Adaptive Control and Synchronization of Sprott J System With Estimation Of Fully Unknown Parameters

Abstract

Abstract. This communication develops an adaptive scheme for control and synchronization of Sprott J system with fully unknown parameters. The scheme provides an elegant strategy of designing estimators for identification of the unknown parameters of the underlying dynamical system. Adaptive control and update laws are proposed to globally stabilize the chaotic Sprott J system. A pair of identical Sprott J systems with unknown parameters are globally synchronized with the help of adaptive control and parameter update laws. The results are established using LaSalle invariance principle, which lays down weaker restrictions on the derivatives of the Lyapunov function, and producing more general results. All the results obtained in the paper are global in nature. Numerical simulations are performed to illustrate the validity and effectiveness of the proposed adaptive control and synchronization scheme in the context of the Sprott J system. The parameter identification capability of the scheme is also explored.

Simple finite-time sliding mode control approach for jerk systems

“…3 With these values, the fundamental frequency obtained is f = 10 4 =2p, and then the dimensionless time is t = 2pf 3 t d . Figures 2 and 3 present the numerical results of equation (5) obtained with the controller in equation (8), using the values presented in Table 1 and considering equations (2a)-(2g), respectively. These figures show that the fast finite-time convergence is achieved for each error system and display their corresponding magnified images.…”

“…These results improve those of Xu 12 where with two different systems only the asymptotic convergence could be obtained. Figure 6 presents the numerical results of equation (5) obtained with the controller of equation (8), the values in Table 2 and the response systems (2a)-(2d) of equation (2). Figure 8 presents the numerical results of equation (5) obtained using the controller of equation (8a), the values of Table 1 and systems (2f) and (2e) corresponding to the drive and response systems, respectively.…”

“…A common feature in this literature is that the convergence is achieved with two systems of equations using various control methods with kernel being based on the system state variables as usually applied on nonlinear circuits. 2,[8][9][10][11][12][13][14][15][16][17] However, with this approach the control error is not accurate enough because it is subject to either chattering phenomenon or the closeness to initial conditions. This led scientists to develop new approaches.…”