Moments method in problems of optimal control of nonlinear models of logistic type

S.V. Chernyshenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0002-2852-6878

Abstract


We investigate the problem of optimal control of two nonlinear models of mathematical ecology: logistic model and model of development in adversary environment. We consider four statements of optimal control problem, two criteria of quality (quadratic and linear ones). The solution is obtained either analytically, or numerically, by iterative approximations method.

References


Alekseev V.M., Tikhomirov V.M., Fomin S.V. Optimal Control, Nauka, 1979. (in Russian)

Antomonov Yu.G. (ed.) Methods of analysis and synthesis of biologic control systems, Vyshcha shkola, 1983. (in Russian)

Bellman R. Dynamic Programming, Izd-vo inostr. lit., 1960. (in Russian)

Van-Rijn M. "On some theoretical and methodological aspects of environment problem", Economical and extra-economical estimate of human influence on environment, 1981; pp. 80-83. (in Russian)

Glushkov V.M., Dobrov G.M., Tereshchenko V.I. Conversations on Control, Nauka, 1974. (in Russian)

Gurman V.I. (ed.) Models of natural resources control, Nauka, 1981. (in Russian)

Zaslavskii B.G., Poluektov R.A. Control of ecologic systems, Nauka, 1988. (in Russian)

Krasovskii N.N. Theory of motion control, Nauka, 1968. (in Russian)

Novoseltsev V.N. Control Theory and Biosystems, Nauka, 1978. (in Russian)

Pontriagin L.S., Boltianskii G., Gamkrelidze R.V., Mishchenko Ye.F. Mathematical theory of optimal processes, Nauka, 1969. (in Russian)

Svirezhev Yu.M. "On mathematical models of biological populations and related problems of control and opimization", Matem. model. v biologii, 1975; pp. 30-52. (in Russian)

Timchenko I.Ye., Igumnova Ye.M., Primalennyi A.A. Control of ecological-economical systems, Gidrofizika, 1999. (in Russian)

Travleev A.P. "Scientific bases of technogenic biogeocenology", Biogeocenologic researches of forests of technogenic landscapes of steppe zone, 1989; pp. 4-9. (in Russian)

Fedorenko R.P. Approximate solving of optimal control problems, Nauka, 1978. (in Russian)

Kholing K.S. (ed.) Ecological systems. Adaptive estimation and control, Mir, 1981. (in Russian)

Chernyshenko S.V. "Iterative method of reduction of nonlinear optimal control problem to moments problem", Diff. Equat. and their Applic., Dnipropetrovsk, 1982; pp. 132-138. (in Russian)

Chernyshenko S.V. "Theorem on convergence of combined Newton-Kantorovich method", Methods of nonlinear problem solving and data processing, Dnipropetrovsk, 1985; pp. 193-199. (in Russian)

Chernyshenko S.V. "Some mathematical aspects of optimization problem of pesticide expenses at oppression of pest population", Problems of steppe afforestation and sci. bases of forest recultiv. of lands, Dnipropetrovsk, 1985; pp. 104-110. (in Russian)

Chernyshenko S.V. "Modelling of concurrent substitutions in phytocenosises", Ecology and Noospherology, 2000; 9(1): pp. 107-121. (in Russian)

Chernyshenko S.V. "Problems of optimal control of forest recultivation processes for disturbed lands", Ecology and Noospherology, 2003; 13(1-2): pp. 136-150. (in Russian)

Gragg U.B., Stewart G.W. "A stable variant of the secant method for solving nonlinear equations", SIAM J. Numer. Anal., 1976; 13(6): pp. 889-903. doi:10.1137/0713070

Hoppensteadt F.C. Mathematical methods of population biology, Cambridge Univ. Press, 1982.

Krebs C.J. Ecological methodology, Addison Wesley, 1999.

Martinez J.M., Lopes T.S. "Combination of the sequential secant method and Broyden's method with projected updates", Computing, 1980; 25(4): pp. 379-386. doi:10.1007/BF02285232




DOI: https://doi.org/10.15421/240819

  

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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