Study Of A Class Of Hybrid Dynamic System Modeling And Optimal Scheduling

With the development of information technology, a class of high-tech complex man-made systems have emerged in the areas such as communication, manufacture, traffic management, military command, et al., and prompt the development of the theory of discrete event dynamical systems (DEDS). DEDS theory reflects the dynamical inherent law of these man-made systems. Along with the thorough research, people start to realize the importance and the challenge of a kind of hybrid dynamic system (HDS) which is mixed and interacted with the discrete events and continuous dynamic variables. Hybrid dynamic systems consist of the conventional continuous variable dynamic system (CVDS) and discrete event dynamical system, and both of. them interact with complex mechanisms. As a result of these factors, the hybrid dynamic system modeling and analysis face with comparatively major difficulties. At the same time, the research on these hybrid system has the vital significance because many existing systems have the hybrid nature. In this dissertation, the research has been conducted to study the HDS modeling and the simulation from continuous and discrete aspects. The main work and contributions are summarized as follows:1. We proposed and studied a novel method and algorithm of optimization based on the extended Petri net and genetic algorithm, and a job-shop scheduling (JSS) problem was solved with the proposed optimization method. Based on timed Petri nets and Colored Petri nets, we presented an extended Petri net (EPN). A job-shop scheduling(JSS) problem was modeled with this extended Petri net. By definition of a new condition matrix Q, we combined the extended Petri net with genetic algorithm for solving the JSS optimization problem. A job-shop scheduling problem was optimized with the proposed method. First, a EPN model of JSS was set up. Then a single populated genetic algorithm was used to optimize the model. Experimental results indicated the efficacy and validity of themodeling and optimization method.2. We investigated the wavelet network performance and the problems related to its modeling, and presented three methods to select the wavelet nodes of the network hidden layer with theoretical analysis and algorithms. Based on the structure of radial basis function (RBF) networks and the theory of single-scaling wavelet frame, we constructed a multi-dimensional single-scale radial wavelet network by reducing the frame redundancy as much as possible. The sparseness of available training samples was analyzed and the duplicate nodes were eliminated in the hidden layer according to the training samples. The Curse of dimensionality had been overcome, and the satisfactory results are achieved with the proposed methods.3. We proposed and studied a new hybrid Petri net by introducing inhibiting arcs, testing arcs, speed functions and wavelet networks in this Petri net. The method for modeling and simulation of hybrid dynamic systems was presented. This kind hybrid Petri net can be used to describe hybrid dynamical systems (HDS) in which continuous and discrete dynamics are strongly interacted. With the wavelet net in this model, the nonlinear parts of a hybrid system can be represented accurately.This study was supported by the National 863 High-tech Foundation of China and the Science Foundation of Shandong Province.