This analysis reveals a condition for turnpike property in optimal control systems, emphasizing stability and detectability.
We deduce a sufficient condition for 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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Li et al. (2025) studied this question.
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