Reach-Avoid Model Predictive Control with Guaranteed Recursive Feasibility via Input Constrained Backstepping

TL;DR

This paper introduces a new sampled-data model predictive control method for nonlinear systems that guarantees reach-avoid objectives and recursive feasibility while respecting input constraints.

Contribution

It develops a backstepping-based approach to synthesize reach-avoid invariant sets that ensure safety and feasibility under physical input limits.

Findings

Guarantees recursive feasibility under fast sampling.

Successfully steers nonlinear systems into target sets safely.

Numerical results confirm the approach's effectiveness.

Abstract

This letter proposes a novel sampled-data model predictive control framework for continuous control-affine nonlinear systems that provides rigorous reach-avoid and recursive feasibility guarantees under physical constraints. By propagating both input and output constraints through backstepping process, we present a constructive approach to synthesize a reach-avoid invariant set that complies with control input limits. Using this reach-avoid set as a terminal set, we prove that the proposed sampled-data MPC framework recursively admits feasible control inputs that safely steer the continuous system into the target set under fast sampling conditions. Numerical results demonstrate the efficacy of the proposed approach.