Model Predictive Control of Hybrid Dynamical Systems

TL;DR

This paper formulates a model predictive control approach for hybrid dynamical systems, providing stability conditions and structural analysis of the optimization problem.

Contribution

It introduces a hybrid MPC algorithm with stability guarantees based on control Lyapunov functions and analyzes its structural properties.

Findings

Provided sufficient conditions for asymptotic stability.

Developed a hybrid MPC algorithm inspired by hybrid time domains.

Illustrated results with examples.

Abstract

The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid equations, involving a differential equation and a difference equation with inputs and constraints. The proposed hybrid MPC algorithm uses a suitable prediction and control horizon construction inspired by hybrid time domains. Structural properties of the hybrid optimization problem, its feasible set, and its value function are provided. Checkable conditions to guarantee asymptotic stability of a set are provided. These conditions are given in terms of properties on the stage cost, terminal cost, and the existence of static state-feedback laws, related through a control Lyapunov function condition. Examples illustrate the results throughout the paper.