KALMAN FILTERING FOR FUZZY DYNAMIC SYSTEMS

December 21, 2000

Dan Simon
332 Stilwell Hall
Department of Electrical Engineering
Cleveland State University
1960 East 24th Street
Cleveland, OH 44115

web: http://csaxp.csuohio.edu/~simon/
email: simon@csvax.csuohio.edu

A Kalman filter can be used to estimate the states of a nonlinear dynamic system that is approximated with a Takagi-Sugeno (T-S) model.  A backing up truck-trailer example is used to illustrate the effectiveness of the proposed state estimator.  This file describes the m-files that were downloaded along with this readme file.  The m-files can be run in the MATLAB environment.  M-files are written in a very high-level language that can be easily read, almost like pseudo code. The files included with this download are as follows.

ARESolutions.m - This gives the algebraic Ricatti solutions for the optimal controllers and the Kalman filters for each local T-S model.

Controller.m - This computes the global optimal control for the T-S model, which approximates the nonlinear truck-trailer system.

FuzzyModel.m - This computes the T-S model system matrices and the current membership function values.

Kalman.m - This computes the optimal state estimate of the linear time-varying T-S model.

KalmanTS.m - This runs a monte-carlo simulation of the steady state Kalman filter for the T-S model.

Member.m - This plots the membership grade functions for the T-S model.

ModelLinear.m - This runs one time step of the linear time-varying T-S model.

ModelNonlinear.m - This runs one time step of the nonlinear model.

TruckTrailer.m - This simulates the truck-trailer system, the optimal control, and the state estimate.


Look in the m-files themselves for more information.  In order to run these m-files,  run MATLAB and make sure that the location of the files on your hard drive is part of your MATLAB path. (For example, if you downloaded the files to the c:\kalmanfuzzy directory on your hard drive, type "path(path, 'c:\kalmanfuzzy');" at MATLAB's command prompt.) 

After downloading these files you can set (for example) sigx=[.05 .05 .25] and sigy=[.2 .2 1].  This sets the standard deviation of the process noise (sigx) and the measurement noise (sigy).  Then type "TruckTrailer(sigx,sigy,0,1)" at MATLAB's command prompt.  (The 0 means simulate the steady state Kalman filter, and the 1 means plot the results.)  If you instead type "TruckTrailer(sigx,sigy,1,1)" then you will be simulating the time-varying Kalman filter, which theoretically performs better but requires more computational effort.

You can type "KalmanTS(sigX,sigY,0)" to see monte-carlo performance results for the steady state Kalman filter.  Type "KalmanTS(sigX,sigY,1)" to see monte-carlo performance results for the time-varying optimal Kalman filter.

Feel free to contact me at simon@csvax.csuohio.edu with any comments or questions.