Recent developments in Boolean networks control

The aim of this survey paper is to provide the state of the art of the research on control and optimal control of Boolean control networks, under the assumption that all the state variables are accessible and hence available for feedback. Necessary and sufficient conditions for stabilisability to a limit cycle or to an equilibrium point are given. Additionally, it is shown that when such conditions are satisfied, stabilisation can always be achieved by means of state feedback. Analogous results are obtained for the safe control problem that is investigated for the first time in this survey. Finite and infinite horizon optimal control are subsequently considered, and solution algorithms are provided, based on suitable adaptations of the Riccati difference and algebraic equations. Finally, an appropriate definition of the cost function allows to restate and to solve both stabilisation and safe control as infinite horizon optimal control problems.

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

[2]  Xinhe Xu,et al.  Generalized Petri Nets for a Class of Hybrid Dynamic Systems , 1996 .

[3]  Panos J. Antsaklis,et al.  Hybrid Control Systems Usind Timed Petri Nets: Supervisory Control Design Based on Invariant Properties , 1997, Hybrid Systems.

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

[5]  Aurélien Naldi,et al.  Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle , 2006, ISMB.

[6]  Aniruddha Datta,et al.  Optimal infinite horizon control for probabilistic Boolean networks , 2006, 2006 American Control Conference.

[7]  Tania G. Leishman,et al.  The Emergence of Social Consensus in Boolean Networks , 2007, 2007 IEEE Symposium on Artificial Life.

[8]  M. Ng,et al.  Control of Boolean networks: hardness results and algorithms for tree structured networks. , 2007, Journal of theoretical biology.

[9]  Aniruddha Datta,et al.  Optimal Constrained Stationary Intervention in Gene Regulatory Networks , 2008, EURASIP J. Bioinform. Syst. Biol..

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

[11]  T. Akutsu,et al.  Optimal control policy for probabilistic Boolean networks with hard constraints. , 2009, IET systems biology.

[12]  Daizhan Chengy,et al.  Stabilization of Boolean control networks , 2009, CDC 2009.

[13]  Daizhan Cheng,et al.  Stabilization of Boolean control networks , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[14]  J. Imura,et al.  Observability analysis of Boolean networks with biological applications , 2009, 2009 ICCAS-SICE.

[15]  Yiguang Hong,et al.  Multi-agent decision in Boolean networks with private information and switching interconnection , 2010, Proceedings of the 29th Chinese Control Conference.

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

[17]  T. Zhou,et al.  Optimal control for probabilistic Boolean networks. , 2010, IET systems biology.

[18]  Daizhan Cheng,et al.  Vector metric of Boolean matrices and its application to stability and stabilization of Boolean networks , 2010, IEEE ICCA 2010.

[19]  Wai-Ki Ching,et al.  On finite-horizon control of genetic regulatory networks with multiple hard-constraints , 2010, BMC Systems Biology.

[20]  Daizhan Cheng,et al.  A Linear Representation of Dynamics of Boolean Networks , 2010, IEEE Transactions on Automatic Control.

[21]  Daizhan Cheng,et al.  Disturbance Decoupling of Boolean Control Networks , 2011, IEEE Transactions on Automatic Control.

[22]  Xiaoming Hu,et al.  A boolean control network approach to pursuit evasion problems in polygonal environments , 2011, 2011 IEEE International Conference on Robotics and Automation.

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

[24]  D. Cheng,et al.  Stability and stabilization of Boolean networks , 2011 .

[25]  Daizhan Cheng,et al.  Optimal Control of Logical Control Networks , 2011, IEEE Transactions on Automatic Control.

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

[27]  M. Margaliot,et al.  A Pontryagin Maximum Principle for Multi – Input Boolean Control Networks ⋆ , 2011 .

[28]  Fangfei Li,et al.  Stability and stabilization of Boolean networks with impulsive effects , 2012, Syst. Control. Lett..

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

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

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

[32]  Michael Margaliot,et al.  Symbolic dynamics of Boolean control networks , 2013, Autom..

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

[34]  Tianguang Chu,et al.  State Feedback Stabilization for Boolean Control Networks , 2013, IEEE Transactions on Automatic Control.

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

[36]  Qiuli Liu.  Optimal finite horizon control in gene regulatory networks , 2013 .

[37]  Leslie Hogben,et al.  Combinatorial Matrix Theory , 2013 .

[38]  Ettore Fornasini,et al.  On the periodic trajectories of Boolean control networks , 2013, Autom..

[39]  Daizhan Cheng,et al.  On finite potential games , 2014, Autom..

[40]  Ettore Fornasini,et al.  Feedback stabilization, regulation and optimal control of Boolean control networks , 2014, 2014 American Control Conference.

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

[42]  M. Humayun Kabir,et al.  Mathematical modelling of a context-aware system based on Boolean control networks for smart home , 2014, The 18th IEEE International Symposium on Consumer Electronics (ISCE 2014).

[43]  Ettore Fornasini,et al.  Output feedback stabilization of Boolean control networks , 2015, Autom..

[44]  Jiandong Zhu,et al.  Kalman decomposition for Boolean control networks , 2015, Autom..

[45]  Ettore Fornasini,et al.  Fault Detection Analysis of Boolean Control Networks , 2015, IEEE Transactions on Automatic Control.