Geodesic
The hypodifferential descent method in the problem of constructing an optimal control
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2016), pp. 106-125 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper considers the problem of optimal control of an object, whose motion is described by a system of ordinary differential equations. The original problem is reduced to the problem of unconstrained minimization of a nonsmooth functional. For this, the necessary minimum conditions in terms of subdifferential and hypodifferential are determined. A class of problems, for which these conditions are also sufficient, is distinguished. On the basis of these conditions, the subdifferential descent method and the hypodifferential descent method are applied to the considered problem. The application of the methods is illustrated by numerical examples. Refs 16. Tables 4.
Keywords: nonsmooth functional, variational problem, program control, hypodifferential descent method. 
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A. V. Fominykh. The hypodifferential descent method in the problem of constructing an optimal control. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2016), pp. 106-125. http://geodesic.mathdoc.fr/item/VSPUI_2016_3_a9/

[1] Karelin V. V., “Penalty functions in a control problem”, Automation and Remote Control, 2004, no. 3, 483–492 | DOI | MR | Zbl

[2] Demyanov V. F., Giannessi F., Karelin V. V., “Optimal control problems via exact penalty functions”, Journal of Global Optimization, 12 (1998), 215–223 | DOI | MR | Zbl

[3] Baranov A. Y., Khazarinov Y. F., Khomenuk V. V., “Gradient optimization methods of nonlinear systems of automatic control”, Proc. “Applied Tasks of Technical Cybernetics” (1966), 307–316

[4] Kelly H. J., “Gradient theory of optimal flight paths”, ARS Journal, 30:10 (1960), 947–954 | DOI

[5] Kelly H. J., “Method of gradients”, Optimiz. techn. applic. aerospace syst., Acad. Press, New York–London, 1962, 205–254 | DOI | MR

[6] Moiseev N. N., Elements of the theory of optimal systems, Nauka Publ., M., 1975, 528 pp. (In Russian) | MR | Zbl

[7] Egorov A. I., Basics of the control theory, Fizmatlit Publ., M., 2004, 504 pp. (In Russian) | MR

[8] Antipin A. S., Khoroshilova E. V., “Linear programming and dynamics”, Proc. of the Institute of Mathematics and Mechanic UrO RAS, 19, no. 2, 2013, 7–25 | MR

[9] Demyanov V. F., Rubinov A. M., Approximate methods of solving extremal problems, Leningrad University Publ., L., 1968, 178 pp. (In Russian)

[10] Tamasyan G. Sh., “Numerical methods in problems of calculus of variations for functionals depending on higher order derivatives”, Journal of Mathematical Sciences, 188:3 (2013), 299–321 | DOI | MR | Zbl

[11] Demyanov V. F., Rubinov A. M., Basics of nonsmooth analysis and quasidifferentiable optimization, Nauka Publ., M., 1990, 432 pp. (In Russian) | MR

[12] Daugavet V. A., Numerical methods of quadratic programming, Saint Petersburg State University Publ. House, Saint Petersburg, 2001, 128 pp. (In Russian)

[13] Krasovskij N. N., Motion control theory, Nauka Publ., M., 1968, 476 pp. (In Russian) | Zbl

[14] Kumar V., “A control averaging technique for solving a class of singular optimal control problems”, Intern. J. Control, 23:3 (1976), 361–380 | DOI | Zbl

[15] Srochko V. A., Khamidulin R. G., “The method of successive approximations in optimal control problems with boundary conditions”, USSR Computational Mathematics and Mathematical Physics, 188:2 (1986), 113–122 | DOI | MR

[16] Evtushenko Yu. G., Methods for solving extreme problems and their application to systems of optimization, Nauka Publ., M., 1982, 432 pp. (In Russian) | MR