Tube MPC scheme based on robust control invariant set with application to Lipschitz nonlinear systems

The paper presents a tube model predictive control (MPC) scheme of continuous-time nonlinear systems based on robust control invariant set. The optimization problem considered has a general cost functional rather than the quadratic one. The scheme has the same online computational burden as the standard MPC with guaranteed nominal stability. Robust stability, as well as recursive feasibility, is guaranteed if the optimization problem is feasible at the initial time instant. Furthermore, an optimization based control scheme is proposed, which inherits the robust properties of the tube MPC scheme. The related optimization problem is solved only at the initial time instant. In particular, we consider a scheme to obtain robust control invariant set for Lipschitz nonlinear systems, and show the effectiveness of the proposed schemes by a simple example.