【作者】 邹恩；

【导师】 张泰山；

【作者基本信息】 中南大学 ， 控制理论与控制工程， 2005， 博士

【摘要】 混沌现象在自然界中普遍存在,它揭示了非线性科学的共同特性:确定性和随机性的统一,有序性和无序性的统一,它具有遍历性、随机性和规律性等特点,能在定义域内按自身的规律不重复地遍历所有状态。近年来,随着混沌理论研究的不断深入,作为非线性研究的核心内容,混沌的应用已成为了国内外关注的学术热点和前沿课题,并在混沌理论探索和混沌应用等方面取得了可喜的成果,混沌优化也成为了当前混沌学研究领域的一个重要课题。随着生产过程自动化水平的提高和优化方法在控制领域应用中的深入,人们对提高生产效率、提高产品质量和降低生产成本提出了越来越高的要求,许多实际的控制问题归结为控制器参数的优化问题。同时,随着工业过程复杂程度的提高,很多控制过程都存在着非线性、强约束、随机性、大规模等特性,内在机理十分复杂,建立精确的数学模型十分困难。而有些传统的优化方法中,如果初始值选择不好,就会容易陷入局部极小和优化时间较长,使优化效果达不到实际系统的要求。 混沌优化是一种利用混沌变量搜索的有效方法,在搜索中,利用混沌运动的随机性和遍历性特点,可以在定义域内连续搜索,而且不会陷入局部极小。因此,比起随机搜索方法而言,混沌搜索对优化问题有着更高的效率,能够快速地搜索到全局最优解。本论文对混沌理论及混沌优化方法作了较为全面、系统的研究,提出了新的混沌优化方法,并对模糊控制系统的混沌优化方法做了创新性研究工作,最后,设计了一个基于混沌优化的海底作业车智能控制系统。 本论文主要通过六章的篇幅展开了以下几个方面的研究工作: 第一章讨论了控制系统中的优化方法、优化理论及优化问题,分别讨论了基于导数的优化方法和智能优化方法的特点,详细介绍了国内外混沌优化的现状。 第二章简要介绍了混沌的发展史、混沌的几种定义和基本概念,分析和讨论了Logistic映射的Lyapunov指数特征,用图形形象地描述了Logistic映射在参数μ发生改变时,系统运动出现倍周期分岔最终进入混沌的现象。并对混沌动力学系统作了理论分析,从混沌动力学系统的定义和定理出发,讨论了Logistic映射的演化规律,提出了混沌理论的一些定义与定理并做出了证明,对Logistic映射产生的混更多还原

【Abstract】 Phenomena of chaos exists everywhere, it opens out the same behavior of nonlinear science, that is oneness between rigid regularity and randomicity, and oneness between regularity and out-of-order character. Ergodic, randomicity and regular properties are the characteristic of chaos, which means it can track any state in itself scope without repetition, according to its regularity. With the deeper research of chaos theory, as the core contents of nonlinear science research, the chaos application has become one of important issues and forefront project, and has been paid great attention in recent year, many desired research results have been achieved in the study of chaotic theory and its application, chaos optimization is one of important fields in chaotic scientific research, too.With the advance of industrial process automation and the deeper of optimal method in field of control, not only the high production efficiency, but also the high quality and low costs are required, a lot of practical control projects are summed up into optimal problems of the parameter of controller. And with increase of the complex industrial processes, it is very difficult to get the precise mathematical model because many practical problems of control project have the nonlinear, strong-constraint, random and large scale characters etc, and immanence mechanism is very complex. Some conventional optimal methods have disadvantages of tendency to become trapped in local minimum easily and slow convergence if initial values are not suitable, so the optimal effect can’t reach request of system.Chaos optimization is an effective method that makes use of chaotic variables for optimal search, using the features of ergodicity and randomness of chaotic motion does the search process, it can continually search for the optimum solution, and overcome the local minimum problem. Compared to the stochastic search, chaos optimization seems to realize an efficient search for a variety of optimization problems, it can fast search global optimal solution.In this dissertation, the chaos theory and optimal method are roundly studied, the new chaos optimal method is proposed, and the innovatory researches are chaos optimization methods of fuzzy control system. In the end, an intelligent control system of model vehicle based on chaos optimization is designed.The main contributions of this dissertation are as follows.In chapter 1, the optimal methods and optimal theory and optimal problems about control system are particular studied. The characteristics of optimization method base on differential and intelligent are discussed, the status quos of chaos optimization in China and abroad are introduced.In chapter 2, the chaotic phylogeny, some basic definitions and conceptions are brief introduced; the Lyapunov exponent character of Logistic map is analyzed. We can find from figure of Logistic map, when parameter μ is changed, the track of system occur doubling period bifurcation and come into chaos finally. The theory of chaos dynamic system is analyzed, set out from definition and theorem, evolvement rule of Logistic map is discussed, some definitions and theorems of chaos theory are presented and proved, the dissertation provides basic theories of chaos optimization by quantificational analyzing the ergodicity and statistic properties of chaos series generated by Logistic map.The studies of chaos arithmetic of function optimization are discussed in chapter 3, in order to avoid blind searching of chaos optimization in searching space, an improving imitative space chaos optimization algorithm is proposed. The algorithm counts better value for every searching and sets a sign A in the chaos searching, when the numbers of better value searched is equal to A, the searching space is dynamic reduced according scale, and the above course is repeated in the lesser scale till global optimal value is found. The simulation results show that algorithm is simple and local searching ability is better, and the efficiency is higher than that of imitative scale chaos optimization.It is difficult to tune parameters of controller of fuzzy control system, and control rules and membership functions of FC are hard to obtain optimization too, therefore, the control results show strong overshoot andoscillation often. Chaos optimization methods of fuzzy control system are detailed researched in chapter 4. The fuzzy controller is constructed based on chaos algorithm off-line optimize the parameters and conjugate gradient descend method in-line tune the parameters. For inverted pendulum system, its four-dimensional output is directly decomposed into input of a pair of two-dimension fuzzy controller, the system is double-loop controlled, and the inner-loop regulates the angle of pendulum, while the outer-loop is for positioning the cart. The parameters optimization of controllers adopt chaos method, simulation result show that the system is steady. And than, the fuzzy neural network controller is designed based on chaos global optimize the structure and parameters, gradient descend method partial search the parameters. Simulations prove that optimization programs are simple and system is high control precision.In chapter 5, a control system of self-propelled sea-bed service vehicle is designed, which adopt closed loop of double loops in series. Fuzzy neural network is controller of outside loop, and fuzzy controller is inside loop. The structure and parameters of fuzzy neural network and parameters of fuzzy controller use off-line chaos optimization arithmetic, and then, the parameters optimized are connected to controllers. In the end, the conjugate gradient descend method is used to in-line tuned the parameters of fuzzy neural network in order to improve self-adaptive ability, thereby control effect is good.In chapter 6, the research results are concluded and further development is pointed out.更多还原