Distributed optimization for a class of high‐order nonlinear multiagent systems with unknown dynamics

Abstract

Summary In this paper, we study a distributed optimization problem for a class of high‐order multiagent systems with unknown dynamics. In comparison with existing results for integrators or linear agents, we need to overcome the difficulties brought by the unknown nonlinearities and the optimization requirement. For this purpose, we employ an embedded control‐based design and first convert this problem into an output stabilization problem. Then, two kinds of adaptive controllers are given for these agents to drive their outputs to the global optimal solution under some mild conditions. Finally, we show that the estimated parameter vector converges to the true parameter vector under some well‐known persistence of excitation condition. The efficacy of these algorithms was verified by a simulation example.

Distributed Optimal Output Consensus of Uncertain Nonlinear Multi-Agent Systems over Unbalanced Directed Networks via Output Feedback

“…The DOOC problem of multi-agent systems with nonlinear agent dynamics in output feedback form over undirected networks is addressed in [13]. Later, the authors in [14] develop an adaptive controller to tackle the difficulty brought by unknown nonlinear agent dynamics though still over undirected networks. It is worth noting that the controller developed in [14] is based on a twolayer framework, which consists of an optimal coordinator generating the optimal solution and a decentralized output feedback controller driving each agent to track its individual optimal coordinator.…”

“…Later, the authors in [14] develop an adaptive controller to tackle the difficulty brought by unknown nonlinear agent dynamics though still over undirected networks. It is worth noting that the controller developed in [14] is based on a twolayer framework, which consists of an optimal coordinator generating the optimal solution and a decentralized output feedback controller driving each agent to track its individual optimal coordinator. Then, in our preliminary work [15], the two-layer framework is extended to solve the DOOC problem of disturbed second-order nonlinear systems but over unbalanced directed networks.…”

“…2) Unlike the works [6], [7], [13], [14], [16], [17] that study undirected or balanced directed graphs, this work considers more general and also more challenging weight-unbalanced directed networks. It is shown that the proposed controller is able to deal with the imbalance resulting from general directed networks and drive the agent outputs to the optimal solution.…”

Optimal Output Consensus for Nonlinear Multi-agent Systems with Both Static and Dynamic Uncertainties

“…Note that this optimal solution can only be determined and reached in a distributed way. Some interesting attempts have been made in [8]- [11] for integrator agents, [12] for linear agents, and [13], [14] for special classes of nonlinear agents. However, optimal output consensus for more general nonlinear multi-agent systems is still far from being solved, especially for agents being heterogeneous and subject to uncertainties.…”

Achieving optimal output consensus for discrete‐time linear multi‐agent systems with disturbance rejection

“…For a multi-agent system with general linear dynamics, the authors in [18] proposed an embedded control scheme to solve this kind of optimal coordination problems in a modular way. Some special classes of non-linear multiagent systems were also investigated in literature to achieve such an optimal consensus goal in [19,20]. However, in contrast with these papers for continuous-time high-order agents, there is still no general result to our best knowledge on achieving optimal consensus for discrete-time multi-agent systems with nonintegrator dynamics.…”