SLOW DECAY AND TURNPIKE FOR INFINITE-HORIZON HYPERBOLIC LINEAR QUADRATIC PROBLEMS

Zuazua Iriondo E, Han ZJ (2022)

Publication Type: Journal article

Publication year: 2022

Journal

SIAM Journal on Control and Optimization Society for Industrial and Applied Mathematics

Book Volume: 60

Pages Range: 2440-2468

Journal Issue: 4

DOI: 10.1137/21M1441985

Abstract

This paper is devoted to analyzing the explicit slow decay rate and turnpike in infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Under suitable weak observability or controllability conditions, lower and upper bounds of the corresponding algebraic Riccati operator are proved. Then based on these two bounds, the explicit slow decay rate of the closed-loop system with Riccati-based optimal feedback control is obtained. The averaged turnpike property for this problem is also further discussed. We then apply these results to LQ optimal control problems constrained to networks of one-dimensional wave equations and also some multidimensional ones with local controls which lack a geometric control condition.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Tianjin University (TJU) / 天津大学 CN China (CN)

How to cite

APA:

Zuazua Iriondo, E., & Han, Z.J. (2022). SLOW DECAY AND TURNPIKE FOR INFINITE-HORIZON HYPERBOLIC LINEAR QUADRATIC PROBLEMS. SIAM Journal on Control and Optimization, 60(4), 2440-2468. https://doi.org/10.1137/21M1441985

MLA:

Zuazua Iriondo, Enrique, and Zhong Jie Han. "SLOW DECAY AND TURNPIKE FOR INFINITE-HORIZON HYPERBOLIC LINEAR QUADRATIC PROBLEMS." SIAM Journal on Control and Optimization 60.4 (2022): 2440-2468.

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