On the solvability of control synthesis problems for nonlinear oscillatory optimization processes described by integro-differential equations

A. K. Kerimbekov ; E. F. Abdyldaeva ; A. A. Anarbekova

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 63-71.

Résumé

The solvability of synthesis problems for distributed and boundary controls in minimizing problems for piecewise linear functionals for oscillatory processes described by partial integro-differential equations with Fredholm integral operators are examined. For the Bellman functional, a specific integro-differential equation is obtained. An algorithm for constructing a solution of the control synthesis problem of distributed and boundary controls is described. A procedure for determining controls as functions (functionals) of the state of the controlled process is constructed.

Détail

Keywords: integro-differential equation, Fredholm operator, generalized solution, Bellman functional, Fréchet differential, optimal control synthesis.

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