Geodesic
On the solvability of the problem of guaranteed package guidance to a system of target sets
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 344-354 Cet article a éte moissonné depuis la source Math-Net.Ru

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Control theory is a section of modern mathematics being actively developed at present time. The class of problems investigated within the framework of this theory is quite extensive and includes issues related to the existence of solutions as well as issues related to the effective methods for constructing controls. One of the approaches to solving control problems under lack of information was suggested by Yu. S. Osipov in the fundamental paper published in the Russian Mathematical Surveys in 2006. Later, this approach, called the method of program packages, was developed, in particular, in the articles cited in this paper. This approach is based on a suitable modification of the method of non-anticipatory strategies (quasi-strategies) for solving control problems with unknown initial states. As is known, quasi-strategies reflecting the Volterra properties of program realizations of closed-loop controls in corresponding program disturbances are oriented to the investigation of problems with known initial states under the presence of unknown dynamical disturbances. Such disturbances are usually absent in standard control problems with incomplete information and incompleteness of information is due to a lack of information about the initial state of the system. So, program packages became an analogue of the properties of nonanticipativeness for problems with unknown initial states. It should be noted that in all previous works related to the method of program packages, the guidance problems to one single target set were considered. In the present paper the guaranteed guidance problem to a collection of target sets under incomplete information about the initial state is considered for a linear autonomous control dynamical system. The criterion for the solvability of that problem is established. It is based on the method of program packages. An illustrative example is given.
Keywords: linear systems, control, incomplete information. 
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V. I. Maksimov; P. G. Surkov. On the solvability of the problem of guaranteed package guidance to a system of target sets. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 3, pp. 344-354. http://geodesic.mathdoc.fr/item/VUU_2017_27_3_a4/

[1] Krasovskii A. N., Krasovskii N. N., Control under lack of information, Birkhauser, Boston, 1995, 324 pp. | MR

[2] Krasovskii N. N., Subbotin A. I., Game-theoretical control problems, Springer, New York, 1988, 517 pp. | MR | Zbl

[3] Osipov Yu. S., “Control packages: an approach to solution of positional control problems with incomplete information”, Russian Mathematical Surveys, 61:4 (2006), 611–661 | DOI | DOI | MR | Zbl

[4] Kryazhimskiy A. V., Osipov Yu. S., “On the solvability of problems of guaranteeing control for partially observable linear dynamical systems”, Proceedings of the Steklov Institute of Mathematics, 277 (2012), 144–159 | DOI | MR | Zbl

[5] Kryazhimskii A. V., Strelkovskii N. V., “An open-loop criterion for the solvability of a closed-loop guidance problem with incomplete information. Linear control systems”, Proceedings of the Steklov Institute of Mathematics, 291, suppl. 1 (2015), 113–127 | DOI | MR | Zbl

[6] Grigorenko N. L., “A control problem with dominating uncertainty”, Proceedings of the Steklov Institute of Mathematics, 287, suppl. 1 (2014), 68–76 | DOI | MR

[7] Maksimov V. I., “Differential guidance game with incomplete information on the state coordinates and unknown initial state”, Differential Equations, 51:12 (2015), 1656–1665 | DOI | DOI | MR | Zbl

[8] Rozenberg V. L., “A control problem under incomplete information for a linear stochastic differential equation”, Proceedings of the Steklov Institute of Mathematics, 295, suppl. 1 (2016), 145–155 | DOI | MR

[9] Surkov P. G., “The problem of package guidance by a given time for a linear control system with delay”, Proceedings of the Steklov Institute of Mathematics, 296, suppl. 1 (2017), 218–227 | DOI | DOI | MR

[10] Maksimov V. I., “Tracking a given solution of a nonlinear distributed second-order equation”, Differential Equations, 52:1 (2016), 128–132 | DOI | DOI | MR | Zbl

[11] Strelkovskii N. V., “Constructing a strategy for the guaranteed positioning guidance of a linear controlled system with incomplete data”, Moscow University Computational Mathematics and Cybernetics, 39:3 (2015), 126–134 | DOI | MR | Zbl