An open plus nonlinear closed loop control of chaotic oscillators

An open plus nonlinear closed loop control law is presented for chaotic oscillations described by a set of non-autonomous second-order ordinary differential equations. It is proven that the basins of entrainment are global when the right-hand sides of the equations are given by arbitrary polynomial functions. The forced Duffing oscillator and the forced van der Pol oscillator are treated as numerical examples to demonstrate the applications of the method.