Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients

Abstract

Abstract-In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop. In addition, the output of the system is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

An adaptive extended fuzzy function state-observer based control with unknown control direction

“…Lemma 1 [23] Let smooth functions V(t), ζ(t) are defined on [0, t f ) with V(t) > 0, ∀ t ∈ [0, t f ), and N(ζ) be an even, smooth and Nussbaum-type function. If the following inequality holds:…”

Adaptive neural control for uncertain nonlinear systems in pure-feedback form with hysteresis input

“…Lemma 1: [14] Let V (·), ζ(·) be smooth functions defined on [0, t f ) with V (t) ≥ 0, ∀t ∈ [0, t f ), and N (·) be an even smooth Nussbaum-type function. If the following inequality holds:…”

An Adaptive Fuzzy Neural Network Based on Self-Organizing Map (SOM)

“…Besides, there are other growing strategies for constructing the RBF neural network (Liying Ma & K. Khorasani, 2005;R. Sentiono, 2001; S. S. Ge, F. Hong, & T. H. Lee, 2003). Based on the GCS and GH-SOM a new Adaptive Growing Self-Organizing Fuzzy Neural Network (SFNN) will be introduced in the following sections.…”