On Finite-Dimensional Approximations of the Time-Optimal Control Problem for the Heat Equation in a Rod

Abstract

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.