Abstract
Consideration was given to a class of problems that are inverse to the dynamic processes described by the discontinuous systems of ordinary differential equations changing their form depending on the membership of the current process state to one or another subdomain of the state space. In this problem, it is both the object parameters and the surfaces themselves defining the boundaries of the sub-domains where the differential equations retain their form that are identified as the object parameters.
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Velichenko, V.V., Optimal Control Problems for Equations with Discontinuous Right-Hand Sides, Autom. Remote Control, 1966, vol. 27, no. 7, pp. 1153–1163.
Ashchepkov, L.T., Optimal’noe upravlenie razryvnymi sistemami (Optimal Control of Discontinuous Systems), Novosibirsk: Nauka, 1987.
Troitskii, V.A., Variational Problems of Optimization of the Control Processes for Equations with Discontinuous Right-hand Sides, Prikl. Mat. Mekh., 1962, vol. 26, no. 2, pp. 233–246.
Xu, X. and Anstasklis, P.J., Optimal Control of Switching Systems, Automatica, 2005, vol. 41, pp. 11–27.
Li, R., Teo, K.L., Wong, K.H., and Duan, G.R., Control Parameterization Enhancing Transform for Optimal Control of Switched Systems, Math. Comput. Modeling, 2006, vol. 43, pp. 1393–1403.
Hedlund, S. and Rantzer, A., Optimal Control of Hybrid Systems, Proc. 38th IEEE Conf. Decision Control, 1999, pp. 3972–3977.
Rozenvasser, E.N., General Sensitivity Equations of Discontinuous Systems, Autom. Remote Control, 1967, vol. 28, no. 3, pp. 400–404.
Vasil’ev, F.P., Metody optimizatsii (Methods of Optimization), Moscow: Faktorial Press, 2002.
Polyak, B.T., Vvedenie v optimizatsiyu, Moscow: Nauka, 1983. Translated into English under the title Introduction to Optimization, New York: Optimization Software, 1987.
Aida-zade, K.R. and Kuliev, S.Z., On a Class of Inverse Problems for Discontinuous Systems, Kibern. Sist. Anal., 2008, no. 4, pp. 142–152.
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Original Russian Text © K.R. Aida-Zade, S.Z. Kuliev, 2012, published in Avtomatika i Telemekhanika, 2012, No. 5, pp. 25–38.
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Aida-Zade, K.R., Kuliev, S.Z. On numerical solution of one class of inverse problems for discontinuous dynamic systems. Autom Remote Control 73, 786–796 (2012). https://doi.org/10.1134/S0005117912050037
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DOI: https://doi.org/10.1134/S0005117912050037