Open Access
2009 Convexity of the Set of Fixed Points Generated by Some Control Systems
Vadim Azhmyakov
J. Appl. Math. 2009: 1-14 (2009). DOI: 10.1155/2009/291849


We deal with an application of the fixed point theorem for nonexpansive mappings to a class of control systems. We study closed-loop and open-loop controllable dynamical systems governed by ordinary differential equations (ODEs) and establish convexity of the set of trajectories. Solutions to the above ODEs are considered as fixed points of the associated system-operator. If convexity of the set of trajectories is established, this can be used to estimate and approximate the reachable set of dynamical systems under consideration. The estimations/approximations of the above type are important in various engineering applications as, for example, the verification of safety properties.


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Vadim Azhmyakov. "Convexity of the Set of Fixed Points Generated by Some Control Systems." J. Appl. Math. 2009 1 - 14, 2009.


Published: 2009
First available in Project Euclid: 2 March 2010

zbMATH: 1175.93102
MathSciNet: MR2556825
Digital Object Identifier: 10.1155/2009/291849

Rights: Copyright © 2009 Hindawi

Vol.2009 • 2009
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