Constrained Predictive Control For Singular Systems

All kinds of constraints exist in actual control systems. Model predictive control is areceding horizon control strategy, and provides a systematic approach to handle theconstraints. However, in the presences of the constraints, both the control action ofconstrained MPC and the closed-loop system display nonlinearity, then how to guarantee thestability of the closed-loop system was a difficult problem once. So the constrainedpredictive control method based on Lyapunov stability theory arises at the historic moment.However, the main work is concerned to general systems. Singular systems exist in variousfields, and it is very important to study the problem of constrained predictive control forsingular systems.Based on the research methods of general systems, this paper studies the problem ofconstrained predictive control for singular systems. The main contents are stated as follows:the constrained predictive control problem is considered for discrete-time singularsystems based on terminal invariant set. On the basis of stability analysis, a sufficient andnecessary condition for a class of discrete-time singular systems to be regular, causal andstable is proposed. Then a controller is designed to drive the state into a terminal invariant set.In the terminal invariant set, a fixed feedback control law is used to guarantee the systemadmissible.we consider the stabilization of linear discrete time singular systems with respect to inputconstraints based on model predictive control scheme. One problem that must be overcome isthe avoidance of noncausal, this is achieved by enforcing the input to be included a functionwhich is sufficiently often differentiable. Stability of the closed-loop is achieved utilizing asuitable terminal penalty term and a constraint. Predictive control scheme is designed for theinitial state in the predictive horizon to drive the state in the terminal region where a localcontroller is used.The model predictive control by dynamic compensation for rectangular descriptorsystem is considered. Combining with the system admissibility condition, and associatematrix inequality and lyapunov equation have a solution in order to obtained a simple form ofoptimal problem. To solve the optimal problem, the proposed lyapunov equation istransformed into a bilinear matrix inequality, and a corresponding path-following algorithm to minimize performance index, The closed-loop system is also admissible.