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Russia Nizhni Novgorod
Year
2013
Issue
1
Pages
83-98
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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.
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