Abstract
This paper presents a method for designing a nonlinear system which has the hysteresis in the input stage. The hysteresis is usually described by a two-valued nonlinear function. Therefore it is more difficult to design the system with hysteresis.
By using the idea of topology, we consider first how to represent the hysteresis as a one-valued function. To this modified nonlinear system, we construct a Riemannian geometric nonlinear optimal regulator which has been proposed by the authors. Because this nonlinear regulator is homeomorphic to a linear optimal regulator, the superior properties of a linear regulator (i.e. asymptotic stability, feedback construction, and so on) are also to be reflected to the nonlinear regulator. As an example, the temperature control system with a bimetal thermal sensor is investigated.
