Analysis of linear‐quadratic optimal control via a hybrid control lens

Linear‐quadratic regulator (LQR) is a landmark problem in the field of optimal control, which is investigated based on the method of hybrid dynamic system and continuous‐time optimization algorithms. We show that the above‐mentioned hybrid system converges exponentially to the optimal feedback gain...

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Veröffentlicht in:Asian journal of control Jg. 27; H. 4; S. 1914 - 1925
Hauptverfasser: Feng, Lechen, Ni, Yuan‐Hua
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hoboken Wiley Subscription Services, Inc 01.07.2025
Schlagworte:
Algorithms
Dynamical systems
forward‐Euler method
Hybrid control
hybrid dynamic system
Hybrid systems
hybrid‐dynamics‐based gradient descent
linear‐quadratic regulator
Optimal control
Optimization
Zeno‐free
ISSN:1561-8625, 1934-6093
Online-Zugang:Volltext
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Zusammenfassung:Linear‐quadratic regulator (LQR) is a landmark problem in the field of optimal control, which is investigated based on the method of hybrid dynamic system and continuous‐time optimization algorithms. We show that the above‐mentioned hybrid system converges exponentially to the optimal feedback gain with any order, and the solution trajectory is Zeno‐free. Then, the forward‐Euler method is utilized to discretize the hybrid system, and a new algorithm called hybrid dynamics‐based gradient descent (HGD) is proposed that could converge to the optimal controller exponentially.
Bibliographie:Funding information
This work is supported in part by the National Natural Science Foundation of China (62173191).
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ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.3551