STUDY ON MODELLING OF NONLINEAR SYSTEM AND SELF-VALIDATING MUMERICAL METHOD

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Recently, the study of nonlinear systems and nonlinear technologes has made a great advance. For example, the studies of optical fiber soliton communications, neural networks, fuzzy systems, analogue VLSI and so on have achieved much interests. Since such systems essentially use nonlinearity , new modelling techniques and reliable simulation techniques are required. Moreover, in the field of computer assisted design of nonlinear systems, it is very important to guarantee the accuracy of the result of calculation. For example, in the VLSI design, if we can validate the accuracy of modeling and numerical simulation, it enables to reduce the cost and period of design.In this study, taking the accuracy of modeling into consideration, and guarantteng the accuracy of numerical simulation of the modeling, we have develpoed a numerical validation method through the total simulation process of nonlinear system.In this year, we have improved the theory, algorithm and system developed until last year, and have made them more practical.1.Effectiveness of our fuzzy modeling theory is confirmed by numerical simulation.2.Automatic numerical validation method for general ordinary differential equations is developed. It provides a rigorous method for transient analysis.3.Extending the technique used in all solution method for nonlinear equations, we have developed a inclusion method for solution sets of set-valued functions. It gives a more rigorous system analysing method together with modeling method with guaranteed accuracy .