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Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems

Zhong-Jie Han, E. Zuazua, Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems (2021)

Abstract: This paper is devoted to analysing the explicit slow decay rate and turnpike in the infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Assume that some weak observability or controllability are satisfied, by which, the lower and upper bounds of the corresponding algebraic Riccati operator are estimated, respectively. 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 the LQ optimal control problems constraint to networks of onedimensional wave equations and also some multi-dimensional ones with local controls which lack of GCC (Geometric Control Condition).

Read Full Paper

Arxiv: 2108.10240

Tags:
optimal control problemsRiccati operatorslow decay rateturnpike propertyweak controllability and observability
Last updated on March 17, 2022

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  • Protected: Model Predictive Control with Random Batch Method for Linear-Quadratic Optimal Control: Introduction and Matlab Implementation
  • Benasque Workshop-Summer School: PDE’s, Optimal Design and Numerics
  • A framework for randomized time-splitting in linear-quadratic optimal control
  • Nonuniqueness of minimizers for semilinear optimal control problems
  • Enrique Zuazua awarded 2022 W.T. and Idalia Reid Prize
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