Optimal Output Consensus of Second-Order Uncertain Nonlinear Systems on Weight-Unbalanced Directed Networks

TL;DR

This paper presents a novel distributed control scheme for second-order uncertain nonlinear multi-agent systems on weight-unbalanced directed networks, enabling agents to reach optimal output consensus without requiring global Lipschitz conditions or prior uncertainty knowledge.

Contribution

It introduces a two-layer control strategy combining a distributed optimal coordinator and a reference-tracking controller, handling unbalanced networks and nonlinear uncertainties adaptively.

Findings

Successfully achieves optimal output consensus in simulations.

Handles nonlinear uncertainties without global Lipschitz assumptions.

Does not require prior knowledge of uncertainties or disturbances.

Abstract

This paper investigates the distributed optimal output consensus problem of second-order uncertain nonlinear multi-agent systems over weight-unbalanced directed networks. Under the standard assumption that local cost functions are strongly convex with globally Lipschitz gradients, a novel distributed dynamic state feedback controller is developed such that the outputs of all the agents reach the optimal solution to minimize the global cost function which is the sum of all the local cost functions. The controller design is based on a two-layer strategy, where a distributed optimal coordinator and a reference-tracking controller are proposed to address the challenges arising from unbalanced directed networks and uncertain nonlinear functions respectively. A key feature of the proposed controller is that the nonlinear functions containing the uncertainties and disturbances are not required to be globally Lipschitz. Furthermore, by exploiting adaptive control technique, no prior knowledge of the uncertainties or disturbances is required either. Two simulation examples are finally provided to illustrate the effectiveness of the proposed control scheme.