On controllability of nonlinear distributed systems on a set of discretized controls

A. V. Chernov

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2013), pp. 83-98

Résumé

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.

Détail

Keywords: nonlinear distributed systems, controllability, discretized controls, Volterra functional operator equation.

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