A continuous-time violation-free multi-agent optimization algorithm and its applications to safe distributed control

TL;DR

This paper introduces a continuous-time distributed optimization algorithm that guarantees zero constraint violation and is applicable to safe multi-agent control with control barrier functions, demonstrating efficiency in numerical experiments.

Contribution

It presents a novel continuous-time algorithm ensuring violation-free optimization with applications to safe distributed control, including a finite-time convergence law for CBF-induced QPs.

Findings

Algorithm guarantees zero violation of coupling constraints.

Efficient in sparse coupling scenarios with reduced memory and communication.

Achieves finite-time convergence in CBF-induced quadratic programs.

Abstract

In this work, we propose a continuous-time distributed optimization algorithm with guaranteed zero coupling constraint violation and apply it to safe distributed control in the presence of multiple control barrier functions (CBF). The optimization problem is defined over a network that collectively minimizes a separable cost function with coupled linear constraints. An equivalent optimization problem with auxiliary decision variables and a decoupling structure is proposed. A sensitivity analysis demonstrates that the subgradient information can be computed using local information. This then leads to a subgradient algorithm for updating the auxiliary variables. A case with sparse coupling constraints is further considered, and it is shown to have better memory and communication efficiency. For the specific case of a CBF-induced time-varying quadratic program (QP), an update law is proposed that achieves finite-time convergence. Numerical results involving a static resource allocation problem and a safe coordination problem for a multi-agent system demonstrate the efficiency and effectiveness of our proposed algorithms.