Controller Scheduling: A Possible Algebraic Viewpoint

In the applications, one common way to design a control system for a nonlinear plant is to localize its behavior along lines of operation specified by the plant manufacturer, to develop linear multivariable controls for these localizations, and to schedule those controls with key plant variables which vary smoothly along operating lines. An important part of practical design lore, the art of controller scheduling has received little modern attention from the conceptual point of view. This paper describes four basic types of scheduling questions and outlines some of the theoretical issues associated with them. Schedules are considered in terms of state equations; however, some relations with the input/output description are discussed, together with an analysis of the effects on the overall configuration of approximations made to the individual subsystems.