受限布尔网络发展现状

Recent development of Boolean networks with constraints

布尔网络可以简洁有效地描述作用在有限集上的动态离散模型.然而,随着研究的深入以及一些实际问题的需要,传统的布尔网络已经不能满足建模的需求,由此衍生出受限布尔网络,通过矩阵半张量积,该类型的网络可以转化为便于处理的等价代数表示.鉴于此,对受限布尔(控制)网络的来源、受限形式和相关问题,作了概括与总结.对于受限布尔网络中出现的典型问题、规范化与可解性,理清了其发展脉络与研究现状;对受限布尔网络的拓扑结构整理了相关结果.另一方面,在受限布尔控制网络部分,着重总结其能控性的发展现状,将现有的能控性分析方法归为Dimitriy-Michael方法和预反馈方法两大类,并分别介绍其分析过程.总结受限布尔控制网络在设计能控、镇定、最优控制信号等问题中的一些常用方法(输入-状态关联矩阵方法和Floyd算法),以及牵引控制和干扰解耦等其他研究方向.

The Boolean network is an effective tool to characterize dynamic discrete models established on finite sets.However, as the research goes deeper and new demands of some practical issues come into being, traditional Boolean networks fail to model suitably. In this case, Boolean（control） networks with constraints（B（C）NWCs） are proposed. By resorting to semi-tensor product of matrices, the network can be converted equivalently into its algebraic representation,which is convenient to analyze. In this paper, the sources and the types of BNWCs are summarized. Subsequently, the development and status of typical problems including normalization and solvability of BNWCs, are presented. Moreover,some relative results about topological structures of BNWCs are outlined. On the other hand, we pay more attention to controllability of BCNWCs, which are Boolean networks with constraints and inputs. The analysis procedures of controllability in BCNWCs are recommended in term of two categories, which are the Dimitriy-Michael approach and the pre-feedback approach, respectively. Finally, common approaches to design controllable and stabilizable controllers and optimal input signals, the input-state incidence matrix method and the Floyd＇s algorithm, and some other research orientations such as pinning control and disturbance decoupling, are summarized.