Intelligent control of chaos using linear feedback controller and neural network identifier

A method for controlling chaos when the mathematical model of the system is unknown is presented in this paper. The controller is designed by the pole placement algorithm which provides a linear feedback control method. For calculating the feedback gain, a neural network is used for identification of the system from which the Jacobian of the system in its fixed point can be approximated. The weights of the neural network are adjusted online by the gradient descent algorithm in which the difference between the system output and the network output is considered as the error to be decreased. The method is applied on both discrete-time and continuous-time systems. For continuous-time systems, equivalent discrete-time systems are constructed by using the Poincare map concept. Two discrete-time systems and one continuous-time system are tested as examples for simulation and the results show good functionality of the proposed method. It can be concluded that the chaos in systems with unknown dynamics may be eliminated by the presented intelligent control system based on pole placement and neural network.