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.

Keywords

• prescribed performance control
• tracking control
• adaptive dynamic programming