Stochastic control techniques applied to chaotic nonlinear systems

Chaotic nonlinear systems exhibit behavior similar in many respects to noise-corrupted systems. The use of stochastic control techniques, in particular a state estimator based on the Kalman filter, enables implementation of a control algorithm for control of these systems whose performance is improved with respect to that obtainable by use of a controller utilizing only the conditional mean of the system state vector. The method is applied to two typical chaotic nonlinear systems, and their behavior with control is explored numerically. It is shown that chaotic nonlinear systems appear to retain their chaotic dynamics when control signals are applied