Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

Abstract

In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed.Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed-loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods. K E Y W O R D Sinput delay, neural networks, nonlinear systems, saturation INTRODUCTIONIn recent years, adaptive control problem for nonlinear systems has attracted considerable attention and remarkable developments have been obtained in nonlinear control area. Among these results, adaptive control by using backstepping technique has received much attention because of its advantages over the conventional approaches (see References 1-5 and references therein). In addition, fuzzy logic systems and neural network have also be widely used in nonlinear control area due to their ability of approximating unknown nonlinear functions. 6-10 Although fruitful results have been obtained for nonlinear systems, there are still some challenging problems waiting to be solved. It is well known that control problem of input-delayed systems is one of the fundamental problems for time-delay systems because of its practical and theoretical significance. At present, many approaches have been proposed for system with state delay (see References 9-13). However, they all ignored the input delay. Compared with state delay, control problem of input delay is more complicated and the traditional Lyapunov-Krasovskii functional based methods are not effective to deal with the input delay. Therefore, it is noteworthy for us to investigate the systems with input delays. A basic idea in dealing with input delay is the predictor feedback. 14,15 However, traditional predictor-based methods have difficulties in practical implementation because of the distributed term. Therefore, to avoid the infinite-dimensionality of feedback laws, truncated predictor feedback was studied in References 16 to 20 to ignore the distributed term.Although fruitful results have been obtained for linear input-delay systems, the adaptive control problem for uncertain nonlinear system is still a challenging problem because nonlinear systems' states are not easy to be predicted with the existence of the nonlinearity and uncertainty. Considering this factor, some other methods need to be proposed to deal with the input delay. At present, there are a few results reported on uncertain nonlinear systems with input delay. 21-34 Specifically, Int J Robust Nonlinear Control. 2020;30:2593-2610.wileyonlinelibrary.com/journal/rnc

Observer‐based adaptive neural networks control for Markovian jump nonlinear systems with partial mode information and input saturation

“…Remark Assumption 1 is a standard assumption, which has been widely applied in the literature of adaptive control, such as the works 14,24,45,48 . Thus, it is a reasonable assumption.…”

“…Therefore, it is very important and meaningful to get a satisfactory control performance by using the defective control input. For instance, the authors 11,40–45 considered adaptive control problem under input saturation. However, sign function was involved in saturation functions in the works of Liu et al 11 and Jiang et al 41 and a sharp corner was formed, which thus is nondifferentiable at these points.…”

Anti‐disturbance adaptive sampled‐data observers for a class of nonlinear systems with unknown hysteresis

“…It should be known that unmatched disturbances exist inevitably in practical systems, with which the state of the whole system will be unstable 30,31 . In References 32‐35, because of superior adaptability and approximation, RBFNN and fuzzy logic systems were used to compensate and eliminate effectively the influence of the unmatched disturbances.…”

Command filter‐based event‐triggered adaptive neural network control for uncertain nonlinear time‐delay systems

“…However, it should be pointed out that the above research results required the functions in nonlinear systems were known or the unknown parameters appeared linearity. To relax these restrictions, the fuzzy logic systems or neural networks (NNs) could provide effective solutions 7‐16 . To mention a few, an adaptive tracking controller was designed in Reference 11 for stochastic nonstrict feedback nonlinear systems via fuzzy logic systems and adaptive backstepping design approach.…”

“…In view of the barrier Lyapunov function and NNs, a novel finite‐time tracking controller was constructed in Reference 14 for nonlinear systems. Recently, by using NNs and backstepping design, an adaptive neural control scheme was designed in Reference 16 for nonlinear systems with input delay and saturation.…”