The supervisory control problem for discrete event system (DES) under control involves identifying the supervisor, if one exists, which, when synchronously composed with the DES, results in a system that conforms to the control specification. In this context, we consider a non-deterministic DES under complete observation and control specification expressed in action-based propositional μ-calculus. The key to our solution is the process of quotienting the control specification against the plan resulting in a new μ-calculus formula such that a model for the formula is the supervisor. Thus the task of control synthesis is reduced a problem of μ-calculus satisfiability. In contrast to the existing μ-calculus quotienting-based techniques that are developed in deterministic setting, our quotienting rules can handle nondeterminism in the plant models. Another distinguishing feature of our technique is that while existing techniques use a separate μ-calculus formula to describe the controllability constraint (that uncontrollable events of plants are never disabled by a supervisor), we absorb this constraint as part of quotienting which allows us to directly capture more general state-dependent controllability constraints. Finally, we develop a tableau-based technique for verifying satisfiability of quotiented formula and model generation. The runtime for the technique is exponential in terms of the size of the plan and the control specification. A better complexity result that is polynomial to plant size and exponential to specification size is obtained when the controllability property is state-independent. A prototype implementation in a tabled logic programming language as well as some experimental results are presented.

中文翻译：

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使用商法控制具有$\mu$-微积分规范的非确定性系统


受控离散事件系统 (DES) 的监督控制问题涉及识别监督者（如果存在），当与 DES 同步组合时，会产生符合控制规范的系统。在这种情况下，我们考虑在基于动作的命题 μ 演算中表达的完整观察和控制规范下的非确定性 DES。我们解决方案的关键是将控制规范与计划进行引用，从而产生新的 μ 微积分公式，该公式的模型就是监督者。因此，控制综合的任务减少了μ-演算可满足性问题。与在确定性环境中开发的现有基于μ微积分商的技术相比，我们的商规则可以处理植物模型中的非确定性。我们技术的另一个显着特征是，虽然现有技术使用单独的 μ 微积分公式来描述可控性约束（植物的不可控事件永远不会被监管者禁用），但我们将此约束吸收为商的一部分，这使我们能够直接捕获更一般的状态相关可控性约束。最后，我们开发了一种基于表格的技术来验证商公式和模型生成的可满足性。该技术的运行时间根据计划的大小和控制规范呈指数级增长。当可控性属性与状态无关时，可以获得更好的复杂性结果，即与对象尺寸成多项式且与规范尺寸成指数。给出了表格逻辑编程语言的原型实现以及一些实验结果。