Model Predictive Control with Infeasible Reference Trajectories

TL;DR

This paper analyzes the stability of Model Predictive Control when using infeasible reference trajectories, providing conditions for ISS and asymptotic stability, supported by a robotic joint example.

Contribution

It establishes theoretical conditions under which MPC remains stable with infeasible references and demonstrates stability towards an optimal reference.

Findings

MPC can be ISS with infeasible references under certain conditions.

Proper terminal conditions ensure asymptotic stability towards an optimal reference.

Theoretical results validated with a robotic joint example.

Abstract

Model Predictive Control (MPC) formulations are typically built on the requirement that a feasible reference trajectory is available. In practical settings, however, references that are infeasible with respect to the system dynamics are used for convenience. In this paper, we prove under which conditions an MPC formulation is Input-to-State Stable~(ISS) in closed-loop when an infeasible reference is used, and that with proper terminal conditions, asymptotic stability towards an optimal reference may be achieved. We illustrate the theoretical results with a four-dimensional robotic joint example.