离散事件动态系统的模糊概率模型及最优监控研究

For uncertain systems with fuzzy and stochastic properties, the approach existed is difficult to model, and crisp RW model can not solve the supervisory control problem effectively. By using fuzzy and probabilistic theory, fuzzy-probabilistic automata and languages are given in the project. Under the condition of no following effects, logical supervisory control problem is effectively solved by using iterative algorithm of markov decision processes. The following contents are presented. (1)Fuzzy membership functions and probability distribution functions of state transition processes are presented in the automata. On fuzzy conditional probability, fuzzy probabilistic map is defined, and then fuzzy probabilistic model is given. (2)Under the assumption of no following effects for fuzzy probability of state transition, the specification with uncertain information are used to substitute the given specification. By introducing cost for occurring event, optimal cost function is given to show that the language achieved by strings with finite cost value is equivalent to the specification with uncertain information. (3)By calculating the optimal cost value, algorithm on iterative characterize of cost function is given to obtain the specification with uncertain information, and then the supervisory control problem can be solved. A class of uncertain model and an effective approach to supervisory control are presented in the project, which can promote the development of uncertain systems and has the important theory significance.

针对于同时出现模糊性与随机性的系统，现有不确定系统模型难以建模，传统RW模型解决监控问题效率差的缺点，本项目利用模糊概率理论提出模糊概率自动机，定义模糊概率语言，并在无后效性的条件下，利用马氏决策过程迭代算法实现高效的逻辑监控。本项目提出：（1）在自动机中引入状态转移的隶属度函数与概率分布函数，基于模糊条件概率，定义模糊概率影射，建立模糊概率模型；（2）在状态转移的模糊概率满足无后效性的假设下，用基于容许度不确定信息的控制目标代替额定控制目标，通过赋予事件的发生费用，建立最优费用函数，提出获得有限最优费用值的系统行为与不确定信息控制目标的等价关系；（3）利用性能函数的迭代特性，通过计算最优费用值，建立迭代算法获得基于不确定信息的控制目标，完成监控综合。本项目提出了一类不确定性系统的结构模型和一种有效的监控方法，对促进不确定系统的发展，具有重要的理论意义。

当系统的不确定性表现为模糊性与随机性时，单一模型就不能描述系统了，并且对于不确定系统，子语言的概念对于控制问题也就不适合了，基于此，本项目提出了模糊随机离散事件系统的不确定模型，并利用基于容许度的不确定控制目标来解决其控制综合问题。本项目基于自动机模型，通过定义隶属度函数与概率分布函数，提出模糊随机系统模型，通过研究模糊概率语言，了解模糊随机系统的性质。对于该模型，通过提出基于控制模式的模糊可控的概念，获得了一种模糊控制综合的存在条件。之后，又基于容许度信息的控制目标，通过建立最优化方程，计算最优费用与相应串的隶属度，获得解决模糊控制问题的一种迭代方法。本项目提出了一类不确定系统的模型结构和一种迭代方法来解决监控综合问题，对于不确定离散事件动态系统的发展，具有重要的理论意义。