| Since chaotic systems are frequently encountered in various fields, research on chaotic systems thus has great practical significance. Deterministic chaos with some special characters brings two effects on its research, one is that the character of positive Lyapunov exponents is intrinsically associated with a loss of long term predictability, the other is that some good characters of chaotic behaviors provide creative opportunities for conventional science and are helpful to scientific studies in other fields.System modeling is one of the most important tools for analyzing systems. With fast development of global economy and increasingly intense competition, every part of the industries needs to tightly cooperate each other. These make system modeling be faced with new challenges.Under these situations, many advance technologies and theories such as neural networks, robust algorithms and adaptive algorithms are introduced here. The methods of modeling and predicting chaotic time series with rapid speed, simple model structures and good anti-noise abilities are studied hi this paper.Research on the application of chaotic systems is also considered. Some good characters of chaotic behavior are introduced into studies of continuous optimization problems to skip local optimal solutions. The main contributions of this thesis are as follows:1. Based on conventional methods of local predicting chaotic time series, local intervals method is proposed. Here a new concept, interval neighboring points, is defined for building up a data list. The list for finding neighboring points is gradually established in the procedure of forecasting future values. It is convenient that all neighboring points are obtained from the list, instead of searching in history data.Also the method can continually update the list and supply new types of neighboring points for the list.2. The disadvantages of existent global methods for forecasting chaotic time series are analyzed. To take advantage of NF-GMDH (Neurofuzzy GMDH, GMDH is the abbreviation of Group Method of Data Handling) and GMDH-FL (GMDH with a feedback loop), the neurofuzzy GMDH with a feedback loop (NF-GMDH-FL) is proposed. The feedback loop of NF-GMDH-FL is investigated and improved here. The neurofuzzy GMDH with an improved feedback loop (NF-GMDH-IFL) is developed, in which the redundant combinations and computations are discarded. NF-GMDH-IFL has faster training speed and less training time than that of NF-GMDH-FL. Our simulations show that the capability of NF-GMDH-IFL is better than NF-GMDH and NF-GMDH-FL. Furthermore, the enormous time and memory are saved in NF-GMDH-IFL. The identification and prediction performance for nonlinear systems is obviously improved.3. A robust LMS algorithm with the properties of rapid convergence and strong anti-noise ability is developed. Based on the algorithm, a robust adaptive nonlinear model is proposed for predicting chaotic time series. The models have high efficiency in estimating the parameters, and good predictive performance for chaotic time series.4. Chaos optimization algorithm based on dividing intervals (COA-DI) is presented for improving the searching efficiency. The COA-DI is based upon the pioneer work of Li and Jiang, who proposed chaos optimization algorithm (COA). The basic idea of COA-DI is to subdivide the intervals of optimized variables, and search the global optimum in all subdivided intervals, simultaneously. Compared with CO A, COA-DI is more effective and has higher approximate degree.5. To skip the local minimum and avoid searching every state in the whole space, a new hybrid optimization algorithm is proposed, which combines COA-ID with conventional optimization method. The convergence of the hybrid algorithm is also proved.6. The chaotic simulated anneal, successfully used for combinatorial optimization, is seldom applied to solve continuous optimization, especially multi-variable continuous optimization. Here, a chaotic simulated annealing neural network for multi-va...
|
PDF Full Text Request