基于Ledley先行解的一般逻辑系统的状态反馈镇定
State Feedback Stabilization of Generic Logic Systems via Ledley Antecedence Solution
摘要：
本文提出了Ledley先行解在一般逻辑系统状态反馈镇定器设计中的应用。为了使该方法可行，对原有的Ledley先行解理论作了两个修改：（i）将预赋逻辑函数从一组方程扩展到一个容许集;（ii）将自变量域从整个状态空间扩展到一个受限子集.在所提出的方法中，状态反馈控制被看作是一组扩展的Ledley先行解，它们是在其相应的限制子集上设计的迭代容许集.在此基础上，提出了一种算法来验证问题的可解性，并同时提供所有可能的状态反馈稳定器时，问题是可解的。所有的稳定器都是最优的，它们能在最短的时间内将逻辑系统从任何初态稳定到目标状态/状态集。该方法首先证明了布尔控制网络实现点镇定。然后，与一些小的修改，所提出的方法也被证明是适用于集稳定问题。最后，它表明，在$k$值和混合值逻辑系统，所提出的方法仍然是有效的。
英文摘要：
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.
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