TY - JOUR
A2 - Agrachev, Andrei
AU - Azhmyakov, Vadim
PY - 2009
DA - 2009/10/21
TI - Convexity of the Set of Fixed Points Generated by Some Control Systems
SP - 291849
VL - 2009
AB - 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.
SN - 1110-757X
UR - https://doi.org/10.1155/2009/291849
DO - 10.1155/2009/291849
JF - Journal of Applied Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -