A Hybrid Adaptive Inverse for Uncertain SISO Linear Plants with Full Relative Degree

We propose a hybrid adaptive feed-forward regulator for single-input single-output linear plants with full relative degree. The scheme includes an adaptive law that estimates the inverse of the plant and provides a feed-forward control calculated on the basis of the desired output and its derivatives. The adaptation is performed during discrete time events, called jumps, while the feed-forward action is continuous. This combination leads to a full hybrid system. The advantage of this framework is a conceptual separation between the adaptation dynamics, which is discrete, and the plant dynamics, which is continuous. Under an assumption of a persistence of excitation, we show through examples that the output asymptotically tracks the desired reference and that the estimate of the parameters of the inverse converges.