Model order reduction based on Laguerre orthogonal polynomials for parabolic equation constrained optimal control problems

Abstract

In this paper, two model order reduction methods based on Laguerre orthogonal polynomials for parabolic equation constrained optimal control problems are studied. The spatial discrete scheme of the cost function subject to a parabolic equation is obtained by Galerkin approximation, and then the coupled ordinary differential equations of the optimal original state and adjoint state with initial value and final value conditions are obtained by Pontryagin's minimum principle. For this original system, we propose two kinds of model order reduction methods based on the differential recurrence formula and integral recurrence formula of Laguerre orthogonal polynomials, respectively, and they are totally different from these existing researches on model order reduction only for initial value problems. Furthermore, we prove the coefficient-matching properties of the outputs between the reduced system and the original system. Finally, two numerical examples are given to verify the feasibility of the proposed methods.

Keywords:

• Model order reduction
• advective-diffusion equation
• Laguerre polynomials
• optimal control

Mathematics Subject Classifications:

• 65L10 (2020)
• 65M99 (2020)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the Natural Science Foundation of China (NSFC) under grant 12271426, Key Research and Development Program of Shaanxi Province under grant 2023-YBSF-399, China Postdoctoral Science Foundation under grant 2023M732869, and Natural Science Basic Research Program of Shaanxi under grant 2024JC-YBQN-0049.