Stability Region Analysis And Output Feedback Control For Constrained System

There extensively exist input and output constrains in real control systems. Thecontrol performance must be analyzed if the constraints cannot be ignored, otherwisethe expected control objectives cannot be satisfied. Currently, the control problemof constrained system has been receiving increasing attention due to its importanttheoretical and practical significance.This thesis is composed of six chapters in which the problems of stability regionanalysis, disturbance attenuation and design of state and output feedback control lawfor constrained systems are discussed. The keys of this work are focused on expand-ing domain of attraction for constrained system and designing H_∞output feedbackcontrol law. Furthermore, one method proposed in this thesis is applied to VehicleActive Suspensions.In Chapter 2, the problem of attraction domain estimation for continuous/discretesystems subject to actuator saturation is investigated. To approximate the attractiondomain more precisely, a largest ellipsoid set which contains state trajectories derivedfrom all initial states and satisfies the closed-loop system stability is obtained. Byintroducing two slack matrices, the sufficient LMI condition that guarantees the el-lipsoid set to be invariable in attraction domain is presented, and can be solved mucheffectively. Based on this idea, a state feedback controller design method that guaran-tees the largest ellipsoid set is developed.As an extension of Chapter 2, Chapter 3 discusses the reduced-order output feed-back controller design and attraction domain estimation for constrained system. In theformulation of LDI (linear differential inclusion) of saturation function, the sufficientcondition which guarantees the ellipsoid set to be invariable in attraction domain isobtained by using auxiliary feedback matrix, and a reduced-order output feedbackcontroller design method that guarantees larger domain of attraction is presented.In Chapter 4, a dynamic output feedback control via moving horizon H_∞strat-egy for constrained system is developed. For the constrained system with boundedexogenous disturbances, an output feedback control approach is presented to guar-antee H_∞performance in the framework of linear matrix inequalities (LMI). It is a challenge to accurately estimate the largest energy of the disturbance for the actualsystem. To avoid the conservatism derived from over-estimation and constraints un-satisfaction derived from under-estimation, a new dissipative constrained condition isfurther employed and a moving horizon output feedback control law which guaranteesH_∞performance is presented by optimizing the H_∞performance index on-line. Themethod can automatically trade-off between satisfying control constraints and enhanc-ing performance, and the control constraint are still satisfied even if the estimation ofthe largest energy of disturbance is too small.To simplify the design and realization of controller, the method of robust H_∞static output feedback is discussed in Chapter 5. By searching the condition that guar-antees the given performance index based on S-procedure technique, an H_∞staticoutput feedback control design method is proposed for constrained system. Moreover,the dissipative constrained conditions and the elliptical set that contains output trajec-tory are cast as LMIs, and introduced into the optimization problem, then a movinghorizon H_∞control using static output feedback is presented. The proposed methodis simpler in construction and implementation, in contrast with the strategy in Chapter4.In Chapter 6, the moving horizon H_∞control strategy is extended to continuouscontrol systems and applied to the Vehicles Active suspension control. The controllerdesign of Vehicles active suspension, which is a multi-objective control problem, canbe formulated as a LMI optimal problem with H_∞norm as a performance index toimprove comfort. In this Chapter, the feasibility of applying the method in Vehiclesactive suspension control is analyzed. The simulation results show that the method isclose to the case of state feedback in performance, and on premise that constraints aresatisfied the system can reduce the impact of disturbance on output, improve comfortand have a good prospect of application.