<p>The paper establishes the exponential turnpike property for a class of mean-field stochastic linear-quadratic (LQ) optimal control problems with periodic coefficients. It first introduces the concepts of stability, stabilizability, and detectability for stochastic linear systems. Then, the long-term behavior of the associated Riccati equations is analyzed under stabilizability and detectability conditions. Subsequently, a periodic mean-field stochastic LQ problem is formulated and solved. Finally, its optimal pair is shown to be the turnpike limit of the initial optimal control problem.</p>

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Periodic Exponential Turnpike Phenomenon in Mean-Field Stochastic Linear-Quadratic Optimal Control

  • Jingrui Sun,
  • Lvning Yuan,
  • Jiaqi Zhang

摘要

The paper establishes the exponential turnpike property for a class of mean-field stochastic linear-quadratic (LQ) optimal control problems with periodic coefficients. It first introduces the concepts of stability, stabilizability, and detectability for stochastic linear systems. Then, the long-term behavior of the associated Riccati equations is analyzed under stabilizability and detectability conditions. Subsequently, a periodic mean-field stochastic LQ problem is formulated and solved. Finally, its optimal pair is shown to be the turnpike limit of the initial optimal control problem.