Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

Abstract

This article presents an adaptive sliding mode control (SMC) scheme for the stabilization problem of uncertain time-delay chaotic systems with input dead-zone nonlinearity. The algorithm is based on SMC, adaptive control, and linear matrix inequality technique. Using Lyapunov stability theorem, the proposed control scheme guarantees the stability of overall closed-loop uncertain time-delay chaotic system with input dead-zone nonlinearity. It is shown that the state trajectories converge to zero asymptotically in the presence of input dead-zone nonlinearity, time-delays, nonlinear real-valued functions, parameter uncertainties, and external disturbances simultaneously. The selection of sliding surface and the design of control law are two important issues, which have been addressed. Moreover, the knowledge of upper bound of uncertainties is not required. The reaching phase and chattering phenomenon are eliminated. Simulation results demonstrate the effectiveness and robustness of the proposed scheme.

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

“…A chaotic system is an extremely complex nonlinear dynamical system [1][2][3][4]. The important characteristic of chaotic systems is their high sensitivity to initial conditions and parametric uncertainties [5][6][7][8].…”

Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity

“…Multiplying both sides of (37) by (s 2 (t)) 2 ≥ 0, it yields s 2 (t) (u(t)) ≤ −(σ 2 +η 2 ) s 2 (t) (38) Using (26), (29), (32), (33), and (38), it yieldṡ…”

“…Since chaos control problem was firstly considered by [6], the stabilization of chaotic systems has been paid much attention and various control strategies have been applied to realize chaos control and synchronization such as adaptive control [7][8][9][10][11][12][13][14][15], sliding mode control [2,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], fuzzy control [31,32], linear feedback control [33,34], polynomial approach [35] and harmonic approach [36][37][38][39]. In addition, several design methods [40][41][42][43][44][45] for the stabilization of systems with uncertainties have been investigated.…”

A Novel Approach to Numerical Modeling of Metabolic System: Investigation of Chaotic Behavior in Diabetes Mellitus

“…As ρ i and η i are positive for i = x, y, z, the Lyapunov first derivative (15) is a negative definite function which infers that the controller is stable as per the theorem discussed in [39,40] and is valid for any bounded initial conditions. For numerical simulations, the initial conditions are taken as 2.6, 1, and 0.825 and the sliding surface initial conditions are defined as −2.6, −1, and −0.825 with the time delays Figure 6 shows the estimated parameters with parameter update laws and controllers in action at t = 0 s.…”