Model Predictive Control For It?-type Stochastic Systems

Stochastic phenomenon is common in nature, there are a lot of actual systems with random factors, for example, the influence of random factors by signal into a noisy random process in the transmission process, the plane encountered in flight gust, all kinds of noise in electronic device and all kinds of random fluctuation in the production process etc. Therefore, the stochastic model has been widely used in many fields of natural science, engineering and stochastic system has attracted more and more attention.It? stochastic systems as a kind of important stochastic dynamical systems, it has important applications in mathematical finance, aerospace, power systems, network communications and other fields. So the study of it has important significance to control problem of stochastic systems.The validity of the model predictive control is strong applicability, consideration of the existence of the finite domain advantages of all kinds of soft and hard constraints in the design. Since the predictive control algorithm is proposed, it has made great progress in theory and also has a wide range of industrial applications.This paper aims at studying on predictive control synthesis problem of a class of continuous time It? stochastic systems with persistent disturbances. The main contents are stated as follows:1. The problem of predictive control is investigated for a class of continuous time It? stochastic systems. By using Lyapunov function and It? formula, the stochastic programming problem is changed into a min-max optimization problem and we can get the sufficient conditions for the existence of state feedback controller.2. The H_∞ predictive controller is designed for a class of continuous time It?stochastic systems with persistent disturbances. Through the combination of H_∞ control method and receding horizon optimization principle, the receding horizon H_∞ control law and the sufficient conditions are given. The control law guarantees the closed-loop system stochastically stable and the gain of the disturbance input does not exceed the upper bound.3. The problem of H_∞ predictive control is investigated for a class of continuous time It? stochastic systems with bounded interference and control constraint. With input-to-state stability describing the stability of the system, the H_∞ predictive control law and the sufficient conditions of existence are given by solving a min-max performance index with terminal cost function.