Distributed Continuous-Time Optimization with Time-Varying Objective Functions and Inequality Constraints

TL;DR

This paper introduces a distributed continuous-time optimization algorithm capable of handling time-varying objectives and inequality constraints, ensuring convergence to a trajectory of optimal solutions using local information.

Contribution

It proposes a novel distributed control algorithm combining sliding-mode and Hessian-based methods for time-varying constrained optimization problems.

Findings

Algorithm converges asymptotically to the optimal solution trajectory.

Effective in handling nonlinear inequality constraints.

Validated through simulation example.

Abstract

This paper is devoted to the distributed continuous-time optimization problem with time-varying objective functions and time-varying nonlinear inequality constraints. Different from most studied distributed optimization problems with time-invariant objective functions and constraints, the optimal solution in this paper is time varying and forms a trajectory. To minimize the global time-varying objective function subject to time-varying local constraint functions using only local information and local interaction, we present a distributed control algorithm that consists of a sliding-mode part and a Hessian-based optimization part. The asymptotical convergence of the proposed algorithm to the optimal solution is studied under suitable assumptions. The effectiveness of the proposed scheme is demonstrated through a simulation example.