Kalman
Filtering for Fuzzy Dynamic Systems

Dan
Simon

Department of Electrical and Computer

Cleveland, Ohio

Kalman filters are commonly used to estimate the states of a dynamic system. Fuzzy Takagi-Sugeno (T-S) models can be used to approximate nonlinear dynamic systems. These two technologies are combined to obtain a state estimate of a nonlinear system that is approximated with a T-S model. One local filter is designed for each local T-S model using standard Kalman filter theory. Steady state solutions can be found for each of these local filters. Then a linear combination of the local filters is used to derive a global filter. The local filters are time-invariant, which greatly reduces the computational complexity of the global filter. The global filter is unbiased and (under certain conditions) stable. In addition, under the approximation of uncorrelatedness among the local models, the global filter is minimum variance. A backing up truck-trailer system is used to illustrate the effectiveness of the proposed state estimator.

This web page makes available some m-files (that can be run in the MATLAB environment) that demonstrate Kalman filtering for T-S models. The m-files require the MATLAB Control System toolbox. The specific application demonstrated by these m-files is a nonlinear model of a truck-trailer combination. M-files are written in a very high-level language that can be easily read, almost like pseudo code. The m-files are contained in the following zip file.

KalmanFuzzy.zip - 7 kilobytes

The file **readme.txt** gives you more information about how to use the
m-files. If you download TSKalman.zip to
your hard drive by clicking on the above link, then unzip the file (using, for
example, WinZip), you can run a T-S Model Kalman filter experiment and
reproduce the results in reference [1].
If you don't have software to unzip the file, you can download a free
evaluation version of WinZip from http://www.winzip.com/.

*References*

- D. Simon, “Kalman Filtering
for Fuzzy Discrete Time Dynamic Systems,”
*Applied Soft Computing*, vol. 3, no. 3, pp. 191-207, November 2003 - pdf, 217 KB - postscript, 707 KB

Department of Electrical and Computer Engineering

Last Revised: December 14, 2013