Near-Optimal Control Without Solving HJB Equations and Its Applications

In this paper, an adaptive near-optimal control law, which is inherently real time, is designed to tackle the contradiction between solution accuracy and solution speed for the optimal control of a general class of nonlinear systems with fully unknown parameters. The key technique in the proposed adaptive near-optimal control is to design an auxiliary system with the aid of the sliding mode control concept to reconstruct the dynamics of the controlled nonlinear system. Based on the sliding mode auxiliary system and approximation of the performance index, the proposed control law guarantees asymptotic stability of the closed system and asymptotic optimality of the performance index with time. Two illustrative examples and an application of the proposed method to a van der Pol oscillator are presented to validate the efficacy of the proposed adaptive near-optimal control. In addition, physical experiment results based on a dc motor are also presented to show the realizability, performance, and superiority of the proposed method.