布尔控制网络关于任意输入的能达性、能观性和能检性

在矩阵半张量积理论框架下，研究布尔控制网络关于任意输入的能达性、能观性和能检性问题。首先研究在任意输入下布尔控制网络的能达性，提出任意输入下的能达性和集能达性定义，并构造检验系统在任意输入下能达（集能达）的能达性矩阵（集能达性矩阵）。其次，应用任意输入下集能达性的研究结果，研究布尔控制网络在任意输入下的能观性和能检性问题，获得这两个问题可解的充分必要条件。最后，给出两个例子验证所得理论结果的有效性。

Reachability, Observability and Detectability of Boolean Control Networks W.R.T. Arbitrary Inputs

The reachability, observability, and detectability w.r.t. arbitrary inputs of Boolean control networks (BCNs) are investigated via the semi-tensor product of matrices. The reachability w.r.t. arbitrary inputs of BCNs is studied . The definitions of the reachability and set reachability w.r.t. arbitrary inputs are proposed, and the reachability matrix and set reachability matrix w.r.t. arbitrary inputs are constructed to check the reachability and set reachability of BCNs. As applications of the set reachability w.r.t. arbitrary inputs, the observability and detectability with arbitrary inputs of BCNs are then studied. Necessary and sufficient conditions for the observability and detectability w.r.t. arbitrary inputs of BCNs are obtained. Finally, numerical examples are given to illustrate the obtained theoretical results.