TY - JOUR
T1 - A Tracking Error Based Fully Probabilistic Control for Stochastic Discrete Time Systems with Multiplicative Noise
AU - Herzallah, Randa
AU - Zhou, Yuyang
N1 - © Sage 2020. The final publication is available via Sage at http://dx.doi.org/10.1177/1077546320921608
PY - 2020/12
Y1 - 2020/12
N2 - This article proposes the exploitation of the Kullback–Leibler divergence to characterise the uncertainty of the tracking error for general stochastic systems without constraints of certain distributions. The general solution to the fully probabilistic design of the tracking error control problem is first stated. Further development then focuses on the derivation of a randomised controller for a class of linear stochastic Gaussian systems that are affected by multiplicative noise. The derived control solution takes the multiplicative noise of the controlled system into consideration in the derivation of the randomised controller. The proposed fully probabilistic design of the tracking error of the system dynamics is a more legitimate approach than the conventional fully probabilistic design method. It directly characterises the main objective of system control. The efficiency of the proposed method is then demonstrated on a flexible beam example where the vibration quenching in flexible beams is shown to be effectively suppressed.
AB - This article proposes the exploitation of the Kullback–Leibler divergence to characterise the uncertainty of the tracking error for general stochastic systems without constraints of certain distributions. The general solution to the fully probabilistic design of the tracking error control problem is first stated. Further development then focuses on the derivation of a randomised controller for a class of linear stochastic Gaussian systems that are affected by multiplicative noise. The derived control solution takes the multiplicative noise of the controlled system into consideration in the derivation of the randomised controller. The proposed fully probabilistic design of the tracking error of the system dynamics is a more legitimate approach than the conventional fully probabilistic design method. It directly characterises the main objective of system control. The efficiency of the proposed method is then demonstrated on a flexible beam example where the vibration quenching in flexible beams is shown to be effectively suppressed.
UR - https://journals.sagepub.com/doi/abs/10.1177/1077546320921608?journalCode=jvcb
UR - http://www.scopus.com/inward/record.url?scp=85083509776&partnerID=8YFLogxK
U2 - 10.1177/1077546320921608
DO - 10.1177/1077546320921608
M3 - Article
SN - 1077-5463
VL - 26
SP - 2329
EP - 2339
JO - JVC/Journal of Vibration and Control
JF - JVC/Journal of Vibration and Control
IS - 23-24
ER -