Parametrized guaranteed cost method with prescribed performance via critic‐only ADP for uncertain nonlinear systems and disturbances

Abstract

In this paper, a novel parametrized guaranteed cost control (PGCC) method with prescribed performance control (PPC) is proposed for nonlinear systems with unknown bounded uncertainties and external disturbances described by Euler‐Lagrange (EL) equations. The proposed method is capable of ensuring a robust optimal performance in the presence of dynamics constraints without the specific information of nonlinear perturbation. As a consequence, the conditions in the form of disturbances and uncertainties are also relaxed. The augmented model is converted by transforming the uncertainties and disturbances in the original system to a mismatched term using asymmetric PPC. By designing and modifying the novel guaranteed cost function to account for the maximum value of the nonlinear perturbation, an infinite‐horizon PGCC problem is proposed by the unconstrained stationary optimal control problem. The relevant proposed linear parametrized Hamilton‐Jacobian‐Bellman (PHJB) equation is approximated to solve by a critic‐only neural network (NN) with efficient computationally. Uniformly ultimately bounded stability is guaranteed via a Lyapunov‐based stability analysis. Finally, numerical simulation results demonstrate the effectiveness of the proposed control scheme.