Optimal Control of Several Motion Models

Tan H. Cao (), Nilson Chapagain (), Haejoon Lee (), Thi Phung () and Nguyen Nang Thieu ()
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Tan H. Cao: SUNY Korea
Nilson Chapagain: SUNY Korea
Haejoon Lee: SUNY Korea
Thi Phung: Wayne State University
Nguyen Nang Thieu: SUNY Korea

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 1, No 3, 36 pages

Abstract: Abstract This paper is devoted to studying the dynamic optimization of several controlled crowd motion models in general planar settings. A set of necessary optimality conditions for optimal control problems involving crowd motion models with multiple agents and obstacles was derived and thoroughly analyzed. The analysis provides valuable insights into the primal and dual elements, as well as the degeneracy phenomena. The paper proposes several effective algorithms based on these necessary optimality conditions and presents various nontrivial illustrative examples along with their simulations. The implementation of all the considered motion models can be found via the link: https://github.com/tancao1128/Optimal_Control_of_Several_Motion_Models .

Keywords: Optimal control; Sweeping process; Crowd motion model; Discrete approximation; Necessary optimality conditions; Variational analysis; Generalized differentiation; 49J52; 49J53; 49K21; 49M25; 90C30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02610-x

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