| This thesis is a first step in analyzing model reference adaptive control of an unknown linear system preceded by an unknown hysteresis nonlinearity. The parameters of the hysteresis nonlinearity are adapted much slower than the parameters of the linear system, which are in turn adapted much slower than the plant dynamics. This approach allows the system to be considered under an averaging framework, where slower variables are viewed as constant with respect to faster variables. The problem statement is established and the first steps in analyzing the system are laid out. Challenges that arise in this problem beyond a classical averaging or singular perturbation problem are outlined. Simulation is used to not only show the effectiveness of the control method, but also to gain some additional insight into properties and behaviors of the closed-loop system. |
