对称离散事件系统状态树结构模型的控制函数不变性研究

Invariance Property of the Control Functions in Symmetric Discrete-Event Systems Modeled by State Tree Structures

针对对称离散事件系统中使用监督控制理论计算得到的自动机形式的监督控制器状态数较多且无法清晰反映控制逻辑等问题,提出了基于状态树结构的抽象控制函数计算方法。该方法通过充分利用系统的对称性,对避免缓冲区出现上溢或者下溢的性能指标,采用事件重标记映射提取各组中处于加工完成状态的组件数目,从而省去了各组件复杂的运行细节;然后利用状态树结构计算得到基于抽象状态信息的控制函数;最后,结合各组组件并行工作与串行工作的实例,分析所得控制函数的不变性,即在缓冲区容量固定的前提下,控制函数所需的状态信息与组件总数量无关。实验结果表明:在实际应用中借助控制函数的不变性可在结构相同的组件增减时免于重复计算控制函数;各组中重标记为同一事件的各可控事件可由同一控制函数进行使能,有效减少了控制函数的个数;相比于自动机形式的监督控制器,控制函数状态数更少且能更清晰地描述控制逻辑。

The symmetric discrete-event systems （DES） consist of groups of identical components, For such DES, the supervisor in the form of automata synthesized by the supervisory control theory often has large number of state and is nontransparent in control logic. Thus a computational approach of abstract control function is proposed. This approach fully exploits the symmetry of the system. For the performance index to avoid the underflow or overflow of buffers, the number of components in the status of processing finish is extracted with event relabeling map, thereby the processing details of each component are omitted. Then the abstract control functions are computed with the state tree structures （STS） based on the abstract status information. Finally, by illustrating examples of components working in parallel and serial, the invariance property of control functions are analyzed. Namely, with fixed buffer sizes, the status information required by the control function is irrelevant to the total number of components. The experimental results showed that by utilizing the invariance property of control functions, the repeated computation of control functions is avoided when identical components areadded or deleted. Meanwhile, all controllable events relabeled by the same symbol can be enabled by one abstract control funetion thus the number of control functions is reduced. Moreover, compared with the controller represented by automata, the control functions have fewer states and are more transparent in control logic.