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arXiv · 2108.12888

Differentiability of the Value Function of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems on $L^2(\Omega)$ under Control Constraints

Karl Kunisch·Buddhika Priyasad
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Abstract

An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls is established. It guarantees that the value function satisfies the associated Hamilton-Jacobi-Bellman equation in the classical sense. The applicability of the developed framework is demonstrated for specific semilinear parabolic equations.

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Karl Kunisch, Buddhika Priyasad. 2021-08-29. Differentiability of the Value Function of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems on $L^2(\Omega)$ under Control Constraints. https://doi.org/10.1007/s00245-022-09840-9

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