布尔控制网络的能控性与能观性

利用矩阵的半张量积,布尔控制网络被转化为离散时间系统.本文从离散时间系统的结构矩阵出发,讨论了逻辑控制系统的能控能观性条件,得到了一个新的能控性条件.新的条件简化了原有能控性矩阵的计算复杂性,矩阵的最高阶数由原来的2m+n降到了2n.另外,还得到了检验布尔控制网络能观性的条件.与原有条件相比,新的条件更容易计算检验.最后,给出一个实例,检验给出的能控能观性判断条件的正确性.

Controllability and observability of Boolean control networks

Using the semi-tensor product, we convert the Boolean control network to its algebraic form. From the structure matrix of Boolean control network, the controllability and observability of the Boolean control network are discussed. A novel necessary and sufficient condition for controllability, which improves the recent results, is given. The new controllability condition eliminates the redundant computation of controllability matrix. The highest power of matrix is reduced from 2^{m+n} to 2^n. Also, a sufficient condition for observability is obtained, which can be computed easily. A numerical example is presented to show the applicability of our controllability and observability condition.