Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Abstract

This paper focuses on the adaptive neural output feedback control of a class of uncertain multi-input-multioutput nonlinear time-delay non-integer-order systems with unmeasured states, unknown control direction, and unknown asymmetric saturation actuator. Thus, the mean value theorem and a Gaussian error function-based continuous differentiable model are used in the paper to describe the unknown asymmetric saturation actuator and to get an affine model in which the control input appears in a linear fashion, respectively. The design of the controller follows a number of steps. Firstly, based on the semigroup property of fractional-order derivative, the system is transformed into a normalized fractional-order system by means of a state transformation in order to facilitate the control design. Then, a simple linear state observer is constructed to estimate the unmeasured states of the transformed system. A neural network is incorporated to approximate the unknown nonlinear functions while a Nussbaum function is used to deal with the unknown control direction. In addition, the strictly positive real condition, the Razumikhin Lemma, the frequency-distributed model, and the Lyapunov method are utilized to derive the parameter adaptive laws and to perform the stability proof. The main advantages of this work are that:(1) it can handle systems with constant, time-varying, and distributed time-varying delays, (2) the considered class of systems is relatively large, (3) the number of adjustable parameters is reduced, (4) the tracking errors converge asymptotically to zero and all signals of the closed-loop system are bounded. Finally, some simulation examples are provided to demonstrate the validity and effectiveness of the proposed scheme.

Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

“…where ψ i (x) is generally called "fuzzy basis function" (FBF), (Benzaoui et al 2016;Hamel, Boulkroune, and Bouzeriba 2016;Wang 1994;Zouari et al 2017). This compact expression (17) is widely used in the open fuzzy control literature (Benzaoui et al 2016;Hamel, Boulkroune, and Bouzeriba 2016;Wang 1994;Zouari et al 2017). It ought to be noted that the FBFs, ψ i , should be correctly determined a priori.…”

“…Over a compact set y , the unknown smooth functionh i (y) can be modeled by the linearly parameterized fuzzy systems (17) as follows (Benzaoui et al 2016;Hamel, Boulkroune, and Bouzeriba 2016;Wang 1994;Zouari et al 2017):…”

A novel neural network discrete‐time optimal control design for nonlinear time‐delay systems using adaptive critic designs

“…For solving the time‐delay control problems for DT systems, several important nonlinear optimal control strategies were proposed in References , and by using the neural approximation and dynamic programming algorithm. In Reference , by applying the DSC algorithm, observer‐based adaptive NN‐based control approach was proposed for unknown time‐delay nonlinear stochastic systems, wherein the RBFNNs were used to approach the desired control laws instead of unknown system functions.…”

“…In Reference , by applying the DSC algorithm, observer‐based adaptive NN‐based control approach was proposed for unknown time‐delay nonlinear stochastic systems, wherein the RBFNNs were used to approach the desired control laws instead of unknown system functions. In Reference , an adaptive NN‐based input‐constraint nonlinear control strategy was developed for time‐delay systems with unknown control direction and unmeasured states. In these methods, according to gradient descent algorithm, the estimations of the weights for NNs were trained to minimize the designed performance error indexes.…”

Output feedback fault-tolerant control for a class of nonlinear systems via dynamic gain and neural network

“…Neural networks are widely used in the adaptive control of various nonlinear systems [10]. Compensation to the nonlinear functions is achieved through adaptive weight which further solves the control problem [11].…”