Distributed Convex Optimization for Continuous-Time Dynamics with Time-Varying Cost Function

TL;DR

This paper develops distributed control algorithms for multi-agent systems with continuous-time dynamics to solve time-varying convex optimization problems, including collision avoidance, using both discontinuous and continuous approaches.

Contribution

It introduces novel discontinuous and continuous algorithms for distributed convex optimization in continuous-time multi-agent systems with dynamic cost functions.

Findings

Discontinuous algorithms based on signum function effectively solve the optimization problem.

Continuous algorithms with boundary layers provide smooth approximations of discontinuous control.

The methods incorporate collision avoidance for physical agents in a distributed setting.

Abstract

In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. Two discontinuous algorithms based on the signum function are proposed to solve the problem in each case. Then in the case of double-integrator dynamics, two continuous algorithms based on, respectively, a time-varying and a fixed boundary layer are proposed as continuous approximations of the signum function. Also, to account for inter-agent collision for physical agents, a distributed convex optimization problem with swarm tracking behavior is introduced for both single-integrator and double-integrator dynamics.