By Gang Feng
ISBN-10: 1420092642
ISBN-13: 9781420092646
Fuzzy common sense keep an eye on (FLC) has confirmed to be a well-liked keep watch over technique for lots of advanced structures in undefined, and is usually used with nice good fortune as a substitute to standard regulate options. despite the fact that, since it is essentially version loose, traditional FLC suffers from a scarcity of instruments for systematic balance research and controller layout. to handle this challenge, many model-based fuzzy keep an eye on techniques were constructed, with the bushy dynamic version or the Takagi and Sugeno (T–S) fuzzy model-based ways receiving the best awareness.
Analysis and Synthesis of Fuzzy keep watch over structures: A Model-Based Approach deals a special reference dedicated to the systematic research and synthesis of model-based fuzzy keep an eye on structures. After giving a short assessment of the forms of FLC, together with the T–S fuzzy model-based regulate, it totally explains the elemental recommendations of fuzzy units, fuzzy good judgment, and fuzzy structures. this allows the e-book to be self-contained and offers a foundation for later chapters, which cover:
- T–S fuzzy modeling and id through nonlinear types 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 keep watch over
- Robust fuzzy filtering
- Adaptive regulate of T–S fuzzy structures
A reference for scientists and engineers in structures and regulate, the ebook additionally serves the desires of graduate scholars exploring fuzzy common sense keep watch over. It quite simply demonstrates that traditional keep watch over know-how and fuzzy common sense keep watch over could be elegantly mixed and additional constructed in order that risks of traditional FLC could be shunned and the horizon of traditional regulate know-how significantly prolonged. Many chapters function software simulation examples and functional numerical examples according to MATLAB®.
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Extra resources for Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach
Example text
M E= ∑ µ (x, u)( A x + B u + a ) − f (x, u) . 33) l l =1 In general, this is a nonlinear optimization problem that is difficult to solve. However, in many applications, some simple and typical membership functions, such as triangular, trapezoid, and Gaussian functions, can be utilized. One of the key parameters, that is, the centers of these membership functions can be determined by the operating points (x l, u l ), l = 1, 2, …, m, and the other parameters such as the width and decay rate can be suitably chosen by the designer.
The membership function μR (x, y) ∈ [0, 1] describes the degree of truth of the implication relation between x and y. Alternatively, the fuzzy relation R can be viewed as the fuzzy set with universe X × Y and a two-dimensional membership function μR (x, y). Generally, there are two ways to interpret the fuzzy rule A → B. 28) X ×Y where * is any T-norm operation. The other interpretation of implication A → B is that A entails B, and in this case it can be written as R = A → B = A ∪ B. 4 Fuzzy Reasoning Fuzzy reasoning (also known as approximate reasoning) is an inference procedure used to derive conclusions from a set of fuzzy IF–THEN rules and one or more premises.
However, fuzzy dynamic systems have frequently been referred to as Takagi–Sugeno fuzzy systems recently in the literature, and thus they are used interchangeably in the rest of this book. The fuzzy dynamic model or T–S fuzzy model consists of a family of local linear dynamic models smoothly connected through fuzzy membership functions. The fuzzy rules of the fuzzy dynamic model have the form Rl: IF z1 is F 1l and . . , ν) the fuzzy sets, x(t) ∈ ℜn the state vector, u(t) ∈ ℜg the input vector, y(t) ∈ ℜp the output vector, and (Al, Bl, al, Cl ) the matrices of the lth local model, and z (t ) := [ z1 , z2 , , z ν ] the premise variables, which are some measurable variables of the system, for example, the state variables or the output variables.
Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach by Gang Feng
by Charles
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