TY - JOUR
T1 - Control of multiplicative noise stochastic gene regulation systems by the attractive ellipsoid technique
AU - Lozada-Castillo, Norma
AU - Poznyak, Alexander
AU - Chairez, Isaac
PY - 2014/10
Y1 - 2014/10
N2 - This article describes the application of the so-called attractive ellipsoidal method to solve the trajectory stabilization problem for a class of genetic network systems modelled by a stochastic model. The genetic network model is described by a stochastic quasi-linear system affected by additive and multiplicative noises simultaneously. The solution of the control design provided in this study is based on a linear feedback structure. In this paper the algorithm to construct a suboptimal gain for adjusting the control design is introduced. The attractive ellipsoidal method is the key stone for designing the so-called suboptimal gain. Moreover, the practical stability of the genetic network trajectories is demonstrated on the mean and in almost sure senses. Some numerical simulations show how a set of stochastic trajectories are stabilized by the controller suggested in this study and how the predicted ellipsoid region is achieved by these trajectories.
AB - This article describes the application of the so-called attractive ellipsoidal method to solve the trajectory stabilization problem for a class of genetic network systems modelled by a stochastic model. The genetic network model is described by a stochastic quasi-linear system affected by additive and multiplicative noises simultaneously. The solution of the control design provided in this study is based on a linear feedback structure. In this paper the algorithm to construct a suboptimal gain for adjusting the control design is introduced. The attractive ellipsoidal method is the key stone for designing the so-called suboptimal gain. Moreover, the practical stability of the genetic network trajectories is demonstrated on the mean and in almost sure senses. Some numerical simulations show how a set of stochastic trajectories are stabilized by the controller suggested in this study and how the predicted ellipsoid region is achieved by these trajectories.
KW - Attractive ellipsoid method
KW - gene regulation system
KW - linear feedback control
KW - multiplicative noise in stochastic systems
UR - http://www.scopus.com/inward/record.url?scp=84906876083&partnerID=8YFLogxK
U2 - 10.1007/s12555-013-0226-2
DO - 10.1007/s12555-013-0226-2
M3 - Artículo
SN - 1598-6446
VL - 12
SP - 1018
EP - 1029
JO - International Journal of Control, Automation and Systems
JF - International Journal of Control, Automation and Systems
IS - 5
ER -