Control of chaotic systems using an on-line trained linear neural controller

We propose a control system including an on-line trained linear neural controller to control chaotic systems. The control system stabilizes a chaotic orbit onto an unstable fixed point without using the knowledge of the location of the point and the local linearized dynamics at the point. Furthermore, the control system can track the stabilized orbit to the unstable fixed point whose location and local dynamics vary slowly with a variation of the system parameter. This paper extends a previous paper (Konishi and Kokame, 1995) for more general situations and improves the neural controller proposed in the previous paper both to simplify the training algorithm and to guarantee the convergence of the neural controller. The stability analysis of the control system reveals that some unstable fixed points cannot be stabilized in the control system. Numerical experiments show that the control system works well for controlling high-dimensional chaotic systems.