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Minimal control synthesis adaptive control of nonlinear systems: utilizing the properties of chaos

This paper discusses a novel approach to the control of chaos based on the use of the adaptive minimal control synthesis algorithm. The strategies presented are based on the explicit exploitation of different properties of chaotic systems including the boundedness of the chaotic attractors and their topological transitivity (or ergodicity). It is shown that chaos can be exploited to synthesize more efficient control techniques for nonlinear systems. For instance, by using the ergodicity of the chaotic trajectory, we show that a local adaptive control strategy can be used to synthesize a global controller. An application is to the swing-up control of a double inverted pendulum.