Time-Optimal Control Problem for a Special Class of Control Systems: Optimal Controls and Approximation in the Sense of Time Optimality

Grigory M. Sklyar (), Svetlana Yu. Ignatovich () and Sergey E. Shugaryov ()
Additional contact information
Grigory M. Sklyar: University of Szczecin
Svetlana Yu. Ignatovich: Kharkov National University
Sergey E. Shugaryov: Kharkov National University

Journal of Optimization Theory and Applications, 2015, vol. 165, issue 1, No 4, 62-77

Abstract: Abstract We consider the time-optimal control problem to the origin for a class of nonlinear systems, called dual-to-linear systems. We obtain the general description of possible optimal controls. In particular, we show that optimal controls take the values $$-1$$ - 1 , $$0$$ 0 , and $$+1$$ + 1 only and have a finite number of points of discontinuity. We describe a class of nonlinear affine control systems which can be approximated by dual-to-linear systems in the sense of time optimality.

Keywords: Nonlinear time-optimal control problem; Piecewise constant controls; Algebra of nonlinear power moments; 49K15; 93C10 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-014-0607-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0607-6

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-014-0607-6

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().