Control Of A Chaotic Chemical Reaction Model

The rate equation of the autocatalytic chemical reaction system is essentially nonlinear and the nonlinearity can lead to the spontaneous generation of chaos.The control of chaotic chemical systems poses a new challenge in mathematics,chemistry and physics,and it attracts lots of attention in these fields.In this paper,we study a class of chaotic chemical reaction model,Minimal-Willamowski-Rossler system.First,the equilibria point of MWR system with un-known parameters are calculated,and the stability of the equilibria is discussed based on Hartman-Grobman theorem.Second,the existence of an optimal control law is given by the pontryagin minimum principle,which drive the controlled sys-tem to special equilibrium in finite time interval.Third,an adaptive control law and updated parameter law are proposed to control the MWR system with un-known parameters to special equilibrium,and Lyapunov stability theorem is used to prove the asymptotical stability of the controlled system.Finally,the adaptive control law and updated parameter law are presented based on Lyapunov stabili-ty theorem and adaptive control principle,which drive two chaotic MWR systems with unknown parameters to achieve generalized function projection synchroniza-tion(GFPS).The validity of the control and synchronization results is verified by numerical simulations.