Optimal Synthesis Control for Evolution Equations Subject to Nonlocal Inputs

We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following a perspective akin to the one taken in our previous research work on the LQ problem for integro-differential equation...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 205; no. 2; p. 37
Main Authors Acquistapace, Paolo, Bucci, Francesca
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2025
Springer Nature B.V
Subjects
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Closed loops
Differential equations
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimal control
Optimization
Theory of Computation
35R09
93C23
Linear quadratic problem
Closed-loop optimal control
Riccati equation
49N35
Optimal synthesis
Evolution equations with memory
49N10
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Summary:We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following a perspective akin to the one taken in our previous research work on the LQ problem for integro-differential equations—which combines a variational approach to the minimization problem with the consideration of a suitably enlarged state space—we offer a full (closed-loop, Riccati-based) solution to the optimization problem.
Bibliography:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02661-0