Robust Model Predictive Control For Markovian Jump Systems Based On Transition Probability

Markovian jump system is a special class of hybrid systems.the dynamics random changeaccording to the law of a discrete Markov process. In actual industrial processes, it isinevitable that the uncertain parameters, constraints, and interference by the factors such asthe error of measurement or modeling, all kinds of physical constraints, the externalenvironment mutation. So robustness is necessary for the controlled systems. Robustpredictive control combines the method of robust control with the moving horizon principleof MPC, and has the capability of handling constraints and optimization over someperformance index in a systematic way. The feasibility and robust stability of the closed-loopsystems are guaranteed.The problem of stochastic stability predictive controller design method is investigatedfor Markovian jump systems. To achieve this goal, the relevant theory and approaches, suchas linear matrix inequalities (LMI), invariant set, and the stochastic Lyapunov stability theory,and so on, are employed in the research work. The main contents of this thesis are stated asfollows:(1) The problem of robust predictive controller design method is studied for Markovianjump systems with polytopic uncertainty.Using parameter-dependent stochastic Lyapunovfunction, it reduces the conservatism of controller design. The quadratic optimization problemis transformed into a SDP(semi-definite programming) problem which can reduce onlinecomputation cost.(2) The robust model predictive control strategy for Markovian jump systems withstochastic disturbances, considering probabilistic constraints of state, is proposed. Byadopting the technology of Tube, probabilistic constraints are converted into recursivelyfeasible probabilistic tubes, and the control inputs based on recursively feasible probabilistictubes ensure closed loop system stochastic stability.(3) For a class of non-homogeneous Markovian jump systems with polytopic uncertainty,the design method of robust predictive controller based on state observer is presented.Thepaper adopts the maximum a posterior estimation of transfer probability matrix, to getcorresponding homogeneous systems. Constructing the augmented stochastic Lyapunovfunction, the quadratic programming problem is converted into the problem of positive semidefinite programming problem. The optimization problem of LMI description andexpression and sufficient conditions for the existence an of the control law are got.