Control Problems for Systems with Uncertainty

  • A. V. Il’inEmail author
  • V. V. Fomichev
  • A. S. Fursov

Different forms of control problems for linear systems under essential uncertainty are considered. Specifically, three problems are examined. First, the unknown disturbances are assumed bounded and only their bounds are known. The problem is solved under various assumptions regarding the order of the disturbances and the observed signals, as well as the properties of the system. Second, the estimation of the unknown input (i.e., the inversion problem or the inverse problem) is considered. This problem is solved by the controlled model method with the control designed to stabilize the difference between the observed outputs of the original system and the model. Robust stabilization algorithms produce estimates of the unknown signals with a desired accuracy. The third problem focuses on stabilization of switched systems. The dynamics of the chosen system is described at each instant by one of the systems from a given finite set. Switching between regimes may depend both on time and on the system phase vector. Two problems are solved successively: finding stabilizers (a unique stabilizer if possible) for each plant from the family, and then investigating the conditions when switching between stable regimes does not disrupt the stability of the switched system. Various stabilization methods are obtained for switched systems covering different switching schemes.


automatic control control under uncertainty observation inverse problems delayed systems switched systems 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • A. V. Il’in
    • 1
    Email author
  • V. V. Fomichev
    • 1
  • A. S. Fursov
    • 1
  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia

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