Fault Detection Analysis of Boolean Control Networks

In this technical note, we address the fault detection problem for Boolean control networks (BCNs). We first investigate completeness and T-completeness of the set of input/output trajectories. Next, we introduce the concept of meaningful fault, and prove necessary and sufficient conditions under which meaningful faults can be detected from the input/output trajectories of the BCN. Two fault detection algorithms are provided.

[1]  Yuzhen Wang,et al.  Output feedback stabilization control design for Boolean control networks , 2013, Autom..

[2]  Hideo Fujiwara,et al.  The Complexity of Fault Detection Problems for Combinational Logic Circuits , 1982, IEEE Transactions on Computers.

[3]  P. Frank,et al.  Fault detection via factorization approach , 1990 .

[4]  Daizhan Cheng,et al.  State–Space Analysis of Boolean Networks , 2010, IEEE Transactions on Neural Networks.

[5]  Jan C. Willems,et al.  Models for Dynamics , 1989 .

[6]  Ettore Fornasini,et al.  Fault detection of Boolean control networks , 2014, 53rd IEEE Conference on Decision and Control.

[7]  Inseok Hwang,et al.  A Survey of Fault Detection, Isolation, and Reconfiguration Methods , 2010, IEEE Transactions on Control Systems Technology.

[8]  Edward R. Dougherty,et al.  From Boolean to probabilistic Boolean networks as models of genetic regulatory networks , 2002, Proc. IEEE.

[9]  Ettore Fornasini,et al.  Optimal Control of Boolean Control Networks , 2014, IEEE Transactions on Automatic Control.

[10]  Paul M. Frank,et al.  Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: A survey and some new results , 1990, Autom..

[11]  A. Datta,et al.  Boolean modeling and fault diagnosis in oxidative stress response , 2012, BMC Genomics.

[12]  Aniruddha Datta,et al.  FAULT DETECTION AND INTERVENTION IN BIOLOGICAL FEEDBACK NETWORKS , 2012 .

[13]  Michael Margaliot,et al.  Controllability of Boolean control networks via the Perron-Frobenius theory , 2012, Autom..

[14]  Daizhan Cheng,et al.  Analysis and Control of Boolean Networks , 2011 .

[15]  S. Kauffman.  Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[16]  Yuzhen Wang,et al.  Boolean derivative calculation with application to fault detection of combinational circuits via the semi-tensor product method , 2012, Autom..

[17]  Ettore Fornasini,et al.  Observability, Reconstructibility and State Observers of Boolean Control Networks , 2013, IEEE Transactions on Automatic Control.

[18]  Daizhan Cheng,et al.  Input-State Approach to Boolean Networks , 2009, IEEE Transactions on Neural Networks.

[19]  Michael Margaliot,et al.  A Maximum Principle for Single-Input Boolean Control Networks , 2011, IEEE Transactions on Automatic Control.

[20]  W. Feng,et al.  observability ? , 2013 .