Two novel approaches of adaptive finite‐time sliding mode control for a class of single‐input multiple‐output uncertain nonlinear systems

Abstract

Some systems, in spite of having multiple outputs, have only one control input, which makes their control a challenge. Two novel controllers are proposed that utilise an adaptive finite-time sliding mode control (AFSMC) scheme for a class of single-input multiple-output (SIMO) nonlinear systems in the presence of unknown mismatched uncertainties. To alleviate the inherent chattering phenomenon of sliding mode control, new forms of the two designed controllers are suggested by using new sliding surfaces. Not only can the proposed AFSMC scheme stabilise the system in a finite time, but also it can provide estimated data of the uncertainty upper bound in the controller. Lyapunov stability theory is used to obtain finite-time stability analysis of the closed-loop system. Finally, simulation results are carried out in Simulink/MATLAB for a four-dimensional autonomous hyper-chaotic system with mismatched uncertainties as an example of SIMO uncertain nonlinear systems to reveal the effectiveness of the proposed controllers.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Finite-Time Synchronization Between Two Different Chaotic Systems by Adaptive Sliding Mode Control

“…Remark 3.2: It is worth mentioning that, by using the SMC controller scheme, an unwanted chattering phenomena may occur due to discontinuity of the control law, see [8] and references cited therein. There are several studies on how to alleviate this phenomenon of undesirable chattering, see [14]. In this work, we have focused mainly on a design of ANFTSM to achieve synchronization of two different chaotic systems in which an undesirable chattering phenomenon might still occur as can be seen from Figure 6.…”

“…Two novel controllers NTSMC and ANTSMC methods were designed in [13] for synchronization of smart grid chaotic systems which eliminate the undesirable chattering phenomenon in finite time. In [14], the authors have designed two novel controllers by using AFSMC methods to solve the chattering problem for a class of single-input multiple-out (SIMO) nonlinear systems with unknown mismatched uncertainties in finite time.…”

Adaptive Finite‐Time Sliding Mode Backstepping Controller for Double‐Integrator Systems with Mismatched Uncertainties and External Disturbances

“…Many practical high-order systems are modeled using nonlinear di erential equations due to the stochastic noise, uncertainties in the parameters, and variations in the external environment which are unknown beforehand and may occur in the real system [1]. is makes the control of these systems a challenge and as a result, di erent nonlinear control methods including the nonlinear stability theory [2], backstepping technique [3], Lyapunov function [4], and sliding mode control (SMC) [5][6][7][8] have come into existence.…”

An application of Newton-like algorithm for H∞ proportional–integral–derivative controller synthesis of seesaw-cart system

“…More specifically, the system considered in this paper has only one control variable. According to Alinaghi Hosseinabadi et al (2021), controller design for stabilising the system with only one control input in the presence of disturbance is important topic for the researchers in control of non-linear systems in recent years. Furthermore, although the theory of H ∞ control is well-known and can be considered standard, the synthesis of control law according to the H ∞ optimality criterion in combination with other also known methods is still an intensive area of research in various applications (see, for example, Coskun and Li, 2021; Rigatos et al, 2018 to name a few).…”