Adaptive tracking control for a class of uncertain nonlinear systems with infinite number of actuator failures using neural networks
Lv and Wang Advances in Difference Equations
Adaptive tracking control for a class of uncertain nonlinear systems with infinite number of actuator failures using neural networks
Wenshun Lv
Fang Wang
We consider adaptive compensation for infinite number of actuator failures in the tracking control of uncertain nonlinear systems. We construct an adaptive controller by combining the common Lyapunov function approach and the structural characteristic of neural networks. The proposed control strategy is feasible under the presupposition that the systems have a nonstrict-feedback structure. We prove that the states of the closed-loop system are bounded and the tracking error converges to a small neighborhood of the origin under the designed controllers, even though there are an infinite number of actuator failures. At last, the validity of the proposed control scheme is demonstrated by two examples.
nonlinear systems; actuator failures; adaptive control; backstepping; neural networks; nonstrict feedback
1 Introduction
In recent years, many approximation-based adaptive fuzzy or neural backstepping
controllers have been developed for uncertain nonlinear systems; see [–]. Among them, to
eliminate the problem of ‘explosion of complexity’ inherent in the existing method, in []
a control design strategy was developed for a class of nonlinear systems in strict-feedback
form with arbitrary uncertainty. To deal with the state unmeasured problem, a novel
control scheme was introduced in []. To address the control problem of nonsmooth
hysteresis nonlinearity in the actuator, adaptive neural controllers were constructed for nonlinear
strict-feedback systems with unknown hysteresis in []. It should be noted that the
control schemes mentioned are under the presupposition that the systems have a
nonstrictfeedback structure.
In the nonlinear systems without strict-feedback structure, the unknown nonlinear
functions involve all the state variables, so they cannot be approximated with current
states. To deal with such a structural restriction, in [] a variable separation method was
proposed. The control scheme in [] assured that the tracking performance is achieved
as time variable goes to infinity. Besides the proposed control scheme, many efforts have
been made in relaxing such a restriction of system structure; see [–]. In practical
application, the actuator component is usually employed to execute control actions on the
plant. However, the actuation mechanism may suffer from failures, which results in the
actuator losses of partial or total effectiveness. To prevent the emergence of performance
deterioration and instability of the closed-loop system caused by actuator faults,
accommodating actuator failures should be taken into account in the control design.
In recent years, many control schemes have been proposed to accommodate actuator
failures; see, for example, [–]. By applying backstepping technique for the linear
systems, a systematic actuator failure compensation control was presented in []. Then, in
[] the proposed control method was extended to nonlinear systems with actuator
failures; in [] the problem of accommodating actuator failures was investigated for a lass
of uncertain nonlinear systems with hysteresis input as a follow-up extension. In practice,
the failure pattern in an actuator may change repeatedly, which makes failure parameters
suffer from an infinite number of jumps. Consequently, the considered Lyapunov function
would experience infinite number of jumps. In [], this problem was addressed by
applying a new tuning function under the frame of adaptive control. However, the proposed
control strategy can only apply to the strict-feedback systems.
Motivated by the aforementioned researches, in this paper, we focus on the problem
of adaptive compensation for an infinite number of actuator failures in neural tracking
control for a class of nonstrict-feedback systems. The main contributions in this paper
can be summarized as follows.
() The control scheme in this paper relaxes the restriction of system structure so that a
better approach is proposed to deal with the problem of compensation for an
infinite number of actuator failures, which is more meaningful in practical
application in comparison with [].
() In this paper, combining neural networks and a new piecewise Lyapunov function
analysis, we establish an adaptive control scheme for a class of uncertain nonlinear
systems with a nonstrict-feedback structure.
The remainder of the paper is organized as follows. In the next section, the problem
description and preliminaries are presented. Section shows the major result. In Section ,
the simulation result expounds the validity of the proposed control scheme. Finally, we
give a simple summary.
2 Preliminaries and problem description
2.1 A. System description
We consider the following nonstrict-feedback system form:
x˙i = xi+ + fi(x), ≤ i ≤ n – ,
m
x˙n =
bjσ (...truncated)