Adaptive fuzzy backstepping control for uncertain nonlinear systems with tracking error constraints

Abstract

This article deals with the design of adaptive fuzzy backstepping control for uncertain nonlinear systems in strictfeedback form with tracking error constraints. In this article, a fuzzy system is used to approximate the unknown nonlinear functions and the differential of virtual control law of each subsystem. In order to satisfy the limitation of tracking error constraints, the barrier Lyapunov function is introduced. Moreover, by applying the minimal learning parameters technique, the number of online parameters update for each subsystem is reduced to only 1. The control scheme not only ensures the tracking error is not to transgress the constraint bounds but also solves the problem of ''explosion of complexity'' and greatly reduces the initial control input and the number of the adaptive parameters; this provides the conditions for the practical application. The simulation results show the effectiveness of the proposed method.

Adaptive output feedback control for a class of uncertain non-strict feedback systems with asymmetric time-varying output constraints

“…To further illustrate the contributions of this method, some comparisons with previous results in refs 10,11,18–25,28–32 will be given in this section.…”

“…(3) The constraint considered in refs 18–24 is a symmetric static constraint rather than the asymmetric time-varying constraint discussed in this paper. The control method in refs 21,29–32 can deal with only stable control because it is based on the linear observer (61):…”

“…To solve the problem of these constraints, many studies have used the barrier Lyapunov function (BLF). 18–24 In refs, 18,23 by using BLFs the authors designed an adaptive control method for a class of stochastic nonlinear systems with state constraints. On the basis of neural networks and the BLF, 19,22 proposed an adaptive control for nonlinear constrained systems with an input delay and an input deadzone.…”

“…21 investigated an adaptive fuzzy output feedback control problem for a class of non-strict feedback time delay systems subject to a constraint problem. However, the constraints considered in refs 18–24 are symmetric static constraints, whereas most of the constraints in practical engineering are asymmetric time-varying constraints.…”

Adaptive Dynamic Surface Control Based on Observer for Switched Non-Strict Feedback Systems With Full State Constraints

“…, with ∀t ≥ 0. Assumption 3 [25], [36]: There exist functionsȲ 0 : R + → R + and Y 0 : R + → R + satisfyingȲ 0 <k c1 (t) and Y 0 > k c1 (t), with ∀t > 0, and a positive constant Y 1 such that the desired trajectory y d (t) and its time derivative satisfy Y 0 (t) ≤ y d (t) ≤Ȳ 0 (t) and |ẏ(t)| ≤ Y 1 , with ∀t > 0.…”