Slow decay and turnpike for infinite-horizon hyperbolic linear quadratic problems

This paper is devoted to analysing the explicit slow decay rate and turnpike in the infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Assume that some weak observability or controllability are satisfied, by which, the lower and upper bounds of the corresponding algeb...

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Detalles Bibliográficos
Autores: Han, Zhong Jie, Zuazua Iriondo, Enrique
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/719246
Acceso en línea:http://hdl.handle.net/10486/719246
https://dx.doi.org/10.1137/21M1441985
Access Level:acceso abierto
Palabra clave:Riccati operator
Optimal control problems
Slow decay rate
Turnpike property
Weak controllability and observability
Matemáticas
Descripción
Sumario:This paper is devoted to analysing the explicit slow decay rate and turnpike in the infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Assume that some weak observability or controllability are satisfied, by which, the lower and upper bounds of the corresponding algebraic Riccati operator are estimated, respectively. Then based on these two bounds, the explicit slow decay rate of the closed-loop system with Riccati-based optimal feedback control is obtained. The averaged turnpike property for this problem is also further discussed. We then apply these results to the LQ optimal control problems constraint to networks of one-dimensional wave equations and also some multi-dimensional ones with local controls which lack of GCC(Geometric Control Condition)