Distributed Robust Continuous-Time Optimization Algorithms for Time-Varying Constrained Cost

TL;DR

This paper introduces a distributed continuous-time optimization method for multi-agent systems with time-varying costs and constraints, incorporating disturbance mitigation and ensuring asymptotic convergence to the optimal solution.

Contribution

It proposes a novel framework combining log-barrier functions and sliding mode control for robust, distributed optimization in dynamic environments.

Findings

Achieves zero tracking error in simulations.

Demonstrates convergence via Lyapunov and nonsmooth analysis.

Validates effectiveness through numerical experiments.

Abstract

This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances. By incorporating tools such as log-barrier penalty functions to address inequality constraints, an integral sliding mode control for disturbance mitigation is proposed. The algorithm ensures asymptotic tracking of the optimal solution, achieving a tracking error of zero. The convergence of the introduced algorithms is demonstrated through Lyapunov analysis and nonsmooth techniques. Furthermore, the framework's effectiveness is validated through numerical simulations considering two scenarios for the communication networks.