Archive of Issues
Russia Yekaterinburg
Section  Mathematics 
Title  On the solution of control problems with fixed terminal time 
Author(s)  Ushakov V.N.^{a}, Ershov A.A.^{a} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a} 
Abstract  We consider the nonlinear controlled system in a finitedimensional Euclidean space in a finite time interval. We study the problem of a system approaching a given compact set in finite time. Approximate solution of the approaching problem is discussed. The approach used to construct an approximate solution is based on constructions based on the notion of a set of solvability of the approaching problem. The concept of correcting control with and without additional operating influences is introduced. We propose a scheme of approximate backward construction of the solvability set, as well as the scheme of control software, which allows finding approximately a solution to the approaching problem. In it, the operating influence breaks down into “main” and “correcting”. An estimate of the deviation of the operated system from the target set at the final moment is constructed and it is shown that the use of additional correcting control in the control process can essentially improve the result of control. 
Keywords  control problem, approaching problem, correcting control, controlled system, integral funnel, set of solvability 
UDC  517.977.58 
MSC  49M25 
DOI  10.20537/vm160409 
Received  17 October 2016 
Language  Russian 
Citation  Ushakov V.N., Ershov A.A. On the solution of control problems with fixed terminal time, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 4, pp. 543564. 
References 

Full text 