Adaptive near-optimal consensus of high-order nonlinear multi-agent systems with heterogeneity

In this paper, the near-optimal distributed consensus of high-order nonlinear multi-agent systems consisting of heterogeneous agents is investigated. The consensus problem is formulated as a receding-horizon optimal control problem. Under the condition that the dynamics of all agents are fully known, a nominal near-optimal protocol is designed and proposed via making approximation of the performance index. For the situation with fully unknown system parameters, sliding-mode auxiliary systems, which are independent for different agents, are built to reconstruct the input–output properties of agents. Based on the sliding-mode auxiliary systems, an adaptive near-optimal protocol is finally presented to control high-order nonlinear multi-agent systems with fully unknown parameters. Theoretical analysis shows that the proposed protocols can simultaneously guarantee the asymptotic optimality of the performance index and the asymptotic consensus of multi-agent systems. An illustrative example about a third-order nonlinear multi-agent system consisting of 10 heterogeneous agents with fully unknown parameters further substantiates the efficacy and superiority of the proposed adaptive near-optimal consensus approach.