CLF-Based Control for Hybrid Dynamical Systems

TL;DR

This paper introduces a control method for hybrid dynamical systems using pointwise minimum norm control laws based on control Lyapunov functions, applicable to systems with continuous flows and discrete jumps.

Contribution

It proposes a novel control law framework for hybrid systems that ensures stability by selecting minimal norm inputs to decrease a Lyapunov function.

Findings

Control laws guarantee decrease of Lyapunov function during flows and jumps.

Applicable to systems with individual or common inputs in different modes.

Examples demonstrate effectiveness of the proposed control approach.

Abstract

Pointwise minimum norm control laws for hybrid dynamical systems are proposed. Hybrid systems are given by differential equations capturing the continuous dynamics or flows, and by difference equations capturing the discrete dynamics or jumps. The proposed control laws are defined as the pointwise minimum norm selection from the set of inputs guaranteeing a decrease of a control Lyapunov function. The cases of individual and common inputs during flows and jumps, as well as when inputs enter through one of the system dynamics, are considered. Examples illustrate the results.