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On Bang-bang Controls for Some Nonlinear Systems

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

On Bang-bang Controls for Some Nonlinear Systems

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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.