Robust Predictive Control For Singular Systems Based On The State Observer

The predictive control has been made great progresses with its wider usages in the industrial process control. Because of the complexity of the systems and various factors in industry, the model used to describe the dynamics of controlled system always has some uncertainties. Robust 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 predictive control, 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.At present, the main work is concerned to general systems with the form of the state feedback. However, the singular systems exist in various fields, and it is very important to study the problem of robust predictive control for singular systems. While the states may not be measured directly in the actual control, the state feedback will not be the physical implementation. So the algorithm based on the state observer is proposed when the states are unmeasurable.When the states can't be measured, this paper is devoted to the development of the framework of robust predictive control for various described uncertain singular systems by using of the linear matrix inequalities (LMIs). The main contents are stated as follows:1. The synthesis method of the robust predictive control based on the state observer is presented for singular systems with polytopic uncertainties. By constructing the Lyapunov function with the error term, the sufficient conditions for the existence of observer-based robust predictive control are obtained by linear matrix inequalities, which minimize an upper bound on the'worst-case'objective function. It is proved that the robust stability of the closed-loop singular systems is guaranteed by the initial feasible solutions of the optimization problems.2. When the state can not be measured, the robust predictive control algorithm based on the state observer is proposed for a class of singular systems with norm-bounded parameter uncertainties. The predictive feedback control law is presented by linear matrix inequalities formulation. When the obtained feedback control satisfies some condition, the robust stability and the impulse-free of the closed-loop singular systems are guaranteed by the proposed design method.3. The problem of robust predictive control based on the state observer is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By using of the method of LMIs, the sufficient conditions for the existence of the control law are derived. It is proved that the robust stability of the closed-loop singular systems is guaranteed by the initial feasible solutions of the optimization problems.