Minimum energy control and optimal-satisfactory control of Boolean control network

Abstract In the literatures, to transfer the Boolean control network from the initial state to the desired state, the expenditure of energy has been rarely considered. Motivated by this, this Letter investigates the minimum energy control and optimal-satisfactory control of Boolean control network. Based on the semi-tensor product of matrices and Floydʼs algorithm, minimum energy, constrained minimum energy and optimal-satisfactory control design for Boolean control network are given respectively. A numerical example is presented to illustrate the efficiency of the obtained results.

[1]  Yuzhen Wang,et al.  A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems , 2012, Autom..

[2]  T. Chu,et al.  Synchronization in an array of coupled Boolean networks , 2012 .

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

[4]  Ovidiu Cârja,et al.  On the minimum time function and the minimum energy problem; a nonlinear case , 2006, Syst. Control. Lett..

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

[6]  Fangfei Li,et al.  Controllability of probabilistic Boolean control networks , 2011, Autom..

[7]  Ian R. Petersen,et al.  Minimax LQG optimal control of a flexible beam , 2000 .

[8]  Daizhan Cheng,et al.  Input-state incidence matrix of Boolean control networks and its applications , 2010, Syst. Control. Lett..

[9]  Art Lew,et al.  Dynamic Programming: A Computational Tool , 2006 .

[10]  Jerzy Klamka,et al.  Stochastic controllability and minimum energy control of systems with multiple delays in control , 2008, Appl. Math. Comput..

[11]  James Lam,et al.  Semi-global stabilization of linear time-delay systems with control energy constraint , 2012, Autom..

[12]  D. Cheng,et al.  Analysis and control of Boolean networks: A semi-tensor product approach , 2010, 2009 7th Asian Control Conference.

[13]  Bin Liu.  Initial condition of costate in linear optimal control using convex analysis , 2011, Autom..

[14]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[15]  Daizhan Cheng,et al.  Controllability and observability of Boolean control networks , 2009, Autom..

[16]  John Maloney,et al.  Finding Cycles in Synchronous Boolean Networks with Applications to Biochemical Systems , 2003, Int. J. Bifurc. Chaos.

[17]  Stephen J. Garland,et al.  Algorithm 97: Shortest path , 1962, Commun. ACM.

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

[20]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[21]  Barbara Drossel,et al.  Boolean networks with reliable dynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Zhiquan Wang,et al.  Robust satisfactory fault-tolerant control of uncertain linear discrete-time systems: an LMI approach , 2007, Int. J. Syst. Sci..

[23]  Florian Greil,et al.  Critical Kauffman networks under deterministic asynchronous update , 2007, 0707.1450.

[24]  B. Samuelsson,et al.  Superpolynomial growth in the number of attractors in Kauffman networks. , 2003, Physical review letters.

[25]  B. Drossel,et al.  Number and length of attractors in a critical Kauffman model with connectivity one. , 2004, Physical review letters.

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

[27]  Albert,et al.  Dynamics of complex systems: scaling laws for the period of boolean networks , 2000, Physical review letters.

[28]  Barbara Drossel,et al.  Random Boolean Networks , 2007, 0706.3351.

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