Optimal multi-dimensional OGY controller

A technique which generalizes the standard OGY control scheme and may be applied to higher dimensional systems to stabilize both saddle nodes and fully unstable fixed points is presented. The proposed method is designed for nonlinear flows rather than maps and also provides a powerful technique to assess the controllability of nonlinear systems with OGY type controllers. An optimal OGY control scheme designed for larger dimensional systems having improved convergence properties compared to the standard OGY controller is also presented. Numerical examples for the well known Van der Pol–Duffing oscillator are presented to illustrate the proposed control schemes.