Distributed Optimization for a Class of High-order Nonlinear Multi-agent Systems with Unknown Dynamics

In this paper, we study a distributed optimization problem for a class of high-order multi-agent 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 also 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.