The turnpike property and the longtime behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems

Esteve Yagüe C, Kouhkouh H, Pighin D, Zuazua Iriondo E (2022)


Publication Language: English

Publication Status: Accepted

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2022

Journal

DOI: 10.1007/s00498-022-00325-2

Open Access Link: https://arxiv.org/abs/2006.10430

Abstract

We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained controls.
We prove that, when the time horizon T tends to infinity, the value function asymptotically behaves as [katex]W(x)+cT+\lambda [/katex], , and we provide a control interpretation of each of these three terms, making clear the link with the turnpike property.

As a by-product, we obtain the long-time behavior of the solution to the associated Hamilton-Jacobi-Bellman equation in a case where the Hamiltonian is not coercive in the momentum variable. As a result of independent interest, we showed that linear-quadratic optimal control problems with constrained control enjoy a turnpike property, also particularly when the steady optimum may saturate the control constraints.

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How to cite

APA:

Esteve Yagüe, C., Kouhkouh, H., Pighin, D., & Zuazua Iriondo, E. (2022). The turnpike property and the longtime behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems. Mathematics of Control Signals and Systems. https://dx.doi.org/10.1007/s00498-022-00325-2

MLA:

Esteve Yagüe, Carlos, et al. "The turnpike property and the longtime behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems." Mathematics of Control Signals and Systems (2022).

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