Fuzzy modeling and control
- Department of Control Engineering
In the initial lectures, the control-related fundamentals of fuzzy logic, fuzzy sets, fuzzy operations and relations are covered. Then the methodology of approximate reasoning and its interpretation using a basis of fuzzy rules is explained while deriving various types of inference mechanisms. Fuzzy system is interpreted as a nonlinear mapping, its properties and possibilities for approximation are discussed. These are then exploited for modeling fuzzy systems from measured data using gradient and least-squares techniques. We then cover thoroughly methods of fuzzy clustering analysis using three most popular algorithms: fuzzy c-means, Gustafson-Kessel and Gath-Geva algorithms.
We then dedicate the lectures to the analysis and synthesis of Takagi-Sugeno fuzzy systems, that is, systems based on a model that was obtained either by linearizing along a trajectory or method of sections - both approaches are then compared. Careful discussion of various Lyapunov functions is included - quadratic, piecewise quadratic, fuzzy sharing the same segmentation of the state space as the linear submodels. The problems are formulated as convex optimization invoking the frameworks of linear matrix inequalities (LMI) and sums of squares (SOS).
Finally, we also show basic design methods for fuzzy adaptive regulators, both direct (backstepping, fuzzy sliding mode control) and indirect (Fuzzy Model Reference Adaptive Control). Similar methods are finally applied for control using neural networks.
Basic knowledge of differential calculus and mathematical logics
- Syllabus of lectures:
1. Introduction to fuzzy logic, history of using fuzzy logic in modeling and control
2. Basic terms and principles of fuzzy logic - fuzzy set, fuzzy operation and relation, linquistic variable
3. Approximate reasoning, basis of rules, mechanisms of inference
4. Fuzzy modeling - design of fuzzy systems using gradient techniques and least squares
5. Fuzzy clustering analysis (recursive and nonrecursive fuzzy c-means, Gustafson-Kessel, and Gath-Geva algorithms)
6. Analysis of Takagi-Sugeno fuzzy systems using various Lyapunov functions
7. Synthesis of Takagi-Sugeno fuzzy systems using various Lyapunov functions
8. Using LMI and SOS for analysis and synthesis of Takagi-Sugeno fuzzy systems
9. Design of direct adaptive fuzzy regulators
10. Design of indirect adaptive fuzzy regulators
12. Modeling using neural networks
13. Control of nonlinear systems using fuzzy logic and neural networks - sliding mode control, backstepping
14. Case studies
- Syllabus of tutorials:
Exercises are focused on consultation to semestral project
- Study Objective:
The goal of this course is to make students acquainted with the latest results and trends in the areas of modeling and control of nonlinear systems using fuzzy logic and neural networks. In particular, the focus will be on the analysis and synthesis of Takagi-Sugeno fuzzy systems, the use of fuzzy systems and neural networks for control of nonlinear systems while approximating the unknown functions in the models, and the design of adaptive controllers.
Student will become familiar with these control design philosophies and the mathematics behind the proofs so that they can use these in their own scientific or engineering research.
- Study materials:
Li-Xin Wang: A Course in Fuzzy Systems and Control, Prentice Hall, 1997, ISBN 978-0135408827.
Besides this monograph, students will be assigned reading (papers) from journals such as IEEE Transactions on Fuzzy Control, IEEE Transactions on Systems, Man and Cybernetics, Fuzzy Sets and Systems, IEEE Transactions on Cybernetics.
Tanaka, K. and H.O. Wang: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley and Sons, 2001, ISBN 978-0471323242
Jang, J.-S.R., Sun, C.-T. and Mizutani, E.: Neuro-Fuzzy and Soft Computing, Prentice Hall, 1997, ISBN 978-0132610667
Norgaard, M., Ravn, O., Poulsen, N.K. and L.K. Hansen: Neural Network for Modelling and Control of Dynamic Systems, Springer 2000, ISBN 978-1852332273
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: