Optimal time delays in a class of reaction-diffusion equations. (2nd January 2019)

• Record Type: Journal Article
• Authors: Casas, E.; Mateos, M.; Tröltzsch, F.
• Is Part Of: Optimization. Volume 68:Number 1(2019)
• Page Start: 255
• Page End: 278
• Publication Date: 2019-01-02
• Subjects: Semilinear parabolic equation -- multiple time delays -- Pyragas type feedback -- optimization -- learning controller; 49K20 -- 49M05 -- 35K58; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1509215
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.