Abstract
Here, 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 also as external unmatched bounded disturbances. Such a trade-off between an original uncertain linear time-varying dynamic system and a corresponding higher-order multimodel system containing only matched uncertainties leads to a linear multimodel 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 min–max integral sliding mode control strategy gives an optimal min–max linear quadratic (LQ) control with additional integral sliding mode term. The design of this controller is reduced to a solution of an equivalent min–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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
V. Boltyansky, A. Poznyak, Robust maximum principle in minimax control. Int. J. Control 72(4), 305–314 (1999)
A. Poznyak, T. Duncan, B. Pasik-Duncan, V. Boltyansky, Robust maximum principle for minimax linear quadratic problem. Int. J. Control 75(15), 1170–1177 (2002)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fridman, L., Poznyak, A., Bejarano, F.J. (2014). Multimodel and ISM Control. In: Robust Output LQ Optimal Control via Integral Sliding Modes. Systems & Control: Foundations & Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4962-3_6
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4962-3_6
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-0-8176-4961-6
Online ISBN: 978-0-8176-4962-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)