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DOI: https://doi.org/10.20537/vm170107

Abstract: We consider a linear differential game with a pulse control of the first player. The abilities of the first player are determined by the stock of resources that the player can use when forming his control. At certain instants of time a separation of part of the resources stock is possible, which may implicate an “instantaneous” change of a phase vector, resulting in the complication of the problem. The control of the second player has geometrical constraints. The vectograms of the players are described by the same ball with different time-dependent radii. The terminal set of the game is determined by the condition of belonging the norm of a phase vector to a segment with positive ends. In this paper, a set defined by this condition is called a ring. The aim of the first player is to lead a phase vector to the terminal set at fixed time. The aim of the second player is opposite. With the maximal stable bridge, which has been defined by the authors previously, optimal controls of players are constructed.

Keywords: pulse control, optimal control, differential game.

Received: 12.12.2016

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Citation: V. I. Ukhobotov, I. V. Izmest'ev, “Synthesis of controls in a single-type game problem of pulse meeting at fixed time with a terminal set in the form of a ring”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:1 (2017), 69–85

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This publication is cited in the following articles:

1. Viktor Ukhobotov, Igor' Izmest'ev, 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017, 1  
2. V. I. Ukhobotov, I. S. Stabulit, “Dinamicheskaya zadacha upravleniya pri nalichii pomekhi i s zadannym mnozhestvom momentov korrektsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 74–81      
3. S. A. Nikitina, V. I. Ukhobotov, “Diskretnaya lineinaya zadacha upravleniya s terminalnym mnozhestvom v forme koltsa pri nalichii pomekhi”, Materialy Vserossiiskoi nauchnoi konferentsii «Differentsialnye uravneniya i ikh prilozheniya», posvyaschennoi 85-letiyu professora M. T. Terekhina. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 17–18 maya 2019 g. Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 186, VINITI RAN, M., 2020, 102–107    
4. Igor' V. Izmest'ev, Lecture Notes in Control and Information Sciences - Proceedings, Stability, Control and Differential Games, 2020, 345  
5. I. V. Izmestev, V. I. Ukhobotov, “Minimizatsiya zapasa resursov v odnoi impulsnoi differentsialnoi igre s nevypuklym terminalnym mnozhestvom”, Chelyab. fiz.-matem. zhurn., 6:1 (2021), 22–33    
6. V. N. Ushakov, V. I. Ukhobotov, I. V. Izmestyev, “On a Problem of Impulse Control under Disturbance and Possible Breakdown”, Proc. Steklov Inst. Math. (Suppl.), 315, suppl. 1 (2021), S236–S249          

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Related articles in Google Scholar: Russian articles, English articles