Practically adaptive output tracking control of inherently nonlinear systems preceded by unknown hysteresis

Control of nonlinear systems preceded by unknown hysteresis nonlinearities is usually difficult and challenging due to the nonsmooth and memory characteristics of hysteresis. Focusing on a class of inherently nonlinear systems and with use of available mathematical models of hysteresis nonlinearities, this paper addresses the challenge on how to fuse available hysteresis models with those results for the inherently nonlinear systems to achieve practically adaptive output tracking control. We will show such a possibility by combining the recently developed framework of immersion and invariance (I&I) tools, adding a power integrator technique, and Prandtl-Ishlinshii hysteresis model. The proposed approach has the following two features. First, in order to mitigate the effects of the unknown hysteresis, the proposed approach does not necessarily need to construct a hysteresis inverse; secondly, the adaptive mechanism does not have to satisfy the certainty equivalence principle. It is shown that the developed controller ensures all signals of closed-loop systems are bounded while practically keeping the output tracking error to an arbitrary small neighborhood of the origin.