Min-Max Sliding-Mode Control

Abstract

AbstractThis chapter deals with the Min-Max Sliding-Mode Control design where the original linear time-varying system with unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external bounded disturbances. Such a trade-off between an original uncertain linear time-varying dynamic system and a corresponding higher order multimodel system with complete knowledge leads to a linear multimodel system with known bounded disturbances. Each model from a given finite set is characterized by a quadratic performance index. The developed Min-Max Sliding-Mode Control strategy gives an optimal robust sliding-surface design algorithm, which is reduced to a solution of the equivalent LQ Problem that corresponds to the weighted performance indices with weights from a finite-dimensional simplex. An illustrative numerical example is presented.KeywordsUncertain CaseBounded DisturbanceQuadratic Performance IndexExact RealizationUnknown Bounded DisturbanceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.