Stable MPC Design for Hybrid Mixed Logical Dynamical Systems: $l_{\infty}$-based Lyapunov Approach

TL;DR

This paper introduces an $l_{}$-based Lyapunov approach for designing stable Model Predictive Control for hybrid systems modeled as Mixed Logical Dynamical systems, improving stability guarantees and reducing computational complexity.

Contribution

It proposes exponential stability conditions using an infinity norm Lyapunov function that do not depend on the MPC prediction horizon, enhancing efficiency and simplicity.

Findings

The method guarantees exponential stability of MLD systems under MPC.

It reduces computational complexity compared to traditional terminal constraint methods.

Application to car suspension system demonstrates effectiveness.

Abstract

There are two main challenges in control of hybrid systems which are to guarantee the closed-loop stability and reduce computational complexity. In this paper, we propose the exponential stability conditions of hybrid systems which are described in the Mixed Logical Dynamical (MLD) form in closed-loop with Model Predictive Control (MPC). To do this, it is proposed to use the decreasing condition of infinity norm based Lyapunov function instead of imposing the terminal equality constraint in the MPC formulation of MLD system. The exponential stability conditions have a better performance from both implementation and computational points of view. In addition, the exponential stability conditions of the equilibrium point of the MLD system do not depend on the prediction horizon of MPC problem which is the main advantage of the proposed method. On the other hand, by using the decreasing condition of the Lyapunov function in the MPC setup, the suboptimal version of the control signal with reduced complexity is obtained. In order to show the capabilities of the proposed method, the stabilization problem of the car suspension system is studied.