BACKSTEPPING CONTROL AND SYNCHRONIZATION OF PARAMETRICALLY AND EXTERNALLY EXCITED Φ⁶ VAN DER POL OSCILLATORS WITH APPLICATION TO SECURE COMMUNICATIONS

In this paper recursive and adaptive backstepping nonlinear controllers are designed to, respectively, control and synchronize the triple-well or Φ⁶ Van der Pol oscillators (VDPOs) with both parametric and external excitations. The designed recursive backstepping nonlinear controller is capable of stabilizing the Φ⁶-VDPO at any position as well as controlling it to track any trajectory that is a smooth function of time. The designed adaptive backstepping nonlinear controller globally synchronizes two Φ⁶-VDPOs evolving from different initial conditions and its application to secure communications is computationally demonstrated. The results are all validated by numerical simulations.