Indirect adaptive nonlinear control of discrete-time systems containing a deadzone

In this paper, we develop an indirect adaptive output feedback control result which applies to discrete-time systems containing a deadzone nonlinearity and linear dynamics. The deadzone nonlinearity is significant since it is common in systems containing hydraulic or pneumatic valves, electronic circuits, and temperature regulation circuits. A plant parametrization that is linear in a set of unknown parameters is first developed. This is accomplished by forcing the regional descriptions of the deadzone to be entirely contained in the definition of a regressor. This is convenient for estimation since adaptation for the parameters of the separate regions of the nonlinearities is automatically accommodated by the regressor. Unfortunately, this parametrization necessitates multiple estimates of the zeros of the plant. To overcome the difficulty of designing a feedback/feedforward controller given multiple estimates of the zeros, we implement a nonlinear "zero resolving" prefilter. This prefilter to the plant allows one to design a feedback/feedforward controller based on one set of zeros.