Critic-Only Learning Based Tracking Control for Uncertain Nonlinear Systems with Prescribed Performance

Abstract

A critic-only learning-based tracking control with prescribed performance was proposed for a class of uncertain nonlinear systems. Based on an estimator and an optimal controller, a novel controller was designed to make tracking errors uniformly ultimately bounded and limited in a prescribed region. First, an unknown system dynamic estimator was employed online to approximate the uncertainty with an invariant manifold. Subsequently, by running a novel cost function, an optimal controller was derived by online learning with a critic-only neural network, which ensured that tracking errors can evolve within a prescribed area while minimizing the cost function. Specifically, weight update can be driven by weight estimation error, avoiding introducing an actor-critic architecture with a complicated law. At last, the stability of a closed-loop system was analyzed by Lyapunov theorem, and tracking errors evolved within prescribed performance with the optimal controller. The effectiveness of the proposed control can be demonstrated by two examples.