MODIFICATIONS OF PROJECTION METHODS IN BILINEAR OPTIMAL CONTROL PROBLEMS // BSU bulletin. Mathematics, Informatics. - 2021. №2. . - С. 44-60.

MODIFICATIONS OF PROJECTION METHODS IN BILINEAR OPTIMAL CONTROL PROBLEMS

Работа выполнена при финансовой поддержке Бурятского госуниверситета, проект 2021 г.

In the class of bilinear optimal control problems, methods of nonlocal im- provement of control are considered based on non-standard formulas for the increment of the objective functional that do not contain the remainder of the expansions. Such formulas make it possible to construct conditions for improving control in the form of special fixed point problems of projection control operators. The considered form of control improvement conditions in the form of fixed point problems in the control space makes it possible to apply and modify the fixed point methods known in computational mathematics to find improving controls and construct relaxation control sequences. The conditions for improvement and optimality of control based on fixed point problems are analyzed. Iterative processes of searching for improving controls and constructing relaxation sequences of controls are constructed. The results of analytical and numerical comparison of the effectiveness of the proposed projection optimization methods with the known projection methods on test examples are presented.

bilinear controlled system; operation of projecting; conditions for improving control; fixed point problem; iterative algorithm.

Mohler R. R. Bilinear Control Processes: with Applications to Engineering, Ecology and Medicine. Academic Press, New York, London, 1973. 223 p.

Rudik A. P. Nuclear Reactors and the Pontryagin Maximum Principle. Atomiz- dat, Moscow, 1970. 224 p.

Khailov E. N. On Extremal Controls of a Homogeneous Bilinear System Con- trolled in a Positive Orthant. Trudy MIAN. 1998. (220). Pp. 217–235.

Srochko V. A., Aksenyushkina E. V. Problems of Optimal Control for a Bilinear System of Special Structure // The Bulletin of the Irkutsk State University. Series Mathematics. 2016. (15). Pp. 78–91.

Srochko V. A. Iterative Methods for Solving Optimal Control Problems. Fizmat- lit, Moscow, 2000. 160 p.

Vasiliev O. V. Optimization Methods. World Federation Publishers Company INC, Atlanta, 1996. 276 p.

Samarskii A., Gulin A. Numerical Methods. Nauka, Moscow, 1989. 432 p

Buldaev A. S. Operator Equations and Maximum Principle Algorithms in Optimal Control Problems. Bulletin of Buryat State University. Mathematics, Informatics. 2020. 1. P. 35–53.

Bartenev O. V. Fortran for Professionals. IMSL Math Library. Part 2. Dialogue-MIFI, Moscow, 2001. 320 p.

Rudik A. P. Nuclear Reactors and the Pontryagin Maximum Principle. Atomiz- dat, Moscow, 1970. 224 p.

Khailov E. N. On Extremal Controls of a Homogeneous Bilinear System Con- trolled in a Positive Orthant. Trudy MIAN. 1998. (220). Pp. 217–235.

Srochko V. A., Aksenyushkina E. V. Problems of Optimal Control for a Bilinear System of Special Structure // The Bulletin of the Irkutsk State University. Series Mathematics. 2016. (15). Pp. 78–91.

Srochko V. A. Iterative Methods for Solving Optimal Control Problems. Fizmat- lit, Moscow, 2000. 160 p.

Vasiliev O. V. Optimization Methods. World Federation Publishers Company INC, Atlanta, 1996. 276 p.

Samarskii A., Gulin A. Numerical Methods. Nauka, Moscow, 1989. 432 p

Buldaev A. S. Operator Equations and Maximum Principle Algorithms in Optimal Control Problems. Bulletin of Buryat State University. Mathematics, Informatics. 2020. 1. P. 35–53.

Bartenev O. V. Fortran for Professionals. IMSL Math Library. Part 2. Dialogue-MIFI, Moscow, 2001. 320 p.