Adaptive Control of Continuous-Time Systems by Chaotification

The generation of chaos by a linear system with nonlinear feedback has been extensively studied by many researchers. In this paper, we use a simple method to make an arbitrary nonlinear continuous-time system chaotic. For this, we apply a nonlinear time-delay feedback to the linearized system. Then we propose a model reference adaptive controller to control the resulted system in order to converge to a desired reference trajectory with uncertain parameters. An example is included to show the effectiveness of the method. Simulation results reveal that the controlled system tracks the reference system in spite of uncertain parameter.