Distnbuted Optimal Backstepping Composite Control for Multi-agent System with Output Constraints via Adaptive Dynamic Programming

This paper proposes a novel distributed optimal backstepping control method for a class of nonlinear multi-agent systems in strict-feedback form with output constraints. The virtual and actual controls can be locally optimized by designing their cost functions in every backstepping step. Furthermore, a unified barrier Lyapunov function (UBLF) is designed to prevent the outputs violating the constraints, which is still effective whether the constraints exist or not. By constructing a feedforward+feedback composite control framework, the recursive backstepping design has become to solve the coupled Hamilton-Jacobi-Bellman (HJB) equation in every step. Then, a critic network is built to obtain the approximated solution of HJB equation online through designing updating law of critic weight value. Theoretical analysis reveals that the consensus error is uniformly ultimately bounded (UUB) without violating output constraints. Numerical simulation results illustrate the effectiveness of proposed method.