论文标题
通过莱德利先导解决方案对通用逻辑系统的状态反馈稳定
State Feedback Stabilization of Generic Logic Systems via Ledley Antecedence Solution
论文作者
论文摘要
在本文中，已经提出了莱德利先行解决方案在设计通用逻辑系统的状态反馈稳定器中的应用。为了使方法可行，对原始的莱德利先知解决方案理论进行了两个修改：（i）预签名的逻辑函数已从作为一组方程式扩展到可允许的集合； （ii）参数领域已从整个状态空间扩展到受限制的子集。在拟议的方法中，状态反馈控制被认为是一组扩展的莱德利先知解决方案，用于在相应的限制子集上设计的迭代可允许的集合。基于此，已经提出了一种算法来验证可溶性，并同时提供所有可能的状态反馈稳定器时，当问题解决问题时。所有稳定器都是最佳的，可以在最短时间内从任何初始状态到目标状态的逻辑系统稳定。该方法首先在布尔控制网络上证明，以实现点稳定。然后，通过一些较小的修改，所提出的方法也被证明适用于设定稳定问题。最后，可以表明，在$ k $值和混合价值逻辑系统中，提出的方法仍然有效。
In this paper, the application of Ledley antecedence solutions in designing state feedback stabilizers of generic logic systems has been proposed. To make the method feasible, two modifications are made to the original Ledley antecedence solution theory: (i) the preassigned logical functions have been extended from being a set of equations to an admissible set; (ii) the domain of arguments has been extended from the whole state space to a restricted subset. In the proposed method, state feedback controls are considered as a set of extended Ledley antecedence solutions for a designed iterative admissible sets over their corresponding restricted subsets. Based on this, an algorithm has been proposed to verify the solvability, and simultaneously to provide all possible state feedback stabilizers when the problem is solvable. All stabilizers are optimal, which stabilize the logic systems from any initial state to the destination state/state set in the shortest time. The method is firstly demonstrated on Boolean control networks to achieve point stabilization. Then, with some minor modifications, the proposed method is also proven to be applicable to set stabilization problems. Finally, it is shown that in $k$-valued and mix-valued logical systems, the proposed method remains effective.
