Communications in Mathematical Analysis

On Bang-bang Controls for Some Nonlinear Systems

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

Full-text: Open access


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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

Export citation