The Design Of Model Predictive Controller For Stochastic Systems Based On Elliptic Probability Sets

Model predictive control(MPC)is a computer optimization algorithm that has been widely used in complex industrial processes.It can predict the future behaviors of the controlled object.Stochastic systems are a class of uncertainty systems,also known as probabilistic systems,whose uncertainties satisfy the specific statistical probabilities.The stochastic systems model can describe a large of application fields such as stochastic network control systems,navigation system,the random fluctuation of stock industry and so on.Therefore,the predictive control method for the stochastic systems have attracted greater attention.The research on the predictive control of stochastic systems have good theoretical value and practical significance.In this thesis,the state feedback model predictive problems for uncertain stochastic systems are studied by using the elliptical probability sets.The main contents of this thesis are as follows:1)For a class of discrete-time stochastic systems with Markov jump,MPC for the systems under probabilistic constraints are studied.At each sampling period,by means of multi-layer probabilistic sets method,the optimal problem with infinite horizon objective function was calculated.The sufficient conditions on the existence of the state feedback control were derived.Further,a stochastic model predictive control algorithm is proposed for the on-line synthesis of state feedback controller with the conditions guaranteeing that the systems states are steered into the invariant elliptical set with different probabilities under multi-step feedback control method,the closed-loop stochastic systems are asymptotic stable,and the upper bound of cost function is minimum.2)For a class of discrete-time stochastic systems with convex polyhedron uncertainty,at each sampling period,through introducing a free variable and using an augmented autonomous prediction formulation,the optimal problem with finite horizon objective function is obtained based on multi-layer probabilistic sets method.The sufficient conditions on the existence of the state feedback control are derived.Further,a stochastic model predictive control algorithm is proposed for the on-line synthesis of state feedback controller with the conditions guaranteeing that the systems states are steered into the invariant elliptical set with different probabilities,upper bound of the performance index is minimized in finite time,and the closed-loop stochastic systems are asymptotic stable.3)For a class of discrete time stochastic systems with incomplete state,the state estimator is obtained off-line.At each sampling period,by state estimation method,the optimal problem with infinite horizon objective function is solved.The sufficient conditions on the existence of the state feedback control are derived.Further,a stochastic model predictive control algorithm is proposed for the on-line synthesis of state feedback controller with the conditions guaranteeing that the systems state and state estimation error are constrained in certain ellipses,the systems states are steered into the invariant elliptical set with different probabilities.At last,upper bound of the performance index is minimized and the closed-loop systems are asymptotically stable.