Turnpilke property for infinite-dimensional generalized LQ problem

2022/07/30 by Zhuqing Li, Li, Zhuqing, Guglielmi, Roberto
Computer Science · Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2208.00307

openalex publication_date 2022/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deduce a sufficient condition of the exponential (integral) turnpike property for infinite dimensional generalized linear-quadratic optimal control problems in terms of structural properties of the control system, such as exponential stabilizability and detectability. The proof relies on the analysis of the exponential convergence of solutions to the differential Riccati equations to the algebraic counterpart, and on a necessary condition for exponential stabilizability in terms of a closed range test.

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