On the inherent robustness of optimal and suboptimal nonlinear MPC

Abstract

Suboptimal model predictive control (MPC) is a control algorithm that uses suboptimal solutions to optimal control problems to provide control actions quickly. In MPC, terminal control laws and terminal region constraints are frequently used to ensure recursive feasibility and stability. Suboptimal MPC was proven to be inherently robust for systems with soft terminal region constraints in Pannocchia et al. (2011). We extend that work to systems with hard terminal region constraints. If these hard constraints are defined as sublevel sets of appropriate terminal cost functions, a well-chosen initial guess (warm start) for the optimization algorithm is robustly feasible. As a result, the system controlled by suboptimal MPC admits an ISS-Lyapunov function and is therefore inherently robust.The authors of Yu et al. (2014) noted that the result in Pannocchia et al. (2011) applied only to systems with continuous optimal cost functions. However, discontinuous optimal cost functions may be present in systems with hard terminal region constraints. We include a simple example of a continuous dynamical system with a provably discontinuous optimal value function that, as a consequence of the main result of this work, is inherently robust. This example is to our knowledge the first such system reported in the literature.