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Scientific paper - Original scientific paper
An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem
Algorithms, 16 (2023), 1; 1-15. https://doi.org/10.3390/a16010048
Milić, Vladimir; Kasać, Josip; Lukas, Marin

Institutional repository: Repository of Faculty of Mechanical Engineering and Naval Architecture University of Zagreb

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Milić, V., Kasać, J. & Lukas, M. (2023). An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem. Algorithms, 16. (1), 1-15. doi: 10.3390/a16010048

Milić, Vladimir, et al. "An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem." Algorithms, vol. 16, no. 1, 2023, pp. 1-15. https://doi.org/10.3390/a16010048

Milić, Vladimir, Josip Kasać and Marin Lukas. "An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem." Algorithms 16, no. 1 (2023): 1-15. https://doi.org/10.3390/a16010048

Milić, V., Kasać, J. and Lukas, M. (2023) 'An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem', Algorithms, 16(1), pp. 1-15. doi: 10.3390/a16010048

Milić V, Kasać J, Lukas M. An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem. Algorithms [Internet]. 2023 January 10 [cited 2024 July 31];16(1):1-15. doi: 10.3390/a16010048

V. Milić, J. Kasać and M. Lukas, "An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem", Algorithms, vol. 16, no. 1, pp. 1-15, January 2023. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:235:790750. [Accessed: 31 July 2024]

Metadata
Title (english)An Algorithm for Solving Zero-Sum Differential Game Related to the Nonlinear H∞ Control Problem
AuthorVladimir Milić
AuthorJosip Kasać
AuthorMarin Lukas
Author's institutionUniversity of Zagreb
Faculty of Mechanical Engineering and Naval Architecture
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Mechanical Engineering
Abstract (english)
This paper presents an approach for the solution of a zero-sum differential game associated with a nonlinear state-feedback H∞ control problem. Instead of using the approximation methods for solving the corresponding Hamilton–Jacobi–Isaacs (HJI) partial differential equation, we propose an algorithm that calculates the explicit inputs to the dynamic system by directly performing minimization with simultaneous maximization of the same objective function. In order to achieve numerical robustness and stability, the proposed algorithm uses: quasi-Newton method, conjugate gradient method, line search method with Wolfe conditions, Adams approximation method for time discretization and complex-step calculation of derivatives. The algorithm is evaluated in computer simulations on examples of first- and second-order nonlinear systems with analytical solutions of H∞ control problem.
Languageenglish
Publication typeScientific paper - Original scientific paper
Publication statusPublished
Peer reviewPeer review - international
Publication versionPublished version
Journal titleAlgorithms
Numberingvol. 16, no. 1, pp. 1-15, 48
BPC0 EUR
e-ISSN1999-4893
DOIhttps://doi.org/10.3390/a16010048
URN:NBNurn:nbn:hr:235:790750
Publication2023-01-10
Document URLhttps://www.mdpi.com/1999-4893/16/1/48
Type of resourceText
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-07-17 14:46:55