Robust Risk-Aware Model Predictive Control of Linear Systems with Bounded Disturbances

We propose a robust risk-aware model predictive control (MPC) algorithm for linear discrete-time systems with bounded disturbances. The MPC problem is formulated to maximize the size of the predicted disturbance sets (which are subsets of the maximal disturbance sets) at each time step, under state and control constraints and a reachability specification. It is shown that the proposed scheme has the following properties: i) its feasible state set (i.e., the set of states starting from which the MPC problem is feasible) is as large as that of the MPC problem for the corresponding undisturbed system; ii) it maintains recursive feasibility if the conventional robust MPC problem is feasible. The proposed controller enlarges the feasible state set, at the expense of the risk of possible constraint violation that is quantified by the optimal solution of the problem. When the sets are represented as zonotopes, we further provide a computationally tractable reformulation and design an online implementation algorithm with adaptive prediction horizon. We illustrate the effectiveness of the proposed methods using a simulated example.