Adaptive tracking control of the Chen system

Abstract

The tracking control of chaotic Chen system is realized using a nonlinear single-input controller. According to the structure characteristic of the Chen system, proper feedback form is selected and an adaptive single-input controller is designed, which makes the Chen system track a certain variable of the Rossler system with unknown parameters. The Lyapunov direct method is applied to prove that the error signal asymptotically approaches zero. Numerical simulations show that the proposed control method is feasible, and the identification of unknown parameters can be realized.

Interface evolution of a particle in a supersaturated solution affected by a far-field uniform flow

“…The pattern formations of the spherical particle under different farfield uniform flows obey the same mechanism as those in the convective pure melt and alloy. [16][17][18][19][20]…”

“…[7] Though various experimental observations and numerical simulations explicitly suggest the significant effect of the convection on the interface microstructure formation, theoretical investigations of the morphological evolution of interface during crystallization in the stirred melt and solution are still very limited due to the complicated effects of convection. [2,[8][9][10][11][12][13][14][15][16][17] Hence, there is a strong need for the common analytical method to predict the experimentally observed particle morphologies developed under different flow conditions. A feasible way is to model the growth of spherical particles in the complex flow of the stirred liquid as a singularly perturbed free boundary problem and find its asymptotic solution by using the matched asymptotic expansion method.…”