Department of Mathematics, Jinling Institute of Technology, Nanjing 211169, China.
School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China.
Neural Netw. 2024 Dec;180:106694. doi: 10.1016/j.neunet.2024.106694. Epub 2024 Sep 3.
We show that for stabilization of Boolean control networks (BCNs) with unobservable initial states, open-loop control and close-loop control are not equivalent. An example is given to illustrate the nonequivalence. Enlightened by the nonequivalence, we explore open-loop set stabilization of BCNs with unobservable initial states. More specifically, this issue is to investigate that for a given BCN, whether there exists a unified free control sequence that is effective for all initial states of the system to stabilize the system states to a given set. The criteria for open-loop set stabilization is derived and for any open-loop set stabilizable BCN, every time-optimal open-loop set stabilizer is proposed. Besides, we obtain the least upper bounds of two integers, which are respectively related to the global stabilization and partial stabilization of BCNs in the results of two literature articles. Using the methods in the two literature articles, the least upper bounds of the two integers cannot be obtained.
我们证明了对于具有不可观测初始状态的布尔控制网络（BCN）的稳定性，开环控制和闭环控制是不等价的。通过一个例子来说明这种不等价性。受这种不等价性的启发，我们探索了具有不可观测初始状态的 BCN 的开环集稳定化问题。更具体地说，这个问题是要研究对于一个给定的 BCN，是否存在一个统一的自由控制序列，对于系统的所有初始状态都有效，以将系统状态稳定到给定的集合。我们推导出了开环集稳定化的准则，并针对任何开环集可稳定化的 BCN，提出了每个时间最优的开环集稳定器。此外，我们还得到了两个整数的上确界，这两个整数分别与 BCN 的全局稳定化和部分稳定化有关，这是在两篇文献的结果中得到的。使用这两篇文献中的方法，无法得到这两个整数的上确界。
