Harmonic Control Lyapunov Barrier Functions for Constrained Optimal Control with Reach-Avoid Specifications

TL;DR

This paper proposes harmonic control Lyapunov barrier functions (harmonic CLBFs) that leverage harmonic functions' properties to improve constrained control, enabling initial deployment without training and ensuring safety in reach-avoid tasks.

Contribution

It introduces harmonic CLBFs that exploit harmonic functions' maximum principle for constrained control, allowing immediate application without trajectory-based training.

Findings

Harmonic CLBFs significantly reduce unsafe region entries.

They achieve high success rates in reaching goal regions.

Numerical results validate their effectiveness across systems.

Abstract

This paper introduces harmonic control Lyapunov barrier functions (harmonic CLBF) that aid in constrained control problems such as reach-avoid problems. Harmonic CLBFs exploit the maximum principle that harmonic functions satisfy to encode the properties of control Lyapunov barrier functions (CLBFs). As a result, they can be initiated at the start of an experiment rather than trained based on sample trajectories. The control inputs are selected to maximize the inner product of the system dynamics with the steepest descent direction of the harmonic CLBF. Numerical results are presented with four different systems under different reach-avoid environments. Harmonic CLBFs show a significantly low risk of entering unsafe regions and a high probability of entering the goal region.