Differentiability of the Value Function on H¹(Ω) of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems under Control Constraints

2023/11/26 by Karl Kunisch, Kunisch, Karl, Buddhika Priyasad +1
Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2311.15374

openalex publication_date 2023/11/26 · openalex created_date 2023/11/29 · openalex updated_date 2026/07/28

Abstract

An abstract framework guaranteeing the continuous differentiability of local value functions on H¹(Ω) associated with optimal stabilization problems subject to abstract semilinear parabolic equations in the presence of norm constraints on the control is established. It guarantees the local well-posedness of the associated Hamilton-Jacobi-Bellman equation in the classical sense. Examples illustrate that the assumptions imposed on the dynamical system are satisfied for practically relevant semilinear equations.

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