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arXiv · 2303.05343

Riccati-based solution to the optimal control of linear evolution equations with finite memory

Paolo Acquistapace·Francesca Bucci
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Abstract

In this article we study the optimal control problem with quadratic functionals for a linear Volterra integro-differential equation in Hilbert spaces. With the finite history seen as an (additional) initial datum for the evolution, following the variational approach utilized in the study of the linear-quadratic problem for memoryless infinite dimensional systems, we attain a closed-loop form of the unique optimal control via certain operators that are shown to solve a coupled system of quadratic differential equations. This result provides a first extension to the partial differential equations realm of the Riccati-based theory recently devised by L. Pandolfi in a finite dimensional context.

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Paolo Acquistapace, Francesca Bucci. 2023-03-09. Riccati-based solution to the optimal control of linear evolution equations with finite memory. https://arxiv.org/abs/2303.05343

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