TY - JOUR
T1 - Time Dependent Stabilization of a Hamiltonian System
AU - Yahalom, Asher
AU - Puzanov, Natalia
N1 - Publisher Copyright:
© Published under licence by IOP Publishing Ltd.
PY - 2021/2/3
Y1 - 2021/2/3
N2 - In this paper we consider the unstable chaotic attractor of a Hamiltonian system with Toda lattice potential and stabilize it by an integral form control. In order to obtain stability results, we use a control function in an integral form: =u(t)=int{0}{t} k(t, s) X(s) d s SRC=JPCS17301012089ieqn1.gif in which all the back story of the process X(t) is taken into consideration. Using the exponential kernel =k(t, s)=e{-beta(t-s)} SRC=JPCS17301012089ieqn2.gif, we replace the study of integro-differential system of order 4 with an analysis of 5th order system of ordinary differential equations (without integrals). Numerical solution of the resulting system leads to the asymptotically stabilization of the unstable fixed point.
AB - In this paper we consider the unstable chaotic attractor of a Hamiltonian system with Toda lattice potential and stabilize it by an integral form control. In order to obtain stability results, we use a control function in an integral form: =u(t)=int{0}{t} k(t, s) X(s) d s SRC=JPCS17301012089ieqn1.gif in which all the back story of the process X(t) is taken into consideration. Using the exponential kernel =k(t, s)=e{-beta(t-s)} SRC=JPCS17301012089ieqn2.gif, we replace the study of integro-differential system of order 4 with an analysis of 5th order system of ordinary differential equations (without integrals). Numerical solution of the resulting system leads to the asymptotically stabilization of the unstable fixed point.
UR - http://www.scopus.com/inward/record.url?scp=85101541083&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/1730/1/012089
DO - 10.1088/1742-6596/1730/1/012089
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AN - SCOPUS:85101541083
SN - 1742-6588
VL - 1730
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
IS - 1
M1 - 012089
T2 - 9th International Conference on Mathematical Modeling in Physical Sciences, IC-MSQUARE 2020
Y2 - 7 September 2020 through 10 September 2020
ER -