Optimal Control of ODE Systems with Hysteresis Nonlinearities

摘要: It is well known that many dynamical systems exhibit hysteresis behaviour in one way or another. Usually this connected to some memory mechanism present within the system. Within a mathematical model, such either can be built explicitly, it an implicit consequence of model equations. The former approach has been pursued by Krasnoselskii and several collaborators: They define operator W, which maps scalar input function \(x = x(t)\) output \(y y(t)\) $$y(t) (Wx)(t),$$ by three-step procedure formalizes intuitive content figure 1.