Analysis and Synthesis of Fuzzy Control Systems: A by Gang Feng

By Gang Feng

Fuzzy common sense keep watch over (FLC) has confirmed to be a well-liked keep watch over technique for lots of complicated platforms in undefined, and is frequently used with nice good fortune as a substitute to standard keep an eye on strategies. in spite of the fact that, since it is essentially version unfastened, traditional FLC suffers from a scarcity of instruments for systematic balance research and controller layout. to handle this challenge, many model-based fuzzy regulate ways were constructed, with the bushy dynamic version or the Takagi and Sugeno (T–S) fuzzy model-based techniques receiving the best awareness.

Analysis and Synthesis of Fuzzy keep watch over structures: A Model-Based Approach deals a distinct reference dedicated to the systematic research and synthesis of model-based fuzzy keep watch over structures. After giving a quick evaluate of the types of FLC, together with the T–S fuzzy model-based keep an eye on, it totally explains the elemental suggestions of fuzzy units, fuzzy common sense, and fuzzy platforms. this permits the e-book to be self-contained and offers a foundation for later chapters, which cover:

  • T–S fuzzy modeling and id through nonlinear versions or information
  • Stability research of T–S fuzzy structures
  • Stabilization controller synthesis in addition to strong H∞ and observer and output suggestions controller synthesis
  • Robust controller synthesis of doubtful T–S fuzzy systems
  • Time-delay T–S fuzzy platforms
  • Fuzzy version predictive regulate
  • Robust fuzzy filtering
  • Adaptive keep an eye on of T–S fuzzy platforms

A reference for scientists and engineers in structures and keep watch over, the ebook additionally serves the wishes of graduate scholars exploring fuzzy common sense keep an eye on. It with ease demonstrates that traditional regulate know-how and fuzzy common sense regulate should be elegantly mixed and extra built in order that hazards of traditional FLC might be refrained from and the horizon of traditional keep an eye on expertise enormously prolonged. Many chapters function program simulation examples and functional numerical examples in response to MATLAB®.

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Extra resources for Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach

Sample text

1/13. Then it can be observed that the fuzzy set A is contained in the fuzzy set B; that is, A ⊆ B. Similar to ordinary sets, the operations of complement, union, and intersection can also be defined for fuzzy sets. 10 (Complement of a Fuzzy Set) The complement of a fuzzy set A is denoted by A, whose membership function is defined as µ A ( x ) = 1 − µ A ( x ). 15) µ C ( x ) = µ A ( x ) ∨ µ B ( x ). 17) µ C ( x ) = µ A ( x ) ∧ µ B ( x ). 3 As pointed out by Zadeh (1965), a more intuitive and appealing definition of the union of fuzzy sets A and B is the smallest fuzzy set containing both A and B.

2 The state space partition is called a well-behaved partition (WBP) if it satisfies the following conditions. 1. Only one of the fuzzy sets Sl , l = 1, 2, , m contains the origin. Without loss of generality, it is assumed that the origin x = 0 ∈ S10 and µ1 (0) = 1. 2. X = S1  S2   Sm , Sl = Sl0  ∂Sl , ∂Sl = {x | µ l ( x ) ≥ µ i ( x ), i = 1, 2, , m, i ≠ l , x ∉ Sl0 }. 3. Sl , l = 1, 2, , m are closed convex sets. 2 holds. 2 holds for this kind of membership function. A large number of commonly used membership functions, for example, TSLMFs, satisfy the above two conditions, and thus it is not difficult to obtain a well-behaved partition of the state space.

Let M1 = max( M l , l = 1, 2, , m). Then for any (x, u) ∈ X × U and m one l has f ( x , u) − fˆ ( x , u) = m ∑ ( f (x, u) − f (x, u))µ (x). 16) l =1 By Taylor’s theorem, it follows that  f ( x , u) − fl ( x , u)≤ M1  x − x l 2 , 2 l = 1, 2, , m. 18) l = 1, 2, , m. 18) that d∞( f ( x , u) − fl ( x , u)) ≤ ε , 2 x , x l ∈ Sl0  ∂Sl . 20) m ≤ ε d ( f ( x , u) − fi ( x , u))µ i ( x ). + 2 i =1,i ≠l ∞ l ∑ Because f l (x, u), l = 1, 2, , m are continuous functions on the compact set there exists a finite positive constant M 2 such that sup  fl ( x , u) ≤ M 2 , l = 1, 2, , m.

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