Journal Article

Non-unique and non-bang-bang controls in some linear time-optimal problems

V. R. Nosov, J. A. Meda-Campaña and J. C. Gómez-Mancilla

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 29, issue 2, pages 259-269
Published in print June 2012 | ISSN: 0265-0754
Published online December 2011 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnr042
Non-unique and non-bang-bang controls in some linear time-optimal problems

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In this paper, the time-optimal control for multidimensional linear systems is studied in cases when Kalman controllability conditions does hold, but Gramkrelidze generic position condition does not. The main contribution of this study is the demonstration that time-optimal control for multidimensional linear systems is not restricted to the classical discontinuous bang-bang form with a finite number of switching points. Instead, an infinite number of controls, including continuous ones, can be used to take the system to the origin in minimum time. As an illustrative example for this class of problems, the controllable movement of material point in multidimensional space is considered.

Keywords: controllability; generic position conditions; multidimensional linear systems; time-optimal control

Journal Article.  0 words. 

Subjects: Mathematics

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