布尔控制网络的能观测性综合问题

Synthesis Problem for Observability of Boolean Control Networks

能观测性是布尔控制网络的一个基本性质,用来描述是否可以通过系统的输入–输出值确定其初始状态.基于矩阵半张量积和图论技术,研究了布尔控制网络的能观测性综合问题.用实例说明了带有外部输入的状态反馈控制器有时可使不能观测的布尔控制网络变为能观测的,有时不能;也可使能观测的布尔控制网络变为不能观测的.最后,证明了如果存在标准状态反馈控制器使布尔控制网络变为能观测的,则一定存在带有外部输入的状态反馈控制器使布尔控制网络变为能观测的,反之不成立.

Observability is a fundamental property of Boolean control networks,which describes whether the initial state of a system can be determined by its input-output values.In this article we study the observability synthesis of Boolean control networks based on semi-tensor product of matrices and graph theory.With the use of examples,we report the results that state-feedback controller with external input sometimes can first make an unobservable Boolean control network into observable,sometimes not,and then can also make an observable Boolean control network into unobservable.Finally,we prove that if a Boolean control network can be made observable by standard-state feedback controller,then it can also be made observable by state-feedback controller with external input,but the converse does not hold.