Chattering-Free Terminal Sliding Mode Control Based on Adaptive Barrier Function for Chaotic Systems With Unknown Uncertainties

Abstract

This paper designs and implements a chattering-free terminal sliding mode control approach for a class of chaotic systems with unknown uncertainties. It considers sliding mode control (SMC) to deal with the dynamic model uncertainties of the chaos system, and uses a combination of SMC with an adaptive control approach to solve the upper boundaries problem of unknown model uncertainties and their estimation. Chattering is completely eliminated without over estimating the control gains by adopting an adaptive continuous barrier function in the dynamic switching function. Using the Lyapunov's stability theory, it was shown that the proposed scheme can guarantee the convergence of system states to the vicinity of the sliding surface in finite time. Additionally, the adoption of a sliding surface with a nonlinear and integral switching function resulted in removing the reaching phase of the sliding surface and yielding a controller that is robust to uncertainties from the start. The effectiveness of the proposed control method was assessed using three scenarios implemented to a Liu's uncertain chaotic system in MATLAB/Simulink environment. The obtained results confirmed the ability of the proposed approach to achieve continuous and smooth control rules for such chaotic systems. Among the main attributes of the proposed control method are its ability to completely eliminate chattering and yield a robust performance against model uncertainties and unknown external disturbances; common issues in chaotic systems.INDEX TERMS Terminal sliding mode control, chaotic systems, adaptive barrier function, chattering-free, unknown uncertainty.

Adaptive finite‐time optimal time‐varying formation control for second‐order stochastic nonlinear multiagent systems

“…To break through this limitation, the finite-time control theory has attracted wide attention due to its fast response performance, strong robustness, and high control accuracy. [30][31][32][33][34][35][36] Detailedly, a finite-time distributed adaptive consensus control problem was studied in Reference 36 for nonlinear MASs by using a funnel technique. Currently, the existing research results on finite-time problems of MASs have predominantly focused on consensus control, neglecting other important aspects.…”

“…The various control methods mentioned above can only guarantee that the variables in the system reach equilibrium points in infinite time. To break through this limitation, the finite‐time control theory has attracted wide attention due to its fast response performance, strong robustness, and high control accuracy 30–36 . Detailedly, a finite‐time distributed adaptive consensus control problem was studied in Reference 36 for nonlinear MASs by using a funnel technique.…”

Adaptive barrier function‐based fractional‐order chattering‐free finite‐time control for uncertain chaotic systems

“…In addition, by the combination of this adaptive technique‐based barrier function with a first‐order SMC, a class of first‐order disturbed systems is controlled [57]. A chattering‐free TSMC technique based on the adaptive barrier function for controlling chaotic systems in the presence of unknown uncertainties has been introduced in Sepestanaki et al [58], which is based on the Lyapunov stability theory and the adaptive control method; this method has demonstrated favorable outcomes in controlling chaos in this class of chaotic systems. By implementing the proposed method in the mentioned research, the convergence of the state variables in the chaotic system is guaranteed independent of the uncertainty ranges and keeps them in the around of the origin without high estimated the control gain.…”

Variable Structure Control of Second Order Systems With Nonlinear Uncertain Discontinuous Input Functions Using Approximate Inverses

“…T HE disturbance rejection property of sliding mode control of second order systems has already been widely emphasized in many publications and applications. Many of these previous works assume an affine relation between the control variable and the system acceleration [1]- [6].…”