This paper investigates the output controllability problem of temporal Boolean networks with inputs (control nodes) and outputs (controlled nodes). A temporal Boolean network is a logical dynamic system describing cellular networks with time delays. Using semi-tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems. Some necessary and sufficient conditions on the output controllability via two kinds of inputs are obtained by providing corresponding reachable sets. Two examples are given to illustrate the obtained results.
Mots clés : temporal boolean (control) network, semi-tensor product, output controllability, time delay
@article{COCV_2014__20_1_158_0,
author = {Liu, Yang and Lu, Jianquan and Wu, Bo},
title = {Some necessary and sufficient conditions for the output controllability of temporal {Boolean} control networks},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {158--173},
publisher = {EDP-Sciences},
volume = {20},
number = {1},
year = {2014},
doi = {10.1051/cocv/2013059},
mrnumber = {3182695},
zbl = {1282.93055},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2013059/}
}
TY - JOUR AU - Liu, Yang AU - Lu, Jianquan AU - Wu, Bo TI - Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 158 EP - 173 VL - 20 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2013059/ DO - 10.1051/cocv/2013059 LA - en ID - COCV_2014__20_1_158_0 ER -
%0 Journal Article %A Liu, Yang %A Lu, Jianquan %A Wu, Bo %T Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 158-173 %V 20 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2013059/ %R 10.1051/cocv/2013059 %G en %F COCV_2014__20_1_158_0
Liu, Yang; Lu, Jianquan; Wu, Bo. Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 1, pp. 158-173. doi : 10.1051/cocv/2013059. http://archive.numdam.org/articles/10.1051/cocv/2013059/
[1] , , and , Control of Boolean networks: hardness results and algorithms for tree structured networks. J. Theor. Biol. 244 (2007) 670-679. | MR
[2] and , Exponential stability of discrete-time genetic regulatory networks with delays. IEEE Transactions on Neural Networks 19 (2008) 520-523.
[3] , and , Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Transactions on Neural Networks 17 (2006) 1646-1651.
[4] and , Stability of genetic regulatory networks with time delay. IEEE Transactions on Circuits and Systems I: Fundamental Theory Appl. 49 (2002) 602-608. | MR
[5] and , A new approach for global controllability of higher order Boolean control network. Neural Networks 39 (2013) 12-17.
[6] , Semi-tensor product of matrices and its applicationsa survey. Proc. of ICCM 3 (2007) 641-668. | Zbl
[7] , Input-state approach to Boolean networks. IEEE Transactions on Neural Networks 20 (2009) 512-521.
[8] and , Controllability and observability of Boolean control networks. Automatica 45 (2009) 1659-1667. | MR | Zbl
[9] and , A linear representation of dynamics of Boolean networks. IEEE Transactions on Automatic Control 55 (2010) 2251-2258. | MR
[10] , and , Realization of Boolean control networks. Automatica 46 (2010) 62-69. | MR | Zbl
[11] , and , Analysis and Control of Boolean Networks: A Semi-tensor Product Approach. Springer Verlag (2011). | MR | Zbl
[12] , Linear System Theory and Design (1999).
[13] , On the controllability of linear systems with delay in control. IEEE Transactions on Automatic Control 15 (1970) 255-257. | MR | Zbl
[14] , On the evolutionary inference of temporal Boolean networks. Lect. Notes Comput. Sci. (2003) 494-501.
[15] and , Machine learning and genetic regulatory networks: A review and a roadmap, Foundations of Computational, Intelligence 1 (2009) 3-34.
[16] , and , Boolean delay equations: A simple way of looking at complex systems. Physica D Nonlinear Phenomena 237 (2008) 2967-2986. | MR | Zbl
[17] and , Exact controllability of a multilayer rao-nakra plate with clamped boundary conditions. ESAIM: COCV 17 (2011) 1101-1132. | Numdam | MR | Zbl
[18] and , Exponential synchronization of hybrid coupled networks with delayed coupling. IEEE Transactions on Neural Networks 21 (2010) 571-583.
[19] and , Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks. Experimental Cell Research 261 (2000) 91-103.
[20] , Linear systems, Vol. 1. Prentice-Hall Englewood Cliffs, NJ (1980). | MR | Zbl
[21] , Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22 (1969) 437-467.
[22] , The origins of order: Self organization and selection in evolution. Oxford University Press, USA (1993).
[23] , At home in the universe: The search for laws of self-organization and complexity. Oxford University Press, USA (1995).
[24] and , Approximate controllability by birth control for a nonlinear population dynamics model. ESAIM: COCV 17 (2011) 1198-1213. | Numdam | MR | Zbl
[25] , and , Polynomial-time controllability analysis of Boolean networks. Amer. Control Confer. ACC'09. IEEE (2009) 1694-1699.
[26] and , A maximum principle for single-input Boolean control networks. IEEE Transactions on Automatic Control 56 (2011) 913-917. | MR
[27] and , Controllability of Boolean control networks via Perron-Frebenius theory. Automatica 48 (2012) 1218-1223. | MR | Zbl
[28] and , A pontryagin maximum principle for multi-input Boolean control networks, Recent Advances in Dynamics and Control of Neural Networks. In press.
[29] , and , et al., Discovery of time-delayed gene regulatory networks based on temporal gene expression profiling. BMC bioinformatics 7 (2006) 26.
[30] and , Controllability of Boolean control networks with time delays in states. Automatica 47 (2011) 603-607. | MR | Zbl
[31] , and , Controllability of higher order Boolean control networks. Appl. Math. Comput. 219 (2012) 158-169. | MR
[32] and , Stability and stabilization of Boolean networks with impulsive effects. Systems Control Lett. 61 (2012) 1-5. | MR | Zbl
[33] , and , Observability of Boolean control networks with state time delays. IEEE Transactions on Neural Networks 22 (2011) 948-954.
[34] , and , Controllability of Boolean control networks with impulsive effects and forbidden states. Math. Meth. Appl. Sci. (2013). DOI: 10.1002/mma.2773. | MR | Zbl
[35] and , Controllability for a class of linear time-varying impulsive systems with time delay in control input. IEEE Transactions on Automatic Control 56 (2011) 395-399. | MR
[36] , and , Consensus over directed static networks with arbitrary finite communication delays. Phys. Rev. E 80 (2009) 066121.
[37] , Combining Boolean method with delay times for determining behaviors of biological networks, in Engrg. Medicine Biology Soc. EMBC 2009., IEEE (2009) 4884-4887.
[38] , , Temporal Boolean network models of genetic networks and their inference from gene expression time series. Complex Systems 13 (2001) 61-78. | MR | Zbl
[39] and , On the null-controllability of diffusion equations. ESAIM: COCV 17 (2011) 1088-1100. | Numdam | MR | Zbl
[40] , , , and , Filtering for nonlinear genetic regulatory networks with stochastic disturbances. IEEE Transactions on Automatic Control 53 (2008) 2448-2457. | MR
[41] , , Output controllability of switched linear systems. IEEE International Symposium on Intelligent Control (2003) 134-139.
[42] , and , Necessary and sufficient conditions for controllability of switched impulsive control systems with time delay, in 45th IEEE Conference on Decision and Control (2006) 4093-4098.
[43] , , , and , Estimating uncertain delayed genetic regulatory networks: an adaptive filtering approach. IEEE Transactions on Automatic Control 54 (2009) 892-897. | MR
[44] , and , Input-state incidence matrix of Boolean control networks and its applications. Systems and Control Lett. 59 (2010) 767-774. | MR | Zbl
[45] and , Controllability and observability for a class of time-varying impulsive systems. Nonlinear Analysis: Real World Appl. 10 (2009) 1370-1380. | MR | Zbl
[46] and , Controllability and observability for time-varying switched impulsive controlled systems. Internat. J. Robust Nonl. Control 20 (2010) 1313-1325. | MR | Zbl
[47] and , A geometric approach for reachability and observability of linear switched impulsive systems. Nonl. Anal. Theory, Methods Appl. 72 (2010) 4221-4229. | MR | Zbl
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