Many problems in decision making, monitoring, fault detection, and control require the knowledge of state variables and time-varying parameters that are not directly measured by sensors. In such situations, observers, or estimators, can be employed that use the measured input and output signals along with a dynamic model of the system in order to estimate the unknown states or parameters. An essential requirement in designing an observer is to guarantee the convergence of the estimates to the true values or at least to a small neighborhood around the true values. However, for nonlinear, large-scale, or time-varying systems, the design and tuning of an observer is generally complicated and involves large computational costs. This book provides a range of methods and tools to design observers for nonlinear systems represented by a special type of a dynamic nonlinear model -- the Takagi--Sugeno (TS) fuzzy model. The TS model is a convex combination of affine linear models, which facilitates its stability analysis and observer design by using effective algorithms based on Lyapunov functions and linear matrix inequalities. Takagi--Sugeno models are known to be universal approximators and, in addition, a broad class of nonlinear systems can be exactly represented as a TS system. Three particular structures of large-scale TS models are considered: cascaded systems, distributed systems, and systems affected by unknown disturbances. The reader will find in-depth theoretic analysis accompanied by illustrative examples and simulations of real-world systems. Stability analysis of TS fuzzy systems is addressed in detail. The intended audience are graduate students and researchers both from academia and industry. For newcomers to the field, the book provides a concise introduction dynamic TS fuzzy models along with two methods to construct TS models for a given nonlinear system
Author(s): Robert Babuska, Bart De Schutter, Zsófia Lendek, T. M. Guerra
Series: Studies in Fuzziness and Soft Computing
Edition: 1
Publisher: Springer
Year: 2010
Language: English
Pages: 203
Preface
......Page 5
Contents
......Page 7
Observer Design for TS Fuzzy Systems......Page 10
Outline......Page 12
TS Fuzzy Models......Page 14
Dynamic TS Fuzzy Models......Page 16
The Sector Nonlinearity Approach......Page 20
Linearization......Page 26
Summary......Page 33
Notation......Page 34
Linear Matrix Inequalities......Page 35
Quadratic Stability......Page 39
D-Stability......Page 40
Leaving the Quadratic Stability Framework......Page 42
State Feedback Stabilization......Page 45
H Attenuation......Page 47
Robust Control......Page 50
Output Feedback Stabilization......Page 54
Input-to-State Stability......Page 55
Summary......Page 57
Observer Design for TS Systems......Page 58
Observer Design: Measured Scheduling Vector......Page 61
Observer Design: Estimated Scheduling Vector......Page 71
Observer-Based Stabilization......Page 77
Summary......Page 80
Introduction......Page 81
Cascaded Dynamic Systems......Page 82
Partitioning a Nonlinear System......Page 84
Stability of Cascaded Systems......Page 88
Stability Analysis of Cascaded TS Systems......Page 90
Convergence Rate of Cascaded Systems......Page 96
Cascaded TS Fuzzy Observers......Page 98
Measured Scheduling Vector......Page 100
Estimated Scheduling Vector......Page 104
Summary......Page 110
Introduction......Page 111
Parallel Stability Analysis......Page 114
Sequential Stability Analysis......Page 122
General Framework......Page 133
Sequential Design: Measured Scheduling Vector......Page 138
Sequential Design: Estimated Scheduling Vector......Page 146
Summary......Page 155
Introduction......Page 156
Unknown Input Estimation......Page 158
Measured Scheduling Vector......Page 165
Estimated Scheduling Vector......Page 173
Measured Scheduling Vector......Page 181
Estimated Scheduling Vector......Page 186
Summary......Page 189
Glossary
......Page 190
References......Page 192
