Transition-Dependent Robust MPC for Stochastic Switched Systems

This study is concerned with the robust MPC for discrete-time stochastic switched systems subject to constraints on states and control inputs. Aiming at achieving optimal control synthesis under the requirement of bumpless transfer control (BTC), the min-max MPC formulation is extended to the transition-dependent paradigm, and a weighted performance index is optimized in the receding horizon, such that the abrupt variation in feedback gains can be mitigated. Meanwhile, a class of more general stochastic switching signals is considered, where the sojourn time may follow any distribution, and the recursive feasibility and mean-square stability are theoretically guaranteed. Compared with existing studies on switched MPC or BTC, this work avoids the assumption of the Markov property on mode switching and reduces conservatism by exploiting the statistical information of sojourn time. An illustrative example is provided to show the potential of the obtained results.