Постановка та методи розв’язання задачі оптимального керування тепловими процесами

Abstract

The optimal control of thermal processes is modeled using quasilinear parabolic partial differential equations. Due to strict phase and control constraints, we apply indirect sequential unconstrained minimization methods utilizing penalty or barrier functions. The synthesis of optimal control is formulated as the iterative minimization of a combined target functional using gradient and conjugate direction algorithms. To address complex geometric domains, an analytical-numerical approach based on R-function theory can be used. This framework enables the exact satisfaction of boundary conditions at the analytical level, significantly reducing discretization errors and ensuring high computational accuracy for complex nonlinear thermal control tasks.