Application of the fuzzy system in the N-order linear differential equation
Subject Areas : Fuzzy logic and its applications
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Keywords: N-order linear differential equation, fuzzy system, least squares method, approximate solution,
Abstract :
In this paper, an application of fuzzy systems to least squares method is designed. Since, for many practical systems, important information comes from two sources: one source is experts who describe their knowledge about the system in natural languages and the other is measurements and mathematical models that are derived according to physical laws, then it is important to combine these two types of information into system and this important task is performed by design fuzzy system. Fuzzy systems are knowledge-based or rule-based systems. Hence in here, a fuzzy system is constructed to approximate the system dynamic. Based on this fuzzy approximation, suitable and adaptive laws for uncertain system dynamic is developed. With the proposed adaptive design solution of the Nth order linear differential equation to initial conditions is obtained. By attention to theorems, convergence of the proposed technique is guaranteed. In final, several examples are presented for illustration of the adaptive proposed strategy.
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