Indirect adaptive fuzzy-regulated optimal control for unknown continuous-time nonlinear systems

Abstract

We present a novel indirect adaptive fuzzy-regulated optimal control scheme for continuous-time nonlinear systems with unknown dynamics, mismatches, and disturbances. Initially, the Hamilton-Jacobi-Bellman (HJB) equation associated with its performance function is derived for the original nonlinear systems. Unlike existing adaptive dynamic programming (ADP) approaches, this scheme uses a special non-quadratic variable performance function as the reinforcement medium in the actor-critic architecture. An adaptive fuzzy-regulated critic structure is correspondingly constructed to configure the weighting matrix of the performance function for the purpose of approximating and balancing the HJB equation. A concurrent self-organizing learning technique is designed to adaptively update the critic weights. Based on this particular critic, an adaptive optimal feedback controller is developed as the actor with a new form of augmented Riccati equation to optimize the fuzzy-regulated variable performance function in real time. The result is an online indirect adaptive optimal control mechanism implemented as an actor-critic structure, which involves continuous-time adaptation of both the optimal cost and the optimal control policy. The convergence and closed-loop stability of the proposed system are proved and guaranteed. Simulation examples and comparisons show the effectiveness and advantages of the proposed method.

Keywords

Indirect adaptive optimal control / Hamilton-Jacobi-Bellman equation / Fuzzy-regulated critic / Adaptive optimal control actor / Actor-critic structure / Unknown nonlinear systems

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2021 Zhejiang University Press