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Russia Yekaterinburg
Section Mathematics
Title Numerical investigation of a nonlinear time-optimal problem
Author(-s) Kandoba I.N.ab, Koz’min I.V.ab, Novikov D.A.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract The questions of constructing admissible controls in a problem of optimal control of a nonlinear dynamic system under constraints on its current phase state are discussed. The dynamic system under consideration describes the controlled motion of a carrier rocket from the launching point to the time when the carrier rocket enters a given elliptic earth orbit. The problem consists in designing a program control for the carrier rocket that provides the maximal value of the payload mass led to the given orbit and the fulfillment of a number of additional restrictions on the current phase state of the dynamic system. The additional restrictions are due to the need to take into account the values of the dynamic velocity pressure, the attack and slip angles when the carrier rocket moves in dense layers of the atmosphere. In addition it is required to provide the fall of detachable parts of the rocket into specified regions on the earth surface. For carrier rockets of some classes, such a problem is equivalent to a nonlinear time-optimal problem with phase constraints. Two algorithms for constructing admissible controls ensuring the fulfillment of additional phase constraints are suggested. The numerical analysis of these algorithms is performed. The methodological basis of one algorithm is the application of some predictive control, which is constructed without taking into account the constraints above. Another algorithm is based on special control modes. The results of numerical modeling are presented.
Keywords dynamic system, iterative method, nonlinear control system, optimal control, predictive control, time-optimal control, phase constraints, admissible control
UDC 517.977.5
MSC 49N90, 93C15
DOI 10.20537/vm180401
Received 14 November 2018
Language Russian
Citation Kandoba I.N., Koz’min I.V., Novikov D.A. Numerical investigation of a nonlinear time-optimal problem, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 4, pp. 429-444.
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