Boolean control networks (BCNs) with temporal logic specifications have great potential to deal with multiple tasks or complex environments. We first express the tasks of BCNs with temporal logic specifications, and transform these specifications into finite time sets dwell problems. By using the semi-tensor product (STP), some results that satisfying the specifications of temporal logic through time-varying control are obtained. Our method provides a unified framework for studying the stabilizability, synchronizability, path planning and other issues of BCNs. The controller design algorithms are then proposed to generate state sequences that fulfill the given tasks as much as possible while minimizing the cost function. Finally, two examples are given to verify the effectiveness of the theoretical results.

具有时间逻辑规范的布尔控制网络 (BCN) 具有处理多个任务或复杂环境的巨大潜力。我们首先用时序逻辑规范表达 BCN 的任务，并将这些规范转化为有限时间集驻留问题。利用半张量积(STP)，通过时变控制得到了一些满足时序逻辑规范的结果。我们的方法为研究 BCN 的稳定性、同步性、路径规划等问题提供了一个统一的框架。然后提出控制器设计算法以生成尽可能多地完成给定任务同时最小化成本函数的状态序列。最后通过两个算例验证了理论结果的有效性。