A Control Problem for Parabolic Systems with Incomplete Information

  • Boris I. AnanyevEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)


In this paper, abstract parabolic control systems in Hilbert space are considered. The state of the system is unknown, but there is an equation of measurement in discrete times. The initial state and disturbances are restricted by joint integral constraints. According to measurements, the information set is introduced that contains the true state of the system. This set includes all the states of the system that are compatible with the measurements. The preliminary aim of control consists in minimization of the terminal criterion depending of the information set. We suggest some statements of the problem based on the separation of control and observation processes. The optimal instants of transition from estimation to control are looked for as well. The approach is applied to distributed systems with partial derivatives and to systems with the deviation of time of retarded and neutral types. The approximation scheme are suggested and examples are considered.


Control Evolutionary systems Information sets Incomplete information 


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Authors and Affiliations

  1. 1.N.N. Krasovskii Institute of Mathematics and Mechanics UB of RASYekaterinburgRussia
  2. 2.Ural Federal UniversityYekaterinburgRussia

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