Abstract
In this study, an adaptive nonsingular finite time control technique based on a barrier function terminal sliding mode controller is proposed for the robust stability of nth-order nonlinear dynamic systems with external disturbances. The barrier function adaptive terminal sliding mode control makes the convergence of tracking errors to a region near zero in the finite time. Moreover, the suggested method does not need the information of upper bounds of perturbations which are commonly applied to the sliding mode control procedure. The Lyapunov stability analysis proves that the errors converge to the determined region. Last of all, simulations and experimental results on a complex new chaotic system with a high Kaplan–Yorke dimension are provided to confirm the efficacy of the planned method. The results demonstrate that the suggested controller has a stronger tracking than the adaptive controller and the results are satisfactory with the application of the controller based on chaotic synchronization on the chaotic system.
Highlights
The research in the field of chaos control and synchronization often has shortcomings, such as considering simple models for the system, applying limiting assumptions to system dynamics, and not considering various uncertainties, including variable time indeterminacies [1,2,3,4]
An adaptive barrier function sliding mode control method with guaranteed performance based on output-feedback for nonlinear systems is proposed in [23], where the finite-time convergence of tracking errors to a neighborhood of origin with guaranteed performance is satisfied
For satisfying the convergence of switching function to origin in the finite time and eliminating the chattering problem, the nonsingular terminal sliding mode surface is proposed by θ = kps + ki t s(τ)q/rdτ + kds. , (5)
Summary
The research in the field of chaos control and synchronization often has shortcomings, such as considering simple models for the system, applying limiting assumptions to system dynamics, and not considering various uncertainties, including variable time indeterminacies [1,2,3,4]. An adaptive barrier function sliding mode control method with guaranteed performance based on output-feedback for nonlinear systems is proposed in [23], where the finite-time convergence of tracking errors to a neighborhood of origin with guaranteed performance is satisfied. To the best of the authors’ knowledge, none of the above-mentioned research works have considered the control/synchronization purpose of chaotic system by using the adaptive barrier function-based nonsingular finite time control technique. Consider the nth-order nonlinear system (1) with external disturbance, tracking errors (2), switching function (3), and nonsingular terminal sliding surface (5). The states of the nth-order nonlinear system (1) with external disturbance converge to the nonsingular terminal sliding surface in the finite time and stay on it thereafter. Consider the nth-order nonlinear system (1) with external disturbance, switching function (3) and nonsingular TSMC surface (5). The proposed control technique can be applied for the nonlinear systems with parametric uncertainties and external disturbances
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