Electronic Resource
Springer
Journal of optimization theory and applications
22 (1977), S. 41-49
ISSN:
1573-2878
Keywords:
Controllability
;
nonlinear systems
;
sufficiency theorems
;
control theory
;
comparison theorems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Some sufficient conditions are presented for the controllability of general nonlinear systems. First, the controllability problem is transformed into the problem of existence of fixed points for some operator; using Schauder's theorem, it is derived that a sufficient condition for controllability is the existence of a subsetS inC n+m (T) which is invariant for a derived operator. Secondly, with the aid of the notion of comparison principle, the existence of the subsetS is guaranteed by the existence of solutions for some nonlinear integral inequality or equality equations. For example, one solution for such nonlinear integral equations is obtained under the assumption of the uniform boundedness for a nonlinear term of the differential equation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00936719
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