By Gang Feng
Fuzzy common sense keep watch over (FLC) has confirmed to be a well-liked keep watch over method for plenty of advanced structures in undefined, and is usually used with nice luck as a substitute to standard keep an eye on thoughts. although, since it is essentially version unfastened, traditional FLC suffers from a scarcity of instruments for systematic balance research and controller layout. to deal with this challenge, many model-based fuzzy keep watch over methods were constructed, with the bushy dynamic version or the Takagi and Sugeno (T–S) fuzzy model-based ways receiving the best recognition.
Analysis and Synthesis of Fuzzy keep watch over platforms: A Model-Based Approach deals a distinct reference dedicated to the systematic research and synthesis of model-based fuzzy regulate platforms. After giving a short assessment of the types of FLC, together with the T–S fuzzy model-based keep an eye on, it absolutely explains the elemental suggestions of fuzzy units, fuzzy good judgment, and fuzzy platforms. this allows the booklet to be self-contained and offers a foundation for later chapters, which cover:
- T–S fuzzy modeling and id through nonlinear versions or info
- Stability research of T–S fuzzy platforms
- 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 structures
- Fuzzy version predictive regulate
- Robust fuzzy filtering
- Adaptive keep watch over of T–S fuzzy platforms
A reference for scientists and engineers in structures and regulate, the booklet additionally serves the desires of graduate scholars exploring fuzzy common sense keep watch over. It with ease demonstrates that traditional keep watch over know-how and fuzzy common sense keep an eye on should be elegantly mixed and extra constructed in order that risks of traditional FLC could be shunned and the horizon of traditional keep an eye on expertise tremendously prolonged. Many chapters function program simulation examples and sensible numerical examples in keeping with MATLAB®.
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Extra info for Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach
1 Suppose the region corresponding to the fuzzy set Sl is divided into three subregions Sl = Sl0 ∂Sl Sl∞. 12) The membership function µ l = µ l ( x (t )) satisfying the following conditions in the three subregions is called a trapezoid-shape-like membership function (TSLMF). 1. m ∑ µ (x) = 1. There exists a set of x l , l = 1, 2, , m called the centers of Sl, l = 1, 2, , m such that µ l ( x l ) = 1, x l ∈ Sl0 , l = 1, 2, , m. 13b) 3. 13c) µ l ( x ) ≤ ε µ , if x ∈ Sl∞. 13d) where ε = O( x ρ ) implies that ε = c, x →0 || x ||ρ lim with c being a constant.
6 Fuzzy reasoning for multiple rules with multiple antecedents. let R1 = A1 × B1 → C1 and R2 = A2 × B2 → C2. 39) = C1′ ∪ C2′ , where C1′ and C2′ are the inferred fuzzy sets for Rules 1 and 2, respectively. Furthermore, the interpretation of multiple rules with multiple-antecedent multiple-consequence can be treated as a group of multiple rules with multipleantecedent single-consequence. 5 Fuzzy Models and Fuzzy Systems Fuzzy models or fuzzy systems are rule based or knowledge based models or systems originating from the concepts of fuzzy sets, fuzzy IF–THEN rules, and fuzzy reasoning.
4 Fuzzy reasoning for a single rule with a single antecedent. 5 Approximate reasoning for two antecedents. 37) = w1 ∧ w2 ∧ µ C ( z ), where w1 is the degree of match between A and A′, w2 is the degree of match between B and B′, and w1 ∧ w2 is called the firing strength or degree of fulfillment of this fuzzy rule. 5. The generalization to more than two antecedents is straightforward. Case 2: Multiple Fuzzy Rules The interpretation of multiple rules is usually taken as the union of the fuzzy relations corresponding to the fuzzy rules.
Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach by Gang Feng