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Local and global controllability for nonlinear systems. (English) Zbl 0552.93009

Several results concerning local and global controllability of nonlinear systems of the form \(\dot x=f(x)+ug(x)\), \(x\in {\mathbb{R}}^ n\), with unbounded control functions are presented. More precisely, the author states two conditions for global controllability in the case \(g(x)=b=const.\), \(n=2\). Furthermore, the Hermes-Sussmann condition for local controllability is rederived in the case \(n=2\). Finally, the global controllability conditions are extended to the case \(g(x)=b=const.\), n arbitrary. The method is based on the use of sequences of control functions which approximate Dirac impulses.
Reviewer: A.Bacciotti

MSC:

93B05 Controllability
93B03 Attainable sets, reachability
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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References:

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