Adaptive finite-time control for stochastic nonlinear systems using multi-dimensional Taylor network

Abstract

In this paper, the problem of adaptive finite-time multi-dimensional Taylor network (MTN) control for a class of stochastic nonlinear systems is investigated. By combining the MTN-based approximate method and adaptive backstepping technique, a novel adaptive finite-time MTN control scheme is proposed. In this scheme, the MTNs are used to approximate the unknown nonlinear functions of the systems. The finite-time Lyapunov stability theory is utilized to prove the stability of the close-loop system. The proposed scheme can ensure that all signals in the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood of the origin in a finite time. Three simulation examples are presented to show the effectiveness of the control scheme. It should be pointed that the adaptive MTN controller proposed in this paper has the advantages of fast computational speed and good real-time performance thanks to the simple structure of the MTN.

Adaptive finite‐time control for a class of stochastic nonlinear systems with input saturation constraints: A new approach based on multidimensional Taylor network

“…[41][42][43][44][45][46][47] However, there are few results available on MTN-based adaptive finite-time control for stochastic nonlinear systems with input saturation constraints. 48 Recently, authors in References 16,46,49,50 proposed some adaptive MTN control approaches for stochastic nonlinear systems. Up to present, there are few research achievements about MTN-based finite-time tracking control for stochastic nonlinear systems with input saturation constraints.…”

“…It is worth noting that References 22–25 only paid attention to the convergence of systems in infinite time. Different from References 42,43,49, the issues of input saturation and FTC are considered in this article. Thus, we can draw the conclusion that the research in this article is more representative.…”

Hybrid neural network control design for uncertain switched nonlinear systems with external disturbances: Application to ship maneuvering system

“…In many situations, however, we are unable to obtain a priori knowledge of system uncertainty, which can only be described by completely unknown functions (Sakhre et al, 2017). The approximation ability of NNs or fuzzy logic systems has been investigated in the literature (Li et al, 2011;Singh and Jain, 2016;Yu et al, 2020;Zhu et al, 2022) to solve the control challenges for switched systems. As a result, a number of major results have been presented for uncertainties existing in nonlinear systems (Qi et al, 2018;Roy and Kar, 2016;Wang et al, 2018Wang et al, , 2019.…”

Delay-dependent H∞ dynamic observers for non-linear systems with multiple time-varying delays

“…Many theoretical results have been got since then, and they have been widely used in fault identification, control, fault estimation, and fault diagnosis. In the last decade, the observer model has been extended from linear to a non-linear one (Chu et al, 2021b; Islam et al, 2018b; Zhu et al, 2022). The proportional observer (PO), also called the Luenberger observer, is used in these studies.…”