Aplicação da Função de Lyapunov num Problema de Controle Ótimo de Pragas
DOI:
https://doi.org/10.5540/tema.2002.03.02.0083Abstract
Para reduzir a população de pragas na lavoura e substituir agrotóxicos químicos, cada vez mais o agricultor busca o controle biológico. Usualmente, para realizar o controle biológico, parasitóides e predadores são criados em laboratórios. Ao atingir um número adequado de inimigos naturais eles são liberados com a expectativa que um sistema presa-predador ou hospedeiro-parasitóide seja criado. Em [6] mostra-se que funções de Lyapunov podem ser usadas para investigar a estabilidade de vários modelos presa-predador. Neste trabalho foi considerado um problema de otimização de controle que utiliza, por um lado uma função de Lyapunov e, por outro lado as idéias de otimização de Bellman [1]. Neste problema, foi encontrada uma função de controle ótimo que determina a quantidade de inimigos naturais de pragas que devem ser liberados na lavoura, mantendo a população de pragas abaixo do nível de danos econômicos.References
[1] R. Bellman, “Dynamic Programming”, Princeton, New Jersey, 1957.
A.E. Bryson and Y.C. Ho, “Applied Optimal Control”, Blaisdell, Waltham. Mass., 1969.
P. DeBach, The scope of biological control, in: “Biological Control of Insects Pests and Weeds” (P. DeBach Ed.), pp.3-20, Chapman & Hall, London, U.K., 1964.
D. Dent, Ed., Integrated Pest Management, pp. 356, Chapman and Hall, London, U.K.
R. Freeman and J, Primbs, Control Lyapunov functions: New ideas from and old sourse, in “Proceedings of the 35 IEEE Conference on Decision and Control”, pp. 3926-3931, Kobe, Japan, 1996.
B.S. Goh, “Management and Analisys of Biological Population”, Elsevier Scientific Publishing company, Amsterdam, 1980.
G.W. Harrison, Global Stability of predator-prey interactions, J. Math. Biology, 8 (1979), 159-171.
A.M. Letov, The analytical design of control systems, Automation and Remote Control, 22 (1961), 363-372.
M. Rafikov e C.C. Feltrin, Otimização do controle biológico de pragas: método de funções de Lyapunov, em “Proceedings do Congresso Latino Americano de Biomatemática, X ALAB-V ELAEM”, pp. 71-80, UNICAMP, Campinas, 2001.
E.D. Sontag, A universal construction of Artstein’s theorem on nonlinear stabilization, Syst. Contr. Lett., 13, No. 2 (1989), 117-123.
V. Volterra, ”Leçons sur la Théorie Mathematique de la Lutte Pour la Vie”, Gauthier-Villars, Paris, 1931.
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