Abstract
We analyze a research direction related to the development of methods for study and design of complex system structures, a method founded by academician B.N. Petrov. The progress of structural design methods is outlined along four directions: the ordinal mapping method, structural design based on signal and state digraphs, the structural functions method, and design of nonlinear controller structures based on artificial neural networks.
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References
Aleksandrov, A.G., Sintez regulyatorov mnogomernykh sistem (Controller Design for Multidimensional Systems), Moscow: Mashinostroenie, 1986.
Andreev, Yu.N., Upravlenie konechnomernymi lineinymi ob”ektami (Control for Finite-Dimensional Linear Objects), Moscow: Nauka, 1976.
Baranchuk, E.I., Vzaimosvyazannye i mnogokonturnye reguliruemye sistemy (Interconnected and Multicircuit Controllable Systems), Leningrad: Energiya, 1968.
Besekerskii, V.A. and Popov, E.P., Teoriya sistem avtomaticheskogo regulirovaniya (Theory of Automated Control Systems), Moscow: Nauka, 1975.
Bodner, V.A., Sistemy upravleniya letatel’nymi apparatami (Control Systems for Flying Vehicles), Moscow: Mashinostroenie, 1973.
Voronov, A.A., Ustoichivost’, upravlyaemost’, nablyudaemost’ (Stability, Controllability, Observability), Moscow: Nauka, 1979.
Voronov, A.A., Osnovy teorii avtomaticheskogo upravleniya: avtomaticheskoe regulirovanie nepreryvnykh lineinykh sistem (Fundamentals of Automated Control Theory: Automated Control for Continuous Linear Systems), Moscow: Energiya, 1980.
Vostrikov, A.S., Upravlenie dinamicheskimi ob”ektami (Control for Dynamic Objects), Novosibirsk: Novosib. Elektrotekhn. Inst., 1971.
Krasovskii, A.A., Sistemy avtomaticheskogo upravleniya poletom i ikh analiticheskoe konstruirovanie (Automated Flight Control Systems and Their Analytic Constructions), Moscow: Nauka, 1973.
Meerov, M.V., Sistemy mnogosvyaznogo regulirovaniya (Multiconnected Control Systems), Moscow: Nauka, 1965.
Meerov, M.V., Sintez struktur sistem avtomaticheskogo regulirovaniya vysokoi tochnosti (Structural Design for High Precision Automated Control Systems), Moscow: Nauka, 1967.
Morozovskii, V.G., Mnogosvyaznye sistemy avtomaticheskogo regulirovaniya (Multiconnected Automated Control Systems), Moscow: Energiya, 1970.
Netushil, A.V., Teoriya avtomaticheskogo upravleniya (Automated Control Theory), Moscow: Nauka, 1983.
Smagina, E.M., Voprosy analiza lineinykh mnogomernykh ob”ektov s ispol’zovaniem ponyatiya nulya sistemy (Analysis of Linear Multidimensional Objects with the Notion of a System Zero), Tomsk: Tom. Univ., 1990.
Sobolev, O.S., Metody issledovaniya lineinykh mnogosvyaznykh sistem (Studies in Linear Multiconnected Systems), Moscow: Energoatomizdat, 1985.
Solodovnikov, V.V. and Tumarkin, V.N., Teoriya slozhnosti i proektirovanie sistem upravleniya (Complexity Theory and Control Systems Design), Moscow: Nauka, 1990.
Tsypkin, Ya.Z., Osnovy teorii avtomaticheskikh sistem (Fundamentals of Automated Systems Theory), Moscow: Nauka, 1977.
Chinaev, P.I., Metody analiza i sinteza mnogomernykh avtomaticheskikh sistem (Analysis and Synthesis of Multidimensional Automated Systems), Kiev: Tekhnika, 1969.
Yanushevskii, R.T., Teoriya lineinykh optimal’nykh mnogosvyaznykh sistem upravleniya (Theory of Linear Optimal Multiconnected Control Systems), Moscow: Nauka, 1973.
Bohn, E.V., Design and Synthesis Methods for a Class of Multivariable Feedback Control System Based on Variable Methods, Trans. AIEE, 1962, no. 81, pp. 109–116.
Boksenbom, A. and Hood, R., General Algebraic Method Applied to Control Analysis of Complex Engine Types, NASA Tech. Rept. 980, 1950.
Chen, C.T., Linear System Theory and Design, New York: Holt, Reeinhart and Winston, 1984.
Desoer, C.A., Notes for a Second Course on Linear Systems, New York: Van Nostrand Reinhold, 1970.
Kalman, R.E., Falb, P.L., and Arbib, M.A., Topics in Mathematical System Theory, New York: McGraw-Hill, 1969. Translated under the title Ocherki po matematicheskoi teorii sistem, Moscow: Mir, 1971.
Kavanagh, R.J., The Application of Matrix Methods to Multivariable Control Systems, J. Franklin Inst., 1957, vol. 262(9), pp. 349–367.
Kwakernaak, H. and Silvan, R., Linear Optimal Control Systems, New York: Wiley, 1972.
MacFarlane, J.A.G., Complex Variable Methods for Linear Multivariable Feedback Systems, London: Taylor and Francis, 1980.
Mesarovic, M.D., The Control of Multivariable Systems, New York: Wiley, 1960.
Rosenbrock, H.H., State-Space and Multivariable Theory, London: Nelson, 1970.
Wolowich, W.A., Linear Multivariable Systems, New York: Springer-Verlag, 1974.
Wonham, W.M., Linear Multivariable Control: A Geometric Approach, New York: Springer, 1979.
Optimizatsiya mnogomernykh sistem upravleniya gazoturbinnykh dvigatelei letatel’nykh apparatov (Optimizing Multidimensional Control Systems for Gas Turbine Engines of Flying Vehicles), Shevyakov, A.A. and Mart’yanova, T.S., Eds., Moscow: Mashinostroenie, 1989.
Petrov, B.N., On Construction and Transformation of Structural Circuits, Izv. Akad. Nauk USSR, 1945, no. 12, pp. 1146–1162.
Zadeh, L.A. and Desoer, C.A., Linear System Theory: The State Space Approach, New York: McGraw-Hill, 1963. Translated under the title Teoriya lineinykh sistem. Metod prostranstva sostoyanii, Moscow: Nauka, 1970.
Mason, S.J. and Zimmerman, H.J., Electronic Circuits, Signals, and Systems, New York: Wiley, 1960. Translated under the title Elektricheskie tsepi, signaly i sistemy, Moscow: Inostrannaya Literatura, 1963.
Zhuk, K.D., A Structural Design Method for Multiconnected Systems based on Signal Graphs, Avtom. Telemekh., 1965, no. 6, pp. 53–57.
Raitsyn, T.M., Sintez sistem avtomaticheskogo upravleniya metodom napravlennykh grafov (Synthesis of Automated Control Systems with the Method of Directed Graphs), Moscow: Energiya, 1970.
Kolpakova, N.P. and Petrov, B.N., Structural Design Methods for Multichannel Systems with Graph Theory, in Teoriya i metody postroeniya sistem mnogosvyaznogo regulirovaniya (Theory and Design Methods for Multiconnected Control Systems), Moscow: Nauka, 1973, pp. 18–38.
Babak S.F., Il’yasov B.G., and Rutkovskii V.Yu., A Method for Analytic Computation of Transition Function Coefficients in Multidimensional Systems, Dokl. Akad. Nauk USSR, 1986, vol. 290, no. 3, pp. 557–559.
Bellert, S. and Woźniacki, H., The Analysis and Synthesis of Electrical Systems by Means of the Method of Structural Numbers, Warszawa: WNT, 1968. Translated under the title Analiz and sintez elektricheskikh tsepei metodom strukturnykh chisel, Moscow: Mir, 1972.
Shatikhin, L.G., Strukturnye matritsy i ikh primenenie dlya issledovaniya sistem (Structural Matrices and Their Applications for Systems Research), Moscow: Mashinostroenie, 1974.
Kron, G., Diakoptics, London: Macdonald, 1963. Translated under the title Issledovanie slozhnykh sistem po chastyam. Diakoptika, Moscow: Nauka, 1972.
Bodner, V.A., Ryazanov, Yu.A., and Shaimardanov, F.A., Sistemy avtomaticheskogo upravleniya dvigatelyami letatel’nykh apparatov (Automated Control Systems for Engines of Flying Vehicles), Moscow: Mashinostroenie, 1973.
Morozovskii, V.T., On Cross-Control for Multiconnected Automated Control Systems, in Teoriya i metody postroeniya sistem mnogosvyaznogo regulirovaniya (Theory and Design Methods for Multiconnected Control Systems), Moscow: Nauka, 1973, pp. 39–52.
Yuan, J.S.-C., Structural Instability of a Class of Decoupling Solutions, IEEE Trans. Automat. Control, 1977, vol. 22, no. 5, pp. 843–846.
Pukhov, G.E. and Zhuk, K.D., Sintez mnogosvyaznykh sistem upravleniya po metodu obratnykh operatorov (Multiconnected Control Systems Design with the Method of Inverse Operators), Kiev: Naukova Dumka, 1966.
Petrov, Yu.P., Synthesis of Optimal Linear Systems under Implementability Constraints, Vestn. Mosk. Gos. Uni., 1978, no. 13, pp. 97–102.
Petrov, B.N., Babak, S.F., Il’yasov, B.G., and Yusupov, I.Yu., On the Structures of Linear Stationary Systems, Dokl. Akad. Nauk USSR, 1980, vol. 250, no. 1, pp. 55–58.
Petrov, B.N., Il’yasov, B.G., and Kabal’nov, Yu.S., On the Synthesis of One Class of Automated Control Systems, Dokl. Akad. Nauk USSR, 1979, vol. 228, no. 3, pp. 542–545.
Vasil’ev, V.I. and Shaimardanov, F.A., Sintez mnogosvyaznykh avtomaticheskikh sistem metodom poryadkovogo otobrazheniya (Multiconnected Automated Systems Design with the Method of Ordinal Mapping), Moscow: Nauka, 1983.
Vasil’ev, V.I., Gusev, Yu.M., Efanov, V.N., Krymskii, V.G., et al., Mnogourovnevoe upravlenie dinamicheskimi ob”ektami (Multilevel Control of Dynamical Objects), Moscow: Nauka, 1987.
Osnovy teorii mnogosvyaznykh sistem avtomaticheskogo upravleniya letatel’nymi apparatami (Fundamentals of the Theory of Multiconnected Automated Control Systems for Flying Vehicles. Textbook), Krasil’shchikov, M.N., Ed., Moscow: Mosk. Aviats. Inst., 1995.
Il’yasov, B.G., Munasypov, R.A., and Munasypova, E.S., Structural Design for Complex Dynamical Systems with the Method of Functional Structural Numbers, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1997, no. 3, pp. 3–11.
Intellektual’nye sistemy upravleniya i kontrolya gazoturbinnykh dvigatelei (Intelligent Control and Testing Systems for Gas Turbine Engines), Vasil’ev, S.N., Ed., Moscow: Mashinostroenie, 2008.
Galushkin, A.I., Fundamentals of Neural Control, Neirokomp’yutery: Razrabotka, Primenenie, Moscow: IPRZhR, 2002, no. 9, 10, pp. 87–106.
Vasil’ev, V.I. and Panteleev, S.V., Neural Control-a New Field in Control Theory for Complex Systems, Neirokomp’yutery: Razrabotka, Primenenie, Moscow: IPRZhR, 2005, no. 5, pp. 33–45.
Narendra, K.S. and Parthasarathy, R., Identification and Control of Dynamical Systems Using Neural Networks, IEEE Trans. Neural Networks, 1990, vol. 1, pp. 4–27.
Narendra, K.S., Neural Networks for Control. Theory and Practice, Proc. IEEE, 1996, vol. 84, no. 10, pp. 1385–1405.
Neirokomp’yutery v aviatsii (samolety) (Neurocomputers in Aviation (Aircraft)), Vasil’ev, V.I., Il’yasov, B.G., and Kusimov, S.T., Eds., (Neurocomputers and Their Applications), Moscow: IPRZhR, 2004, book 14.
Vasil’ev, V.I. and Il’yasov, B.G., Intellektual’nye sistemy upravleniya. Teoriya i praktika (Intelligent Control Systems. Theory and Practice), Moscow: Radiotekhnika, 2009.
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Original Russian Text © V.I. Vasil’ev, B.G. Ilyasov, R.A. Munasypov, 2013, published in Avtomatika i Telemekhanika, 2013, No. 3, pp. 192–214.
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Vasil’ev, V.I., Ilyasov, B.G. & Munasypov, R.A. Development of structural methods for the study of complex dynamical systems. Autom Remote Control 74, 471–490 (2013). https://doi.org/10.1134/S0005117913030119
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DOI: https://doi.org/10.1134/S0005117913030119