Research Of Robust Model Predictive Control Or Stochastic Singular Systems

Stochastic singular systems, which are used to describe singular systems with stochasticinterference, widely exist in the real field. Compared with singular systems, stochasticsingular systems describe dynamic systems with stochastic interference more accurately.Furthermore, because of the complexity of the systems and various factors in industry, thesystems always have some uncertainty, so robustness is necessary for the controlled systems.Robust model predictive control (RMPC) which combines the method of robust control withthe moving horizon principle of MPC has the capability of handling uncertainty of systems.The paper is devoted to the research of robust model predictive control for uncertainstochastic singular systems by using of the Lyapunov stability theory、multidimensional Ito formula and linear matrix inequalities (LMI). The main contents are stated as follows:The problem of robust predictive control is investigated for stochastic singular systemswith polytopic uncertainty. Based on stochastic Lyapunov function, using Ito formula, theupper bound of the quadratic performance index are derived, then the infinite time domain“min-max” stochastic programming problems are converted into the minimizing problems ofthe upper bound. Using LMI methods, the expression of the feedback control law is obtainedand the sufficient conditions for the existence of this control law are given. It is proved thatthe stochastic admissible property of the closed-loop singular systems is guaranteed by thecontrol law.When the state is not measured, the robust predictive control algorithm based on theobserver is proposed for a class of stochastic singular systems with polytopic parameteruncertainty. With the Lyapunov function, using multidimensional Ito formula and LMImethods, the “min-max” stochastic programming problem is converted into the solvabilityproblem of a group of LMIs, then, the sufficient conditions for the existence of the controllaw and the expression are given. It is proved that the closed-loop singular systems’ propertyof regular、impulse and stable is guaranteed by the controller.The problem of robust predictive control is investigated for time-delay stochastic singularsystems with polytopic uncertainty. Using the Lyapunov function、multidimensional Ito formula and LMI method, the robust predictive controller is designed and the explicateddisplay 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.The robust predictive control problem is studied for stochastic singular systems withstate and input delay. Based on the Lyapunov function and multidimensional Ito formula, thestochastic admissible constraints are derived, then, using the solutions of a group of LMIs, theexpression of the control law is given. It is proved that the stochastic admissible property ofthe closed-loop singular systems is guaranteed by the controller.