TY - GEN
T1 - Providing a basin of attraction to a target region by computation of Lyapunov-like functions
AU - Ratschan, Stefan
AU - She, Zhikun
PY - 2006
Y1 - 2006
N2 - In this paper, we present a method for computing a basin of attraction to a target region for non-linear ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly, and iteratively reduces the relaxation error by recursively decomposing the state space into hyper-rectangles. Tests on an implementation are promising.
AB - In this paper, we present a method for computing a basin of attraction to a target region for non-linear ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly, and iteratively reduces the relaxation error by recursively decomposing the state space into hyper-rectangles. Tests on an implementation are promising.
UR - https://www.scopus.com/pages/publications/50249132522
U2 - 10.1109/ICCCYB.2006.305705
DO - 10.1109/ICCCYB.2006.305705
M3 - 会议稿件
AN - SCOPUS:50249132522
SN - 1424400716
SN - 9781424400713
T3 - 2006 IEEE International Conference on Computational Cybernetics, ICCC
BT - 2006 IEEE International Conference on Computational Cybernetics, ICCC
T2 - 2006 IEEE International Conference on Computational Cybernetics, ICCC
Y2 - 20 August 2006 through 22 August 2006
ER -