Final-state, Open-loop Control of the Heat equation in Tensorial Domains (full version)
Abstract
In this paper, a quadratic optimal control problem will be considered for the heat equation in tensorial domains with homogeneous Dirichlet boundary conditions, in which the control function (depending only on time) constitutes a source term. These problems involve choosing a control function (with or without "peak-value" constraints) to approximately steer the solution of the heat equation to a desired function at the end of a prescribed (finite) time-interval. To compute approximations to the desired optimal control functions, semi-discrete, spectral (with eigenfunctions) Galerkin approximations to the corresponding heat equation and the corresponding (approximating) control problems are tackled. Two simple, illustrative examples are presented in the final section.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2022
- DOI:
- 10.48550/arXiv.2209.00683
- arXiv:
- arXiv:2209.00683
- Bibcode:
- 2022arXiv220900683C
- Keywords:
-
- Electrical Engineering and Systems Science - Systems and Control
- E-Print:
- 32 pages, 11 figures, submitted