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A Polynomial Adaptive Controller for Nonlinearly Parameterized Systems

This paper extends the conventional linear-in-parameter adaptive control theory to general nonlinearly parameterized (NLP) systems. We propose a polynomial adaptive controller (PAC) which deals with piece-wise linearly parameterized systems as powerful as the traditional adaptive controller for linearly parameterized ones. Since most of the commonly encountered NLP systems can be piece-wise linearly approximated over the unknown parameter region through local linearization, the PAC serves as a general tool for them. Stability of the PAC with bounded disturbance and approximation error is also established. Controllers for several typical classes of NLP systems are provided to demonstrate the applications of the PAC