Fast Robust Model Predictive Control for Nonlinear Jump Markov Systems

Abstract

Abstract This paper proposes a scheme of robust model predictive control (MPC) for discrete-time nonlinear jump Markov systems (JMS) considering polytopic state and input constraints. The approach consists of an offline part and the online optimization: First, a time-varying linear JMS representation of the nonlinear JMS is used to determine time-varying feedback controllers and robust control invariant sets (RCIS) offline, solving a semi-definite program (SDP). Then, an MPC formulation uses online linearization, the determined RCIS, and Lyapunov functions to guarantee constraint satisfaction, mean square stability, and recursively feasibility. The proposed formulation is robust against bounded disturbances and the linearization errors. A simulation study demonstrates that the involved quadratically constrained quadratic programs (QCQP) can be solved quite efficiently, rendering this approach applicable for high-dimensional systems.