The control-package method is applied to solve the problem of constructing guaranteed positional guidance for a linear control dynamical system with a delay under incomplete information about the initial state. The problem is solved for the case when the initial state is contained in a compact functional set. A solvability criterion and a method for the construction of a guidance program package are proposed. The proposed procedure is applied to a particular linear control system of delayed differential equations.
Similar content being viewed by others
References
Yu. S. Osipov, “Control packages: an approach to solution of positional control problems with incomplete information,” UMN, 61, No. 4(370), 25–76 (2006).
A. V. Kryazhimskii and Yu. S. Osipov, “Idealized program packages and positional control problems with incomplete information,” Trudy Inst. Matem. Mekhan. Uro RAN, 15, No. 3, 139–157 (2009).
A. V. Kryazhimskii and Yu. S. Osipov, “Solvability of guaranteed control problems for partially observed linear dynamical systems,” Trudy MIAN, 277, 152–167 (2012).
A. V. Kryazhimskii and N. V. Strelkovskii, “A programmed solvability criterion for positional control problem with incomplete information. Linear control systems,” Trudy Inst. Matem. Mekhan. Uro RAN, 20, No. 3, 132–147 (2014).
N. N. Krasovskii, Game Problems with Oncoming Motions [in Russian], Nauka, Moscow (1970).
A. B. Kurzhanskii, Control and Observation under Uncertainty [in Russian], Nauka, Moscow (1977).
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).
N. N. Krasovskii and Yu. S. Osipov, “Control problem with incomplete information,” Mekhanika Tverdogo Tela, No. 4, 5–14 (1973).
A. I. Subbotin and A. G. Chentsov, Guaranteed Optimization in Control Problems [in Russian], Nauka, Moscow (1981).
V. I. Maksimov, “The problem of finding guaranteed programmed control with incomplete information for a linear system,” Diff. Uravn., 51, No. 12, 1676–1685 (2015).
V. L. Rozenberg, “A control problem with shortage of information for a linear stochastic differential equation,” Trudy Inst. Matem. Mekhan. Uro RAN, 21, No. 3, 292–302 (2015).
N. L. Grigorenko, Yu. A. Kondrat’eva, and L. N. Luk’yanova, “The problem of finding guaranteed programmed control with incomplete information for a linear system,” Trudy Inst. Matem. Mekhan. Uro RAN, 21, No. 2, 41–49 (2015).
N. N. Krasovskii, Some Problems in the Theory of Stability of Motion [in Russian], Fizmatgiz, Moscow (1959).
N. V. Strelkovskii, “Construction of a guaranteed position guidance strategy for a linear control system with incomplete information,” Vestnik MGU, Comp. Math. Cybernet., No. 3, 65–73 (2015).
J. Hale, Theory of Functional Differential Equations [Russian translation], Mir, Moscow (1984).
Author information
Authors and Affiliations
Additional information
Translated from Problemy Dinamicheskogo Upravleniya, No. 7, 2016, pp. 94–108.
Rights and permissions
About this article
Cite this article
Surkov, P.G. The Problem of Package Guidance with Incomplete Information for a Linear Control System with a Delay. Comput Math Model 28, 504–516 (2017). https://doi.org/10.1007/s10598-017-9377-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-017-9377-y