Control Of A Modified Lorenz-stenflo System With Three Quadratic Terms

Chaos occupies an extremely important position in nonlinear scientific research.The Lorenz-Stenflo system is derived from an atmospheric model.By adding cross terms,an improved Lorenz-Stenflo chaotic system with three quadratic terms can be obtained.The generation of chaos often means the instability of the system structure leads to unpredictable or even catastrophic results.Therefore,setting a controlled system and selecting an appropriate control method to control chaos has great research value.In this paper,a modified Lorenz-Stenflo system with three quadratic terms is considered.Firstly,a single-input linear feedback control law is given.Based on the Hurwitz criterion and Hartman-Grobman theorem,the conditions for the asymptotic stability of the system are given,and the system is verified asymptoti-cally stable at the equilibrium.Secondly,the feedback linearization of the system is verified,and the conditions that the system input-state linearization meets and the single-input nonlinear feedback control law are given.Thirdly,chaos control of the system with uncertain parameters is discussed.Based on the Lyapunov sta-bility theory,an adaptive control law and parameter estimation update law are shown,and the asymptotic stability of the controlled system at the equilibrium point is proved.In addition,generalized function projective synchronization of the drive response system is studied,which is made up of two modified Lorenz-Stenflo hyperchaotic systems with uncertain parameters.The adaptive control law and parameter estimation update law are given to prove the stability of the generalized function projective synchronization.Numerical simulations show the effectiveness of the proposed control methods.