Optimal Tracking Control for Uncertain Nonlinear Systems With Prescribed Performance via Critic-Only ADP

This article addresses the tracking control problem for a class of nonlinear systems described by Euler–Lagrange equations with uncertain system parameters. The proposed control scheme is capable of guaranteeing prescribed performance from two aspects: 1) a special parameter estimator with prescribed-performance properties is embedded in the control scheme. The estimator not only ensures the exponential convergence of the estimation errors under relaxed excitation conditions but also can restrict all estimates to predetermined bounds during the whole estimation process and 2) the proposed controller can strictly guarantee the user-defined performance specifications on tracking errors, including convergence rate, maximum overshoot, and residual set. More importantly, it has the optimizing ability for the tradeoff between performance and control cost. A state transformation method is employed to transform the constrained optimal tracking control problem to an unconstrained stationary optimal problem. Then, a critic-only adaptive dynamic programming algorithm is designed to approximate the solution of the Hamilton–Jacobi–Bellman equation and the corresponding optimal control policy. Uniformly ultimately bounded stability is guaranteed via a Lyapunov-based stability analysis. Finally, numerical simulation results demonstrate the effectiveness of the proposed control scheme.