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2013 On Bang-bang Controls for Some Nonlinear Systems
K. V. Sklyar , G. M. Sklyar , Yu. I. Karlovich
Commun. Math. Anal. 14(2): 163-178 (2013).


In the paper we consider the class of nonlinear $n$-dimensional control systems that can be mapped to linear ones by change of variables and an additive change of control ($A$-linearizable systems). We show that for sufficiently small initial points the transferring to the origin is possible by means of bang-bang controls with no more than $n-1$ points of switching. Moreover in some cases such a transferring is extremal in the sense of time optimality. These results are based on technique of the power Markov min-problem. An algorithm of searching the mentioned above bang-bang controls is also given.


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K. V. Sklyar . G. M. Sklyar . Yu. I. Karlovich . "On Bang-bang Controls for Some Nonlinear Systems." Commun. Math. Anal. 14 (2) 163 - 178, 2013.


Published: 2013
First available in Project Euclid: 20 December 2012

zbMATH: 1258.93048
MathSciNet: MR3011527

Primary: 93B28
Secondary: 49K15 , 93B17

Keywords: $A$-linearizable system , bang-bang controls , power min-problem , time optimality

Rights: Copyright © 2013 Mathematical Research Publishers

Vol.14 • No. 2 • 2013
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