The PID parameter tuning of non-linear control system is set as the engineering background. The aim is the optimal design of PID parameter. On the basis of the design and research of the advanced PID parameter tuning, the mathematical model-transfer functionis developed through correlation analysis on statistical method.And with the optimization algorithm under constraint condition, the non-linear, Isqnonlin is set as object function. Then with connection of the non-linear constrain optimization algorithm and simulink technique, a set of adjust parameters which fit the performance index of the control system are found. And optimization design process and steps are provided.

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In recent years, set-valued optimization make much progress. In Chapter 5, based on Clarke tangent cone, we establish epiderivative of a class of set-valued maps and its properties. And furthermore, sufficiency optimization conditions of set-valued optimization are also obtained.

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Generally, the set of temporal types that can be processed by a system and involved in lots of applications, meet totally ordered relation, and the set of TFDs with a totally ordered set of temporal types is closely related to the Armstrong axioms of traditional functional dependencies.

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For a universal set, the set of all elements in the set that are not in a specified subset.

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Set Theory : Sets and Subsets, Set operations and the Laws of Set theory, Counting and Venn Diagrams.

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The vertex set of the complete graph Tof a graph G is the union of the vertex set of G and the edge set of G,two elements are adjacent in T if they are neighbour elements in G.

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Uniqueness of solution for generalized variational inequality related to strongly monotone Lipschitz mapping is shown. A sufficient condition is presented on the connectedness of solution set for the weak vector variational inequality on which the mapping is from a topological vector space X to L , where Y is also a topological vector space. The result is derived by discussing the properties of set-valued mapping induced by solution set of a scalar variational inequality related to the weak vector variational inequality.

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Thirdly, basing on the content of feature selection related in Weka which is an open source data mining tool, we propose a new feature selection algorithm based on rough set theory, which viewed the set of core features as the initial set, and define a symmetrical uncertainty measurement method as features correlation evaluating criterion.

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