SYNTHESIS OF THE OPTIMAL BOUNDARY CONTROL IN MINIMIZING THE PIECEWISE - LINEAR FUNCTIONAL
SYNTHESIS OF THE OPTIMAL BOUNDARY CONTROL IN MINIMIZING THE PIECEWISE - LINEAR FUNCTIONAL
DOI:
https://doi.org/10.52754/16948645_2023_2_90Keywords:
Boundary value problem, generalized solution, functional, Bellman-Egorov scheme, Bellman-type integro-differential equation, boundary control synthesisAbstract
In the paper solvability of the optimal boundary control synthesis problem was investigated in the optimization of thermal processes described by partial integro-differential equations with Fredholm integral operator when the boundary influence function nonlinearly depends on control function. The research was carried out on basis of generalized solution of the boundary value problem for controlled process. Boundary is established of change in parameter values of the integral operator, in which generalized solution exists. In the optimization problem, it is required to minimize the piecewise -linear functional and to find control depended on state of the controlled process. It has been established that the presence of integral operator in the equation significantly affects the solvability of the nonlinear optimization problem, in particular, complicated the structure of the Bellman-type equation. An algorithm has been developed for constructing a synthesizing optimal control .
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