BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, , VARIATIONAL OPTIMALITY CONDITION IN THE CONTROL PROBLEM OF HYPERBOLIC EQUATIONS WITH DYNAMIC BOUNDARY CONDITIONS // BSU Bulletin. Mathematics, Informatics. - 2021. №1. . - С. 13-23.
Title:
VARIATIONAL OPTIMALITY CONDITION IN THE CONTROL PROBLEM OF HYPERBOLIC EQUATIONS WITH DYNAMIC BOUNDARY CONDITIONS
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Annotation:
The paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a quadratic cost functional and boundary condi- tions determined from controlled bilinear ordinary differential equations. These ordi- nary differential equations are linear for state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology, social demographics, and population dynamics. General optimal control methods are used, normally, for these problems because of bilinear ordinary differential equations. The problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact second-order increment formu- las for the cost functional. This treatment allows using some efficient optimal control methods for the problem.
Keywords:
hybrid systems; hyperbolic equations; non-classic increment formulas; reduction of optimal control problems.
List of references:
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Srochko V. A., Antonik V. G. Optimality Conditions for Extremal Controls in Bilinear and Quadratic Problems. Russian Mathematics. 2016. Vol. 60. Pp. 75–80. DOI:10.3103/S1066369X1605008X.
Srochko V. A., Aksenyushkina E. V. Parameterization of Some Linear Systems Control Problems. Bulletin of Irkutsk State University. Series Mathematics. 2019. Vol. 30. Pp. 83–98. DOI:10.26516/1997-7670.2019.30.83.
Demidenko N. Optimal Control of Thermal-engineering Processes in Tube Fur- naces. Chem. Petrol. Eng. 2006. Vol. 186, no. 42. Pp. 128–130.
Petukhov A. Modeling of Threshold Effects in Social Systems Based on Nonlin- ear Dynamics. Cybernetics and Physics. 2019. Vol. 8, no. 4. Pp. 277–287.
Arguchintsev A. V., Poplevko V. P. Optimal Control of Initial Conditions in the Canonical Hyperbolic System of the First Order Based on Nonstandard Increment Formulas. Russian Mathematics. 2008. Vol. 52. Pp. 1–7. DOI:10.1007/s11982-008- 1001-1.
Rozonoer L. I. L. S. Pontryagin’s Maximum Principle in the Theory of Optimum Systems. Part I. Autom. and Remote Contr. 1959. Vol. 20. Pp. 1288–1302.
Riznichenko G. Yu., Rubin A. B. Mathematical Methods in Biology and Ecol- ogy. Biophysical Dynamics of Reproductive Processes. Part 1. Moscow: Urait Publ., 2019. 210 p.
Gabasov R., Kirillova F. M. Singular Optimal Controls. Moscow: URSS Publ., 2018. 256 p.
Godunov S. K. Equations of Mathematical Physics. Moscow: Nauka Publ., 1979. 392 p.
Rozhdestvenskii B. L., Yanenko N. N. Systems of Quasilinear Equations and Their Applications to Gas Dynamics. Moscow: Nauka Publ. 1968. 686 p.
Vasilyev O. V. Lectures on Optimization Methods. Irkutsk: Irkutsk State Univ. Publ., 1994. 340 p.
Srochko V. A. Iterative Methods for Solving Optimal Control Problems. Mos- cow: Fizmatlit Publ., 2000. 160 p.
Rao A. V. A Survey of Numerical Methods for Optimal Control. Advances in Astronautical Sciences. 2009. Vol. 135. Pp. 1–32.
Golfetto W. A., Silva Fernandes S. A Review of Gradient Algorithms for Nu- merical Computation of Optimal Trajectories. J. Aerosp. Technol. Manag. 2012. Vol. 4. Pp. 131–143.
Buldaev A. S. Perturbation Methods in Problem of the Improvement and Opti- mization of the Controlled Systems. Ulan-Ude: Buryat State Univ. Publ., 2008. 260 p.
Buldaev A. S. Operator Equations and Maximum Principle Algorithms in Op- timal Control Problems. Bulletin of Buryat State University. Mathematics, Informatics. 2020. No. 1. Pp. 35–53. DOI: 10.18101/2304-5728-2020-1-35–53.
Srochko V. A., Antonik V. G. Optimality Conditions for Extremal Controls in Bilinear and Quadratic Problems. Russian Mathematics. 2016. Vol. 60. Pp. 75–80. DOI:10.3103/S1066369X1605008X.
Srochko V. A., Aksenyushkina E. V. Parameterization of Some Linear Systems Control Problems. Bulletin of Irkutsk State University. Series Mathematics. 2019. Vol. 30. Pp. 83–98. DOI:10.26516/1997-7670.2019.30.83.
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