae Weon Choi. This work is supported by the National Science Foundation for Distinguished Young Scholars of P. R. China under Grant 60625303, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20060288021, and the Natural Science Foundation of Jiangsu Province under Grant BK2008047. Yashun Zhang received the B.S. and M.S. degrees in Control Science and Control Engineering from Hefei University of Science and Technology in 2003 and 2006. He is currently a Ph.D. student in Control Science and Control Engineering, Nanjing University of Science and Technology. His research interests include fuzzy control, sliding mode control and nonlinear control. Shengyuan Xu received the Ph.D. degree in Control Science and Control Engineering from Nanjing University of Science and Technology in 1999. His research interests include robust filtering and control, singular systems, time-delay systems and nonlinear systems. Jihui Zhang is a Professor in the School of Automation Engineering of Qingdao University, China. His main areas of interest are discrete event dynamic systems, production planning and control, and operations research.     

Finite-horizon ℋ 2/ℋ ∞ control for a class of nonlinear Markovian jump systems with probabilistic sensor failures

This article is concerned with the mixed ?₂/?_∞ control problem over a finite horizon for a class of nonlinear Markovian jump systems with both stochastic nonlinearities and probabilistic sensor failures. The stochastic nonlinearities described by statistical means could cover several types of well-studied nonlinearities, and the failure probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over a given interval. The purpose of the addressed problem is to design state feedback controllers such that the closed-loop system achieves the expected ?₂ performance requirement with a guaranteed ?_∞ disturbance attenuation level. The solvability of the addressed control problem is expressed as the feasibility of certain coupled matrix equations. The controller gain at each time instant k can be obtained by solving the corresponding set of matrix equations. A numerical example is given to illustrate the effectiveness and applicability of the proposed algorithm.     

Mixed H2 /H∞ control under variance constraints

Dual problems, which we call output and input variance constrained H₂ /H_∞ controls, are considered. In these problems, we seek control-laws that satisfy mixed H₂ /H_∞ performance criteria, under multiple variance constraints on either outputs or inputs of time-invariant multivariable systems. The approach taken is to convert the problems into non-linear programming with both equality and inequality constraints. For both problems, the Kuhn-Tucker optimality condition is employed to obtain a first-order necessary condition for a regular point that minimizes an upper bound on the quadratic performance for the given H_∞ constraint. A second-order necessary condition and sufficiency for the strict local minimizer of the upper bound are investigated. Efficient algorithms for synthesizing the desired controllers are proposed.     

Further results on H∞ control for discrete-time Markovian jump time-delay systems

This paper studies the problem of H_∞ control for a class of discrete-time Markovian jump systems with time delay. The purpose is to improve the existing results on H_∞ controller design for Markovian jump systems. A novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality, which is proved to be less conservative than most results in the literature. Then the state feedback controller is designed, which guarantees the stochastic stability of the closed-loop system with a given disturbance attenuation. Numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques.     

Reliable finite-time H∞ control of uncertain singular nonlinear Markovian jump systems with bounded transition probabilities and time-varying delay

This paper investigates the problem of reliable finite-time H_∞ control for one class of uncertainsingular nonlinear Markovian jump systems with time-varying delay subject to partial information on the transition probabilities. Continuous fault model is more general and practical to serve as the actuator fault. Time delay is a kind of positive time-varying differentiable bounded delays. First, based on a state estimator the resulting closed-loop error system is constructed and sufficient criteria are provided to guarantee that the augmented system is singular stochastic finite-time boundedness and singular stochastic H_∞ finite-time boundedness in both normal and fault cases via constructing a delay-dependent Lyapunov–Krasonskii function. Then, the gain matrices of state-feedback controller and state estimator are fixed by solving a feasibility problem in terms of linear matrix inequalities through decoupling technique, respectively. Finally, numerical examples are given to show the validity of the proposed design approach.     

H ∞ control of a suspension with a magnetorheological damper

This research work presents an H _∞ controller based on a Takagi–Sugeno (T–S) fuzzy model for a two-degrees-of-freedom (2-DOF) one-quarter-vehicle semi-active suspension with a magnetorheological damper where the actuator dynamics are included in the control synthesis. These dynamics enclose nonlinear damper phenomena, avoided in many other studies, and that can improve the suspension system by means of a more accurate model. The objective is to obtain a semi-active suspension that considerably improves the passive suspension efficiency based on some frequency domain performance criteria. The advantage of having the T–S system as a reference is that each piecewise linear system can be exposed to the well-known control theory. Besides, the proposed solution is compared with the recent reported work to highlight its advantages. A case of study is included and simulation work supports the results. The methodology applied herein can be extended to a half-vehicle model, and to the four wheels to have a global chassis control in order to maximise passenger comfort and vehicle stability.     

Mixed H2/H∞ state-feedback design for microsatellite attitude control

Owing to a great decrease in size and weight, the pointing accuracy of microsatellite is vulnerable to space environmental disturbances and the internal uncertainty of moment-of-inertia variation. Mixed H₂/H_∞ control, giving consideration to both stability robustness and root-mean-square (rms) performance, is particularly attractive for attitude controller design of microsatellites. By using linear matrix inequality method, the numerical solution of mixed H₂/H_∞ state-feedback controller can be efficiently solved. The performance differences between mixed H₂/H_∞ controller and its two extremes—pure H₂ controller and pure H_∞ controller—are discussed in detail. Mixed H₂/H_∞ controller shows the remarkable capability of achieving a balanced compromise between H₂ and H_∞ performances.     

Security control of positive semi‑Markovian jump systems with actuator faults

Actuator faults usually cause security problem in practice. This paper is concerned with the security control of positive semi-Markovian jump systems with actuator faults. The considered systems are with mode transition-dependent sojourntime distributions, which may also lead to actuator faults. First, the time-varying and bounded transition rate that satisfies the mode transition-dependent sojourn-time distribution is considered. Then, a stochastic co-positive Lyapunov function is constructed. Using matrix decomposition technique, a set of state-feedback controllers for positive semi-Markovian jump systems with actuator faults are designed in terms of linear programming. Under the designed controllers, stochastic stabilization of the systems with actuator faults are achieved and the security of the systems can be guaranteed. Furthermore, the proposed results are extended to positive semi-Markovian jump systems with interval and polytopic uncertainties. By virtue of a segmentation technique of the transition rates, a less conservative security control design is also proposed. Finally, numerical examples are provided to demonstrate the validity of the presented results.     

Finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching

An extension of a fixed transition probability (TP) Markovian switching model to combine time-varying TPs has offered another set of useful regime-switching models. This paper is concerned with the problem of finite-time H_∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying TPs subject to average dwell time switching. The so-called time-varying TPs mean that the TPs are varying but invariant within an interval. The variation of the TPs considered here is subject to a class of slow switching signal. Based on selecting the appropriate Lyapunov–Krasovskii functional, sufficient conditions of finite-time boundedness of Markovian jump systems are derived and the system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method.     

Mode-dependent quantised H∞ filtering for Markovian jump singular system

This paper considers the H_∞ filtering problem for Markovian jump singular systems. In addition, when taking into account the effect of the quantisation, the designed filter not only guarantee admissibility but also satisfy a prescribed H_∞ filtering performance for the filter error system. By using Lyapunov method, a new bounded real lemma is proposed in terms of linear matrix inequalities (LMIs) to ensure that the filtering error system has the mentioned properties. Furthermore, a sufficient condition for the existence of filter is obtained in terms of LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

H∞ filtering for piecewise homogeneous Markovian jump nonlinear systems

This paper concerns the problem of H_∞ filtering for piecewise homogeneous Markovian jump nonlinear systems. Different from the existing studies in the literatures, the existence of variations in transition rates for Markovian jump nonlinear systems is considered. The purpose of the paper is to design mode-dependent and mode-independent filters, such that the dynamics of the filtering errors are stochastic integral input-to-state stable with H_∞ performance index. Using the linear matrix inequality method and the Lyapunov functional method, sufficient conditions for the solution to the H_∞ filtering problem are derived. Finally, three examples are proposed to illustrate the effectiveness of the given theoretical results.     

H∞ control of continuous-time Markov jump linear systems with detector-based mode information†

This paper features new results on H_∞ analysis and control of linear systems with Markov jump disturbances, in a scenario of partial observations of the jump process. We consider the situations in which the jump process can only be measured through a suitable detector. A distinctive feature of the approach here is that it is general enough to encompass particular scenarios such as that of perfect information, no information (mode independent) and cluster observations of the Markov jump process. The main results, comprising a new bounded real lemma and a condition for state feedback synthesis, are expressed via linear matrix inequality-based optimisation problems. The method devised for the design of H_∞ controllers is applied to the control of an unmanned aerial vehicle model.