Multi-agent Optimal Consensus with Unknown Control Directions

TL;DR

This paper develops adaptive control algorithms for multi-agent systems with unknown control directions to achieve consensus at the optimal solution of a distributed optimization problem, even with only real-time gradient information.

Contribution

It introduces a novel adaptive control framework combining optimal signal generators and tracking controllers for heterogeneous high-order agents with unknown control directions.

Findings

Agents reach consensus on the optimal point.

Algorithms work with real-time gradient information.

Numerical examples confirm effectiveness.

Abstract

This paper studies an optimal consensus problem for a group of heterogeneous high-order agents with unknown control directions. Compared with existing consensus results, the consensus point is further required to an optimal solution to some distributed optimization problem. To solve this problem, we first augment each agent with an optimal signal generator to reproduce the global optimal point of the given distributed optimization problem, and then complete the global optimal consensus design by developing some adaptive tracking controllers for these augmented agents. Moreover, we present an extension when only real-time gradients are available. The trajectories of all agents in both cases are shown to be well-defined and achieve the expected consensus on the optimal point. Two numerical examples are given to verify the efficacy of our algorithms.