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.
Riccati-based solution to the optimal control of linear evolution equations with finite memory / Acquistapace Paolo; Bucci Francesca. - In: EVOLUTION EQUATIONS AND CONTROL THEORY. - ISSN 2163-2480. - STAMPA. - 13 (Early access: July 2023):(2024), pp. 26-66. [10.3934/eect.2023035]
Riccati-based solution to the optimal control of linear evolution equations with finite memory
Bucci Francesca
2024
Abstract
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.File | Dimensione | Formato | |
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