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An LQR-Lagrange Algorithm Generated by Interdisciplinary Integration with Optimal Control and Optimization
  • Molin An,
  • Xueshan Han
Molin An
Shandong University
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Xueshan Han
Shandong University

Corresponding Author:xshan@sdu.edu.cn

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Abstract

Interdisciplinary integration is a superior method to improve the optimization algorithm. In this paper, control theory and optimization are combined, and the optimization algorithm is regarded as a control process. Based on the premise of optimal control, the state equation corresponding to Lagrange Algorithm is established with the Karush-Kuhn-Tucker (KKT) conditions as the objective. As an optimal control method, Linear Quadratic Regulator (LQR) is utilized to control the calculation process, and an innovative LQR-Lagrange Algorithm is proposed. The Lyapunov stability criterion is applied to analyze the convergence, and it is proved that the proposed LQR-Lagrange Algorithm is bound to converge as long as the parameter matrices and are positive definite. The analysis indicates that the influence of parameters in LQR-Lagrange Algorithm on the calculation speed is monotonic, and the elements in and has no effect on the convergence. Therefore, the proposed algorithm has a monotonic and user-friendly parameter tuning strategy. The significance and advantages of interdisciplinary integration with control theory and optimization are discussed in the end.
Submitted to Optimal Control, Applications and Methods
29 May 2024Submission Checks Completed
29 May 2024Assigned to Editor
29 May 2024Review(s) Completed, Editorial Evaluation Pending
06 Jul 2024Editorial Decision: Revise Minor
19 Aug 20241st Revision Received
21 Aug 2024Submission Checks Completed
21 Aug 2024Assigned to Editor
21 Aug 2024Review(s) Completed, Editorial Evaluation Pending
23 Aug 2024Reviewer(s) Assigned
27 Sep 2024Editorial Decision: Accept