Tracking control for large‐scale switched nonlinear systems subject to asymmetric input saturation and output hysteresis: A new adaptive network‐based approach

Abstract

For large‐scale switched nonlinear systems subject to asymmetric input saturation and output hysteresis, an adaptive control strategy is put forward by using a novel neural network, that is, multi‐dimensional Taylor network (MTN), which can effectively cope with the output tracking problem of this system. Firstly, asymmetric input saturation is expressed as the combination of a linear function and a bounded error function. Then, the modified Bouc‐Wen hysteresis model is employed to solve the nonlinear problem caused by output hysteresis. Afterwards, based on the approximation ability of MTN, a novel adaptive decentralized control method is designed by combining Lyapunov stability theory with adaptive backstepping technology, which realizes the stability and boundedness of the controlled systems. It should be noted that the asymmetric input saturation, the output hysteresis, large‐scale nonlinear systems and switched nonlinear systems appear in the same framework for the first time. Finally, a practical example and a numerical example are given to verify the availability of the proposed control strategy.

Adaptive control for stochastic nonlinear systems with time‐varying delays via multidimensional Taylor network

“…Compared with the traditional neural network, MTN is essentially a weighted polynomial of network structure, featuring its convenient adjustment of network structure and good real‐time performance. Its better approximation ability than NN was verified via strict mathematical derivation 40,42,46‐48 …”

“…Its better approximation ability than NN was verified via strict mathematical derivation. 40,42,[46][47][48] The present study aims to develop a tractable scheme for effective tracking control of nonlinear discrete-time systems with stochastic disturbance and time-varying delays. An adaptive filter is designed to realize reliable state estimation under stochastic uncertainty.…”

Adaptive decentralized prescribed performance control for a class of large‐scale stochastic nonlinear systems subject to input saturation and full state constraints

“…A new MTN‐based decentralized PPC strategy is proposed via backstepping technique, whch can successfully obtain the ideal control performance under prescribed performance. Although many meaningful MTN‐based results have been proposed for large‐scale nonlinear systems, 13,20,42,43,45 the issues of PPC, input saturation and full state constraints were not considered simultaneously. Specifically, compared with the existing results without considering the effect of the input and state constraints in References 13 and 20 or the external interference in References 42, 43, and 45, this paper obtained results consider more actual situations. In order to overcome the difficulties in controller design brought by the input saturation, a Gaussian error function is employed, which can transform the nonlinear input saturation into a linear function with a bounded error.…”

“…Although many meaningful MTN‐based results have been proposed for large‐scale nonlinear systems, 13,20,42,43,45 the issues of PPC, input saturation and full state constraints were not considered simultaneously. Specifically, compared with the existing results without considering the effect of the input and state constraints in References 13 and 20 or the external interference in References 42, 43, and 45, this paper obtained results consider more actual situations. In order to overcome the difficulties in controller design brought by the input saturation, a Gaussian error function is employed, which can transform the nonlinear input saturation into a linear function with a bounded error. Besides, introducing a novel coordinate transformation, and combining the prescribed performance function and barrier Lyapunov function can ensure the tracking error converges to the predetermined allowable range, and ensure all states are not violating the given constraint bounds. Although input saturation and full state constraints are taken into account in stochastic nonlinear systems, 30,46‐48 this paper studies the PPC of large‐scale stochastic nonlinear systems, which is more significance in practice.…”

Adaptive tracking control for a class of stochastic nonlinear systems with input delay using multidimensional Taylor network

“…With this advantage, the MTN-based adaptive control scheme for stochastic nonlinear systems with unknown nonlinear functions, combined with the classical adaptive technique and backstepping method, has been designed and attracted wide attention [31,33,50,52]. At present, this control strategy has been widely used in nonlinear systems [53][54][55], stochastic systems [56][57][58], switching systems [59][60][61], and so on. However, like the above mentioned, there were few literatures on tracking control of stochastic nonlinear systems with input delay based on MTN, and most of them used Pade approximation to deal with the problem of input delay, while there is no scheme to compensate for the effect of input delay through auxiliary system, which promotes the research of this paper.…”