Research Of Robust Model Predictive Control For Uncertain Singular Systems

Predictive control, which is known as an advanced of computer control approach, has been applied successful in industry. However, the model, which is used to describe the dynamics of controlled system, always has some uncertainty. In order to guarantee the specified performance, model uncertainty must be taken into account properly. Robust model predictive control is referred to the predictive control method which can make the performance index within the acceptable range in the presence of model uncertainty. It combines the method of robust control with the moving horizon principle of MPC, and has the capability of handling constraints and optimization over some performance index in a systematic way. The feasibility and robust stability of the closed-loop systems are guaranteed.Based on the existing theoretical results on model predictive control, this thesis is devoted to the development of the framework of robust model predictive control for uncertain singular systems. To achieve this goal, the relevant theory and approaches, such as linear matrix inequalities (LMI) and Lyapunov stability theory, robust control, sampled-data control and controllable invariant set and so on, are employed in the research work. The main contents of this thesis are stated as follows:1. The problem of robust output feedback model predictive control is studied for uncertain singular systems. Based on the idea of variable transformation and LMI methods, the infinite time domain"min-max"optimization problems are converted into linear programming problems, a piecewise continuous output feedback control law is obtained and the sufficient conditions for the existence of this control law are given. It is proved that the robust stability of the closed-loop singular systems is guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of singular systems are also held.2. For a class of uncertain singular systems with input constraints, an LMI-based state-back solution is presented and conditions for guaranteeing closed-loop H-infinity performance and satisfying the time-domain constraints are given. At each sample time, the piecewise continuous state feedback predictive control law is obtained. It is proved that the asymptotical stability of the singular closed-loop systems is guaranteed, and also the regular, the impulse-free and the H-infinity performance indexγis satisfied. 3. The robust predictive control problem is studied for uncertainties singular systems with state and input delay. By using the Lyapunov function and LMI method, the robust predictive controller is designed and the explicated display is given. It is proved that the robust stability of the closed-loop singular systems is guaranteed and the regular and the impulse-free of singular systems are also held.4. The problem of delay-dependent robust predictive control for a class of uncertain singular time-delay systems is considered. By means of lyapunov theory and the idea of optimal weight matrix and LMI and the modified cone complementarity linearization iterative algorithm, the infinite time domain"min-max"optimization problems are converted into convex optimization problems, and the sufficient conditions for the existence of the delay-dependent robust predictive controller are derived. The feasibility of the optimization problems guarantees that the closed-loop singular systems are robustly stable, regular and impulse free.