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## Archive of Issues

Russia Nizhni Novgorod
Year
2013
Issue
1
Pages
83-98
 Section Mathematics Title On controllability of nonlinear distributed systems on a set of discretized controls Author(-s) Chernov A.V.ab Affiliations Nizhni Novgorod State Technical Universitya, Nizhni Novgorod State Universityb Abstract For nonlinear distributed systems representable as a Volterra functional operator equation in a Lebesgue space, sufficient conditions for pointwise controllability with respect to a nonlinear functional are proved. The controls are assumed to belong to a given set $\mathcal{D}$ of piecewise constant vector functions id est can be regarded as discretized controls. For the equation under study we define the set $\Omega$ of global solvability as the set of all admissible controls for which the equation has a global solution. As an auxiliary result having a separate interest, we also establish under our hypotheses the equality $\Omega=\mathcal{D}$. The reduction of controlled distributed systems to the functional operator equation under study is illustrated by two examples, namely a Dirichlet boundary value problem for a second order parabolic equation and a mixed boundary value problem for a second order hyperbolic equation; both equations of a rather general form. Keywords nonlinear distributed systems, controllability, discretized controls, Volterra functional operator equation UDC 517.957, 517.988, 517.977.1 MSC 47J05, 47J35, 93B05 DOI 10.20537/vm130108 Received 25 November 2012 Language Russian Citation Chernov A.V. On controllability of nonlinear distributed systems on a set of discretized controls, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 1, pp. 83-98. References Vasil’ev F.P. Duality in linear control and observation problems, Differ. Uravn., 1995, vol. 31, pp. 1893–1900. Egorov A.I., Znamenskaya L.N. 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