Nonlinear Control of Hyperchaotic System, Lie Derivative, and State Space Linearization

State space linearization using the concept of Brunovsky form and Lie derivative is applied to the case of a Hyperchaotic Lorentz System. It is observed that the necessary and sufficient conditions can be satisfied, the analytic form of the controller ‘u’ and the final form of the linearized equations can be obtained. Numerical simulation is used to ascertain the feasibility of the procedure in practice. It may be added that the case of an ordinary Lorentz equation is distinctively different as the controller is to be added in a different manner. The most important aspect of the present analysis is that the controller can be determined and not chosen ad hoc.