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Mini-max integral sliding-mode control for multimodel linear uncertain systems

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3 Author(s)
Poznyak, A. ; Departamento de Control Automatico, CINVESTAV-IPN, Mexico City, Mexico ; Fridman, L. ; Bejarano, F.J.

An original linear time-varying system with matched and 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 unmatched bounded disturbances. Such a tradeoff between an original uncertain linear time varying dynamic system and a corresponding higher order multimodel system containing only matched uncertainties leads to a linear multi-model system with known unmatched bounded disturbances and unknown matched disturbances as well. Each model from a given finite set is characterized by a quadratic performance index. The developed minimax integral sliding mode control strategy gives an optimal minimax linear quadratic (LQ)-control with additional integral sliding mode term. The design of this controller is reduced to a solution of an equivalent mini-max LQ problem that corresponds to the weighted performance indices with weights from a finite dimensional simplex. The additional integral sliding mode controller part completely dismisses the influence of matched uncertainties from the initial time instant. Two numerical examples illustrate this study.

Published in:

Automatic Control, IEEE Transactions on  (Volume:49 ,  Issue: 1 )