Robust MPC with event-triggered learning for unknown linear time-varying systems

This paper is concerned with robust model predictive control (MPC) for unknown linear time-varying (LTV) systems where all time-varying system matrices are assumed to belong to an unknown polytope . Based on the current observation only, an event-triggered learning scheme involving a model estimation and a polytope learning is proposed, leading to the reduction of the number of learning iterations and the guarantee of the convergence of learning. With the learned polytope, a robust MPC controller subject to a mixed state-input constraint is purposely designed to minimize the upper bound of a worst-case infinite horizon objective function with a discount factor. A matching error is constructed to connect two consecutive learned polytopes and accordingly the input-to-state stability is analyzed. Two examples are used to show the effectiveness of the proposed approach.