O‘zbekiston matematika jurnali Ҷилди 69 № 4 (2025) · Саҳифаҳои 35-39
On Finite-Dimensional Approximations of the Time-Optimal Control Problem for the Heat Equation in a Rod
Azamov, Abdulla, Bakhramov, Jasurbek
Аннотатсия
The time-optimal problem is considered for the controllable heat conduction process in a rod. Using the Fourier method, the problem is usually reduced to an infinite system of one-dimensional control equations whose control parameters are connected by complex relationships that make it difficult to solve. This article presents a method for regrouping the terms of the Fourier series of the control function, enabling the reduction of the problem to a finite-dimensional framework. The resulting reduced problem facilitates the more effective construction of a suboptimal control.
heat equation, control problem, time optimality, Fourier expansion, regrouping, finite dimensional reduction, suboptimal control.
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