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Russia Yekaterinburg
Section  Mathematics 
Title  Numerical investigation of a nonlinear timeoptimal 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 Sciences^{a}, Ural Federal University^{b} 
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 timeoptimal 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, timeoptimal 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 timeoptimal problem, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 4, pp. 429444. 
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