International Journal of Control, Vol.72, No.7-8, 727-739, 1999
A multi-model solution for the control of chaos
Chaotic behaviour has been identified in a wide range of dynamic systems, including those governing real processes. In many cases this chaotic behaviour is not required and a stable orbit is preferred. Many methods for controlling chaotic behaviour have been proposed, and it has been shown that very small control actions are sufficient to stabilize an unstable orbit embedded in phase space. The many successful methods so far proposed involve linear feedback control in a small region around the desired trajectory. However, in general, linear control laws have only small areas of validity. In order to reduce the time the system spends in an uncontrolled state, we propose a globally non-linear model which consists of many local linear models and control laws. These combine to stabilize the system around an embedded unstable fixed point. The parameters of these models and laws are determined by an on-line optimization procedure. Our method is tested on simulation of the Henon map and the double rotor system. The length of time for the system to converge (the chaotic transient) is compared with the time taken using the linear controller with minimal chaotic transient. The transient is shown to decrease significantly in the case of the Henon map, and to be about the same in the case of the double rotor. However, the optimal linear controllers required the exact system equations, whereas our controller was able to learn a hat it needed by experiment.
Keywords:SYSTEMS