## Analysis and Control of Boolean Networks: A Semi-tensor Product ApproachAnalysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology – fixed points, cycles, transient times and basins of attractors – can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling etc. |

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### Contents

1 | |

19 | |

Matrix Expression of Logic | 54 |

Logical Equations | 67 |

Topological Structure of a Boolean Network | 102 |

InputState Approach to Boolean Control Networks | 141 |

Model Construction via Observed Data | 163 |

State Space and Subspaces | 188 |

Feedback Decomposition of Boolean Control Networks | 297 |

kvalued Networks | 313 |

Optimal Control | 346 |

InputState Incidence Matrices | 371 |

Identification of Boolean Control Networks | 389 |

Applications to Game Theory | 408 |

Random Boolean Networks | 431 |

Appendix A Numerical Algorithms | 451 |

### Other editions - View all

Analysis and Control of Boolean Networks: A Semi-tensor Product Approach Daizhan Cheng,Hongsheng Qi,Zhiqiang Li No preview available - 2010 |

Analysis and Control of Boolean Networks: A Semi-tensor Product Approach Daizhan Cheng,Hongsheng Qi,Zhiqiang Li No preview available - 2013 |

### Common terms and phrases

algebraic form algorithm Assume attractor Boolean control network Boolean network called Chap Cheng columns conjunctive normal form Consider the following Consider the system construct Control of Boolean conventional matrix product convert coordinate frame coordinate transformation Corollary cycle of length defined Definition denoted dimension disjunctive disjunctive normal form easy to calculate easy to check equivalent expressed fixed point following result give an example globally Hence in-degree incidence matrix initial value input invariant subspace k-valued logical Lemma linear logical equations logical function logical matrix logical operator logical variables mapping Nash equilibrium network graph nodes normal form Note obtain open-loop control optimal control ordered multi-index player Proof Proposition reachable set regular subspace satisfies semi-tensor product sequence space straightforward computation strategy structure matrix sub-basis subnet subnetwork swap matrix Theorem trajectory transient period trigger strategy truth table unique vector form Y-friendly subspace