Tropical algebra for noise removal and optimal control

Autor: Chun-Mei Gong, Jiao Peng, Jing Wang
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Journal of Low Frequency Noise, Vibration and Active Control, Vol 42 (2023)
Druh dokumentu: article
ISSN: 1461-3484
2048-4046
14613484
DOI: 10.1177/14613484221126360
Popis: Algorithms for noise removal are either complex or ineffective, and the optimal control with inequality constrains makes the algorithm even more complex. Now the condition is changed completely, and the tropical algebra is an extremely simple tool for this purpose. The tropical algebra-based filter has obvious advantages over traditional ones, and an inequality constrain can be converted to a tropical polynomial, making the tropical algebra much attractive in engineering applications. In this paper, idempotents on multiplicative semigroups of tropical matrices are studied. First, the concepts of tropical algebra and the semigroup of tropical matrices under multiplication are introduced. Second, the structure of idempotents on the semigroup of 3 × 3 tropical matrices under multiplication is given. Finally, as examples, the tropical addition is used as a filter for noise removal, and a simple optimization is given where the constraint is given by the tropical algebra. The paper has opened the path for a new way to noise removal and optimization.
Databáze: Directory of Open Access Journals
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