Constraint Robust Model Predictive Control for Jump Markov Linear Systems with Additive Disturbances

This paper proposes an approach to robust model predictive control (MPC) for discrete-time jump Markov linear systems (JMLS) considering polytopic constraints on the inputs and states. In a first design step, state feedback controllers, that stabilize the JMLS robustly, are calculated offline by means of a semi-definite program (SDP). These controllers are designed to satisfy the constraints and keep the states within disturbance invariant sets (DIS). To reduce the conservatism of the design approach, an SDP formulation in which the controller parameterization is independent of the Lyapunov matrices is employed. The resulting Lyapunov matrices and the DIS are used to formulate quadratic constraints for the first prediction step, that ensure robustness against additive disturbances, stability, constraint satisfaction and recursive feasibility. The stabilizing properties and low computation times of the resulting quadratically constraint quadratic program (QCQP) are illustrated by simulation.