Robust Predictive Control Of Uncertain Descriptor Systems With State Delay

Compared with the normal systems, descriptor systems describe some of the actual systems better. On the other hand, time delay and uncertainty often appear in many control systems, and the existence may lead to systems performance degradation and even cause systems unstable. Therefore, the study to uncertain descriptor systems with time delay has important theoretical significance and application value. As the typical representative of the advanced process control, predictive control is a new class of computer control algorithms in industrial process control field. Robust predictive control problem for uncertain descriptor systems with or without time delay is discussed, an integrated approach to design robust predictive controller has also been given. By using Lyapunov stability theory and linear matrix inequalities method, the quadratic performance index in the infinite horizon optimization problem is approximately solved, and the sufficient conditions for existence of robust predictive controller are presented for the closed-loop systems.According to the above points of view, the main contents of this paper are summarized as follows:1. The main background of the problem discussed in this thesis is introduced. Firstly, the development and research methods of descriptor systems are briefly introduced; then the research background and characteristics of predictive control are introduced, the basic principles of predictive control are also presented. At last, the stability and robustness of predictive control are presented.2. The robust predictive control algorithm based on LMI and its application in uncertain descriptor systems is described. Finally, in the constrained case, how to solve the problem based on the state space model is discussed.3. The robust predictive control problem for uncertain descriptor systems is discussed. First of all, robust model predictive control of the state feedback controller is designed for the uncertain singular systems with norm bounded, and a brief robust predictive control algorithm steps is presented with uncertain descriptor systems. Based on linear matrix inequality approach, a set of piecewise continuous state feedback controller is determined by solving the optimization problem in infinite horizon quadratic performance index. Finally, the asymptotic stability for uncertain descriptor systems is analyzed.4. The Robust model predictive control problem for descriptor systems with state time delay and uncertainty is further discussed. By using Lyapunov stability theory and linear matrix inequalities (LMI) approach, the infinite horizon quadratic performance index "min-max" optimization problem is approximately solved on-line, then the explicit expression of the predictive controller is discussed, and a sufficient condition of existence of the controller is presented. On this basis, the asymptotic stability and no pulse of uncertain descriptor systems are discussed.5. A summary of this thesis is given. At the same time, we give an expectation for the future work.As the conclusions obtained in the thesis, simulation examples are presented to show the feasibility and effectiveness of the proposed methods.