Communications in Mathematical Analysis

On Bang-bang Controls for Some Nonlinear Systems

K. V. Sklyar , G. M. Sklyar , and Yu. I. Karlovich

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Abstract

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.

Article information

Source
Commun. Math. Anal., Volume 14, Number 2 (2013), 163-178.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.cma/1356039039

Mathematical Reviews number (MathSciNet)
MR3011527

Zentralblatt MATH identifier
1258.93048

Subjects
Primary: 93B28
Secondary: 93B17: Transformations 49K15: Problems involving ordinary differential equations

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

Citation

Sklyar , K. V.; Sklyar , G. M.; Karlovich , Yu. I. On Bang-bang Controls for Some Nonlinear Systems. Commun. Math. Anal. 14 (2013), no. 2, 163--178. https://projecteuclid.org/euclid.cma/1356039039


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