Practical Optimal Formation-Containment Tracking Control of Nonlinear Multiagent Systems With Unknown Dynamics

This article considers the practical optimal time-varying formation-containment tracking (FCT) issues of nonlinear multiagent systems (MASs) with unknown dynamics, where the quadratic regulator performance indicators related to errors and control inputs are defined for formation-leaders and followers. The optimal control inputs for minimizing performance indicators are normally obtained by solving the Hamilton–Jacobi–Bellman (HJB) equation. Nonetheless, the nonlinear MASs have nonlinear and coupling properties such that the analytical solution is hard to obtain by solving HJB equation. To address this difficulty, the neural networks are adopted to identify the unknown nonlinear dynamics, and an identifier is constructed to ensure the identification state errors converge asymptotically. Moreover, reinforcement learning with a critic–actor structure is employed to approximate the optimal performance indicators and optimal control inputs. Then, the practical optimal FCT control algorithm is presented to design the protocol parameters. The simulation results are shown to illustrate the effectiveness of the proposed theoretical method.