On the Stability of a Nonlinear MPC Scheme for Avoidance

This work analyzes the stability properties of a nonlinear Model Predictive Control (MPC) scheme for avoidance. This control approach introduces an extra penalty for avoidance within the nonlinear tracking MPC framework. We demonstrate that, under a mild assumption on the avoidance penalty, the closed-loop system is Input-to-State Stable (ISS) with respect to this penalty. Furthermore, we discuss the conditions under which asymptotic stability can be achieved and present a simplified scheme with relaxed terminal constraints. To illustrate the effectiveness of the proposed strategy, we apply it to the control of a van der Pol oscillator subjected to non-convex constraints.