In this paper a new RISE controller is gained to control chaos in a tracking task. The technique copes with the chattering phenomenon whilst works for different classes of nonlinear systems incorporating different relative degrees. This control strategy will be primarily implemented on a Duffing chaotic system. In order to assess performance of the controller, the technique will be implemented on a more complex system, so called Genesio-Tesi dynamic. The result will be finally compared with an optimal controller. The capability of the proposed feedback technique to control the chaos is verified through simulation study with respect to similar classic approaches.

Chaos control is an important subject in control theory. Chaos control usually confronts with some problems due to unavailability of states or losing the system characteristics during the modeling process. In this situation, using an appropriate observer in control strategy may overcome the problem. In this paper, states are estimated using an observer without having complete prior information from nonlinear term based on neural network. Simulation results verify performance of the proposed structure in estimating nonlinear term specifically for an online practical use.