Uniform Turnpike property and singular limits
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Fecha
2024-04
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Springer Science and Business Media B.V.
Resumen
Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of our proof is the justification of the uniform exponential stabilization of the corresponding Riccati equations, which is derived from the uniform null control properties of the model. Then, we focus on a heat equation with rapidly oscillating coefficients. In the one-dimensional setting, we obtain a uniform turnpike property with respect to the highly oscillatory heterogeneous medium. Afterward, we establish the homogenization of the turnpike property. Finally, our results are validated by numerical experiments
Palabras clave
Long time behavior
Optimal control problems
Rapidly oscillating linear parabolic equation
Singular limits problems
Turnpike property
Uniform controllability
Optimal control problems
Rapidly oscillating linear parabolic equation
Singular limits problems
Turnpike property
Uniform controllability
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Materias
Cita
Hernández, M., & Zuazua, E. (2024). Uniform Turnpike property and singular limits. Acta Applicandae Mathematicae, 190(1). https://doi.org/10.1007/S10440-024-00640-7