Supervisory control of fuzzy discrete event systems: a formal approach
Supervisory control of fuzzy discrete event systems: a formal approach
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DOI：
10.1109/tsmcb.2004.840457
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发表时间：
2005-02
期刊：
影响因子：
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通讯作者：
Daowen Qiu
中科院分区：
文献类型：
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作者：
Daowen Qiu
模糊离散事件系统（Fuzzy Discrete Event Systems，DES）是近年来由Lin和Ying提出的一种新的离散事件系统，它可以更好地科普诸如生物医学等领域的模糊性、不精确性和主观性问题。作为本文的继续，我们进一步发展了模糊决策支持系统，通过处理监督控制的模糊决策支持系统。更具体地说：1）重新定义了清晰离散事件系统的并行合成，并定义了与文[1]等价的模糊离散事件系统的并行合成。2）研究了模糊离散事件系统监督控制的若干基本问题，特别是证明了模糊离散事件系统的能控性定理和非阻塞能控性定理，从而给出了模糊离散事件系统中监督器存在的条件; 3）分析了用最大积自动机建模的模糊决策支持系统的模糊可控性条件的统一判别准则的复杂性;特别地，我们详细地提出了一种通用的计算方法，用于检查模糊能控性条件是否成立，如果使用最大-最小自动机来建模模糊DES，用这种方法可以在极大极小自动机中搜索从初始模糊状态可达的所有可能的模糊状态。此外，我们还介绍了一些实际问题的模糊n-能控性条件。4）给出了一些例子来说明所得结果和方法的应用，并研究了与模糊决策支持系统监督控制有关的一些基本性质。最后，提出了一些相关问题供进一步考虑。
Fuzzy discrete event systems (DESs) were proposed recently by Lin and Ying, which may better cope with the real-world problems of fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of, in this paper, we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically: 1) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in . Max-product and max-min automata for modeling fuzzy DESs are considered, 2) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus, present the conditions for the existence of supervisors in fuzzy DESs; 3) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata. Also, we introduce the fuzzy n-controllability condition for some practical problems, and 4) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration.