TY - JOUR
T1 - Adaptive control of bi-directionally coupled Lorenz systems with uncertainties
AU - Wu, Yan
AU - Braselton, Jim
AU - Jin, Yao
AU - Shahat, Adel El
N1 - Publisher Copyright:
© 2018
PY - 2019/2
Y1 - 2019/2
N2 - The bi-directionally coupled Lorenz systems are linked to the modeling of a coupled double loop thermosyphon system where the mass momentum and heat exchange are both considered. As the key parameters of the system, known as Rayleigh numbers, increase, the system of differential equations predicts typical flow dynamics in a thermosyphon from heat conduction to time-dependent chaos. In many applications including the thermosyphon systems, there are uncertainties associated with mathematical models such as unmodeled dynamics and parameter variations. Also, under the high heat environment for a thermosyphon, there exist external disturbances quantitatively linked to the Rayleigh numbers. All these sources constitute uncertainties to the dynamical system. Our objective is to design adaptive controllers to stabilize the chaotic flow in each thermosyphon loop with unknown system parameters and existence of uncertainties. The controllers consist of a proportional controller with an adaptive gain and a wavelet network that reconstructs the unknown functions representing the uncertainties. Explicit stability bounds and adaptive laws for the control parameters are obtained so that the coupled Lorenz systems are globally stabilized.
AB - The bi-directionally coupled Lorenz systems are linked to the modeling of a coupled double loop thermosyphon system where the mass momentum and heat exchange are both considered. As the key parameters of the system, known as Rayleigh numbers, increase, the system of differential equations predicts typical flow dynamics in a thermosyphon from heat conduction to time-dependent chaos. In many applications including the thermosyphon systems, there are uncertainties associated with mathematical models such as unmodeled dynamics and parameter variations. Also, under the high heat environment for a thermosyphon, there exist external disturbances quantitatively linked to the Rayleigh numbers. All these sources constitute uncertainties to the dynamical system. Our objective is to design adaptive controllers to stabilize the chaotic flow in each thermosyphon loop with unknown system parameters and existence of uncertainties. The controllers consist of a proportional controller with an adaptive gain and a wavelet network that reconstructs the unknown functions representing the uncertainties. Explicit stability bounds and adaptive laws for the control parameters are obtained so that the coupled Lorenz systems are globally stabilized.
UR - http://www.scopus.com/inward/record.url?scp=85059319110&partnerID=8YFLogxK
U2 - 10.1016/j.jfranklin.2018.10.029
DO - 10.1016/j.jfranklin.2018.10.029
M3 - Article
AN - SCOPUS:85059319110
SN - 0016-0032
VL - 356
SP - 1287
EP - 1301
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
IS - 3
ER -