Abstract
Consideration was given to the problem of feedback control of a linear system. An algorithm to solve it was presented under the assumption that the linear combinations of the system phase states are measured with error at sufficiently frequent discrete time instants. The algorithm is stable to the information and computation errors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Krasovskii, N.N. and Subbotin, A.I., Pozitsionnye differentsial’nye igry (Positional Differential Games), Moscow: Nauka, 1974.
Krasovskii, N.N., Upravlenie dinamicheskoi sistemoi (Control of the Dynamic System) Moscow: Nauka, 1985.
Subbotin, A.I. and Chentsov, A.G., Optimizatsiya garantii v zadachakh upravleniya (Guarantee Optimization in the Control Problems), Moscow: Nauka, 1981.
Utkin, V.I., Guldner, J., and Shi, J., Sliding Mode Control in Electromechanical Systems, Boca Raton: CRC Press, 2009.
Shtessel, Y., Edwards, C., Fridman, L., et al., Sliding Mode Control and Observation, New York: Birkhauser, 2014.
Polyakov, A., Nonlinear Feedback Design for Fixed-time Stabilization of Linear Systems, IEEE Trans. Automat. Control, 2012, Vol. 57(8), pp. 2106–2110.
Zhuk, S. and Polyakov, A., On Output-based Sliding Mode Control Design Using Minimax Observer, Int. Workshop on Variable Structure Systems, Nantes, 2014, https://halinriafr/hal-01071233v2.
Osipov, Yu.S. and Kryazhimskii, A.V., Inverse Problems for Ordinary Differential Equations. Dynamical Solutions, London: Gordon and Breach, 1995.
Osipov, Yu.S., Kryazhimskii, A.V., and Maksimov, V.I., Metody dinamicheskogo vosstanovleniya vkhodov upravlyaemykh sistem (Methods of Dynamic Restoration of Controllable System Inputs), Yekaterinburg: UrO RAN, 2011.
Osipov, Yu.S., Kryazhimskii, A.V., and Maksimov V.I., N.N. Krasovskii’s Extremal Shift Method and Problems of Boundary Control, Autom. Remote Control, 2009, Vol. 70, No. 4, pp. 577–588
Kryazhimskii, A.V. and Osipov, Yu.S., Idealized Packets of Programs and Problems of Positional Control under Incomplete Information, Tr. Inst. Mat. Mekh. UrO RAN, 2009, Vol. 15, No. 3, pp. 139–157
Kryazhimskii, A.V. and Maksimov, V.I., On Combination of the Processes of Reconstruction and Guaranteening Control, Autom. Remote Control, 2013, Vol. 74, No. 8, pp. 1235–1248.
Blizorukova, M.S. and Maksimov, V.I., A Control Problem under Incomplete Information, Autom. Remote Control, 2006, Vol. 67, No. 3, pp. 461–471
Kappel, F., Kryazhimskii, A.V., and Maksimov, V.I., Dynamic Reconstruction of States and Guaranteeing Control of a Reaction-diffusion system, Dokl. Math., 2000, Vol. 61, No. 1, pp. 143–145
Osipov, Yu.S., Program Packages. An Approach to the Solution of Positional Control Problems under Incomplete Information, Usp. Mat. Nauk, 2006, Vol. 61, No. 4, pp. 25–76
Kryazhimskii, A.V. and Maksimov, V.I., Resourse-saving Tracking Problem with Infinite Time Horizon, Differ. Equat., 2011, Vol. 47, No. 7, pp. 1004–1013.
Samarskii, A.A., Vvedenie v teoriyu raznostnykh skhem (Introduction to the Theory of Difference Schemes), Moscow: Nauka, 1971.
Warga, J., Optimal Control of Differential and Functional Equations, New York: Academic, 1972. Translated under the title Optimal’noe upravlenie differentsial’nymi i funktsional’nymi uravneniyami, Moscow: Nauka, 1979.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.I. Maksimov, 2016, published in Avtomatika i Telemekhanika, 2016, No. 6, pp. 3–21.
This paper was recommended for publication by M.V. Khlebnikov, a member of the Editorial Board
Rights and permissions
About this article
Cite this article
Maksimov, V.I. On a problem of linear system control under incomplete information about the phase coordinates. Autom Remote Control 77, 943–958 (2016). https://doi.org/10.1134/S0005117916060011
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117916060011