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Controllability of Boolean control networks with state-dependent constraints

状态依赖约束下布尔网路的能控性

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Abstract

This paper investigates the controllability of Boolean control networks (BCNs) with state-dependent constraints. A kind of input transformation is proposed to transfer a BCN with state-dependent input constraints into a BCN with free control input. Based on the proposed technique, a necessary and sufficient condition for controllability is obtained. It is shown that state-dependent constraints for the state can be equivalently expressed as input constraints. When a BCN has both input and state constraints, there is a possibility that the sets of admissible controls for some states are the empty set. To treat this kind of BCN, a variation of the input transformation is proposed and the problem of controllability is solved. An illustrative example is provided to explain the proposed method and results.

中文摘要

本文采用输入变换将状态依赖输入约束下的布尔网络化为等价的无输入约束布尔网络, 得到了关于能控性的充分必要条件。当系统同时受到依赖于状态的输入和状态约束时, 某些状态下的可行控制集合可能变为空集。对于这类布尔网络, 证明了状态约束可以等价地表示为输入约束, 并在输入变换中引入零状态, 将原布尔网络转化为有零状态的逻辑系统, 所得到的系统和原布尔网络的非零状态之间的能达性完全等价。基于此, 得到了这类带约束的布尔网络能控性的充分必要条件。

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Correspondence to Yuqian Guo.

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Guo, Y. Controllability of Boolean control networks with state-dependent constraints. Sci. China Inf. Sci. 59, 32202 (2016). https://doi.org/10.1007/s11432-015-5369-8

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Keywords

  • Boolean control network
  • state-dependent constraint
  • controllability
  • semi-tensor product
  • input transformation

关键词

  • 布尔控制网络
  • 状态依赖约束
  • 能控性
  • 矩阵半张量积
  • 输入变换