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Dual-Control-Design : TP and TS Fuzzy Model Transformation Based Control Optimisation and Design
- Author / Creator
- Available as
- Online
Details
- Creator
- Péter Baranyi
- Format
- Books
- Language
- English
- Publication
-
- First edition
- Cham, Switzerland : Springer, [2023]
- ©2023
- Physical Details
-
- 1 online resource (255 pages)
- ISBNs
- 9783031445750, 3031445759, 9783031445743
- Includes bibliographical references.
- Intro -- Preface -- Acknowledgements -- Contents -- Acronyms -- Part I Introduction -- 1 Key Messages of the Book -- 1.1 Mathematical Perspective -- 1.2 TS Fuzzy Modelling Perspective -- 1.3 System Design Perspective -- References -- 2 Outline of the Book -- 2.1 Chapters of the Book -- References -- Part II Basic Concepts -- 3 Notations and Basic Concepts -- 3.1 Notations -- 3.2 Concepts -- 3.3 Tensor Product (TP) Operations -- 3.3.1 Matrix-Tensor Product -- 3.3.2 Multiple Matrix-Tensor Product -- 3.4 Tensor Product Functions -- 3.4.1 Tensor Product Functions in the Form of Vector-Tensor Products -- 3.4.2 TP Functions with Linear Indexing -- 3.5 TS Fuzzy Models Given by TP Operations -- References -- 4 Discretization Via Random and Rectangular Grids Leading to Bi-Linear Approximations -- 4.1 Notations and Basic Concepts -- 4.2 Bi-Linear Approximations Via Discretization on a Rectangular Grid -- 4.3 Bi-Linear Approximations Based on Training via Random Grid -- 4.4 From Random Grids to Rectangular Grid Based Discretizations -- 4.5 Example: Random Versus Rectangular Grid Based Discretizations -- References -- Part III TS Fuzzy Model Transformation -- 5 TP Grid Structure of Functions -- 5.1 Structure of This Chapter -- 5.2 Singular Value Decomposition of Matrices -- 5.2.1 Example: Applying CSVD to Neural Networks -- 5.3 Higher-Order Singular Value Decomposition of Tensors -- 5.4 TP Grid Structure of Functions -- 5.5 HOSVD Based TP Grid Structure of Functions -- 5.6 Example: Eliminating the Difference Between the Random and the Rectangular Grid Based Discretization -- 5.7 Refining the TP Grid Structure -- 5.8 Example: Refining the TP Grid Structure -- References -- 6 TP Model Transformation -- 6.1 Structure of This Chapter -- 6.2 Key Idea in This Chapter -- 6.3 TP Model Transformation -- 6.3.1 Example 1: Parameter Varying Neural Network
- 6.3.2 Example 2: TP Model Transformation -- 6.3.3 Example 3: Refining the TP Function -- 6.3.4 Example 4: Refinement in General -- 6.3.5 Example 5: Refinement Versus Use of a High Density Discretization Grid -- 6.3.6 Example 6: Refinement Does Not Expand to Further Ranks -- 6.4 Reinforcing the Constraints on the Weighting Functions -- 6.4.1 Example 7: Reinforcing the Bounding of the Refined Weighting Functions -- 6.5 PARAFAC Based TP Model Transformation -- 6.5.1 Example: PARAFAC Based TP Model Transformation -- 6.6 Normalised PARAFAC Based TP Model Transformation -- 6.7 Refined PARAFAC Based TP Model Transformation -- 6.7.1 Example: Refined PARAFAC Based TP Model Transformation -- References -- 7 TS Fuzzy Model Transformation -- 7.1 Structure of This Chapter -- 7.2 Transforming the Weighting Functions to Antecedent Membership Functions -- 7.3 TS Fuzzy Model Transformation -- 7.3.1 Example: TS Fuzzy Model Transformation -- 7.3.2 Example: Calculating the Membership Functions During Rank Reduction -- 7.4 Nullpoint Separation -- 7.5 Separating the Constant Elements -- 7.5.1 Example: Separating the Constant Elements Leads to a Different Solution -- 7.5.2 Example: Separating the Constant Elements May Decrease the Rank -- 7.5.3 Example: Separating the Constant Elements May Decrease the Number of Rules -- 7.6 Interpretability Versus Approximation Accuracy -- 7.6.1 Example: Interpretability of the TS Fuzzy Models -- References -- 8 Pseudo TP/TS Fuzzy Model Transformation -- 8.1 Pseudo TP/TS Fuzzy Model Transformation -- 8.1.1 Example: Pseudo TP/TS Model Transformation -- 8.2 Combination of the TP/TS and the Pseudo TP/TS Fuzzy Model Transformations -- 8.2.1 Example: Combining the TS and the Pseudo TS Fuzzy Model Transformations -- References -- 9 Generalized TS Fuzzy Model Transformation -- 9.1 Restructuring the Elements in a Given Function
- 9.2 Generalized TS Fuzzy Model Transformation -- 9.2.1 Example: The Generalised TS Fuzzy Model Transformation -- References -- 10 How to Manipulate the Input Space -- 10.1 Structure of This Chapter -- 10.2 Input Space Transformation in General -- 10.3 Extracting Non-linearities -- 10.4 Introducing Fictive Parameters -- 10.5 Example: Functions with Circular Shape -- 10.6 Example: Transforming Infinite Element TS Fuzzy Models to Finite Element Models -- References -- Part IV Dual-Control Design -- 11 Preparation of TS Fuzzy Models for Further Design -- 11.1 Structure of the Chapter -- 11.2 Basic Concepts -- 11.2.1 State-Space Systems -- 11.3 Convex Hulls Defined by the TS Fuzzy Model -- 11.4 Control Design Schema -- 11.4.1 State/Output Feedback Based Controller Design -- 11.5 Role of the TS Fuzzy Model Transformation in Control Design -- 11.6 Preparing the TS Fuzzy Model of Dynamic Systems -- References -- 12 Example I: TS Fuzzy Model Variants of the TORA System -- 12.1 Structure of the Chapter -- 12.2 Dynamic Model of the TORA -- 12.3 TS Fuzzy Models of the TORA -- 12.4 Input Space Manipulations of the TORA Model -- 12.4.1 Introducing a Fictive Parameter in the TORA Model -- 12.4.2 Extracting Non-linearity and Introduction of a Fictive Parameter in the TORA Model -- 12.4.3 Further TS Fuzzy Model Variants of the TORA -- References -- 13 Example II: TS Fuzzy Model Variants of the Aeroelastic Wing Section -- 13.1 Structure of This Example -- 13.2 Model of the Aeroelastic Wing Section -- 13.3 TS Fuzzy Models of the Aeroelastic Wing Section -- 13.4 Input Space Manipulations to the Aeroelastic Wing Section -- 13.4.1 Extracting Non-linear Components of the Aeroelastic Wing Section -- 13.4.2 Introducing a Fictive Parameter to the Model of the Aeroelastic Wing Section -- 13.4.3 Further TS Fuzzy Model Variants -- References
- 14 Revealing the qLPV Structure Using the TS Fuzzy Model Transformation -- 14.1 Structuring the System Matrix in qLPV Representations -- 14.2 Extracting LPV or qLPV Structures Using the TS Fuzzy Model Transformation -- 14.2.1 Example: Extracting the qLPV Model of the Aeroelastic Wing Section -- 14.3 Refinement in the Case of Linearization Based TS Fuzzy Model Transformation -- 14.3.1 Example: Refining the Extracted qLPV TS Fuzzy Model of the Aeroelastic Wing Section -- References -- 15 Dual-Control Design -- 15.1 TS Fuzzy Model Transformation in the Identification Phase -- 15.2 TS Fuzzy Model Transformation in the Design Phase -- References