Invariant Sets Based Model Predictive Control For Markov Jump Linear Systems

Markov jump systems refer to systems whose structure are subject to random abrupt changes, this phenomenon is common in economic systems, aircraft control systems,communication systems, as well as solar heating systems. Hence Markov jump systems are an important class of systems. In Markov jump systems, due to physical limitations or economical and performance requirements, constraints always exist. When dealing with constraints, owing to the special receding horizon implementation mechanism, model predictive control has some advantages over other control methods. So model predictive control for Markov jump systems is a subject of great significance.The existence of the constraints leads to some difficulty in the design of model predictive controllers for Markov jump systems. To design a model predictive controller with both guaranteed recursive feasibility and good control performance is the key issue in the study of model predictive control for Markov jump systems. To this point, this dissertation focuses on the design of model predictive controllers for Markov jump linear systems in different cases. The main contents and results are as follows.? For constrained Markov jump linear systems with additive disturbance, an efficient algorithm has been developed for the computation of the maximal admissible set.? For Markov jump linear systems with hard constraints, based on ellipsoidal sets,unconstrained and constrained multi-step model predictive controllers have been developed. The recursive feasibility of the resulting algorithms and closed loop mean square stability have been proved. Finally to improve the online computational efficiency, a model predictive controller to reduce its online computational burden has been designed.? For Markov jump linear systems with hard constraints, to overcome the disadvantages of the algorithms developed above when dealing with asymmetric constraints,based on the maximal admissible set(polyhedral set), general interpolation model predictive controller and interpolation model predictive controller with linear objective as well as interpolation model predictive controller with exact constraints handling have been developed. The recursive feasibility of the resulting algorithms and closed loop mean square stability have been proved.? For Markov jump linear systems with probabilistic soft constraints, model predictive controllers have been developed based on the maximal admissible set for two cases:disturbance with finite energy and persistent disturbance. The recursive feasibility of the resulting algorithms and closed loop mean square stability have been proved.? For the structured uncertain systems with time delays modeled by a Markov chain,by introducing a state augmentation, the original system has been transformed into a standard structured uncertain time-delay Markov jump systems, and then a model predictive controller as well as another model predictive controller to reduce the low online computational burden have been developed.? For Markov jump linear systems with quasi-periodicity and expectation constraints,a robust controller, a stochastic controller, as well as a model predictive controller have been developed. The above controllers have been proved with guaranteed constraints satisfaction and closed loop stabilizability.