On Real-time Robust Model Predictive Control

High-speed applications impose a hard real-time constraint on the solution of a model predictive control (MPC) problem,
which generally prevents the computation of the optimal control input. As a result, in most MPC implementations guarantees on feasibility and stability are sacriced in order to achieve a real-time setting. In this paper we develop a real-time MPC approach for linear systems that provides these guarantees for arbitrary time constraints, allowing one to trade o computation time vs. performance. Stability is guaranteed by means of a constraint, enforcing that the resulting suboptimal MPC cost is a Lyapunov function. The key is then to guarantee feasibility in real-time, which is achieved by the proposed algorithm through a warm-starting technique in combination with robust MPC design. We address both regulation and tracking of piecewise constant references. As a main contribution of this paper, a new warm-start procedure together with a Lyapunov function for real-time tracking is presented. In addition to providing strong theoretical guarantees, the proposed method can be implemented at high sampling rates. Simulation examples demonstrate the eectiveness of the real-time scheme and show that computation times in the millisecond range can be achieved.