Adaptive Artificial Neural Network-Based Control Through Attracting-Manifold Design and Lipschitz Constant Projection

Abstract

Abstract This article presents an adaptive artificial neural network-based control scheme that strategically integrates the attracting-manifold design and a smooth Lipschitz-constant projection operator. The essence of the scheme is elaborated through the design of the reference-command-tracking control law of an nth-order single-input uncertain nonlinear system that can be transformed into the Brunovsky form. The method offers two major advantages: First, by employing the attracting-manifold design, it is possible to achieve asymptotic recovery of the ideal (deterministic) closed-loop dynamics. In other words, the perturbation caused by parametric uncertainties will be driven to zero asymptotically as a result of such a design, fostering a superior control performance. Second, the established smooth projection operator ensures the Lipschitz constant of the adaptive artificial neural network is bounded from above, thereby providing a certain degree of robustness against adversarial perturbations. The proposed method is validated through a numerical simulation example and compared with a standard certainty-equivalent neural-adaptive control method to demonstrate its superior performance.