Pragmatical adaptive chaos control from a new double van der Pol system to a new double Duffing system

A new pragmatical adaptive control method for different chaotic systems is proposed. Traditional chaos control is limited to decrease chaos of one chaotic system. This method enlarges the effective scope of chaos control. We can control a chaotic system, e.g. a new chaotic double van der Pol system, to a given chaotic or regular system, e.g. a new chaotic double Duffing system or to a damped simple harmonic system. By a pragmatical theorem of asymptotical stability based on an assumption of equal probability of initial point, an adaptive control law is derived such that it can be proved strictly that the common zero solution of error dynamics and of parameter dynamics is asymptotically stable. Numerical simulations are given to show the effectiveness of the proposed scheme.