Minimax control of a process in a linear uncertain-stochastic system with incomplete data

Abstract

Consideration is given to the control problem in a linear stochastic differential system where constant noise intensities in equations of state and observation are prescribed only accurate within the membership of some known sets. For control optimization, an integral root-mean-square performance criterion is used. The problem is solved by the transition to a dual one, which makes it possible to prove the existence of a saddle point of the criterion and obtain an explicit expression for the minimax control operator as functions of the solution to the dual problem. To solve the latter, an iteration algorithm is proposed; the convergence of the algorithm is proved and investigated by a model example.

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Correspondence to G. B. Miller.

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Original Russian Text © G.B. Miller, A.R. Pankov, 2007, published in Avtomatika i Telemekhanika, 2007, No. 11, pp. 164–177.

This work was supported by INTAS, project no. YSF 04-83-3623, and the Russian Foundation for Basic Research, projects nos. 05-01-00508 and 05-08-17963.

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Miller, G.B., Pankov, A.R. Minimax control of a process in a linear uncertain-stochastic system with incomplete data. Autom Remote Control 68, 2042–2055 (2007). https://doi.org/10.1134/S0005117907110124

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PACS numbers

  • 02.30.Yy
  • 02.50.Ey