Stability of Finite Receding Horizon Control: A Complementary Approach

TL;DR

This paper introduces a novel complementary stability analysis for finite receding horizon control, enabling stability guarantees even with zero or negative terminal costs, thus broadening practical MPC applications.

Contribution

It proposes a new augmented stage cost and a stability condition based on control Lyapunov functions, extending stability guarantees beyond traditional terminal cost methods.

Findings

Stability can be established with zero terminal cost.

The approach relaxes stability conditions for MPC.

It broadens the design space for stable MPC algorithms.

Abstract

This paper presents a complementary approach to establish stability of finite receding horizon control with a terminal cost. First a new augmented stage cost is defined by rotating the terminal cost. Then a one-step optimisation problem is defined based on this augmented stage cost. It is shown that a slightly modified Model Predictive Control (MPC) algorithm is stable if the value function of the augmented one-step cost (OSVF) is a control Lyapunov function. The proposed stability condition is completely complementary to the existing terminal cost based MPC stability conditions in the sense that they are mutually excluded with each other. By using this approach, we are able to establish stability for MPC algorithms with zero terminal cost or even negative terminal cost as special cases. Combining this new approach with the existing MPC stability theory, we are able to significantly relax the stability requirement on MPC and extend the design space where stability are guaranteed. The proposed approach will help to further reduce the gap between stability theory and practical applications of MPC and other optimisation based control methods.