Efficient and smooth robust model predictive control for stochastic switching systems

This study is concerned with the computationally efficient robust model predictive control (MPC) for discrete-time stochastic switching systems. 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, such that the abrupt variation of mode-dependent gains can be mitigated via BTC performance optimization. To address the high computational complexity caused by the transition-dependent variables and constraints, the MPC algorithm is developed with an offline-to-online synthesis strategy, achieving comparable online computation cost to non-switching MPC. Meanwhile, a class of more general stochastic switching signals is considered, where the sojourn time may follow any form of distribution, and the recursive feasibility and mean-square stability are theoretically guaranteed. Compared with existing studies on switching MPC and the ones on 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.