lolimotDemo1 Demo 1: Static process with 1 input and 1 output

LoLiMoT - Nonlinear System Identification Toolbox
Torsten Fischer, 20-October-2011
Institute of Mechanics & Automatic Control, University of Siegen, Germany
Copyright (c) 2012 by Prof. Dr.-Ing. Oliver Nelles
% Training
LMN = lolimot;                   % Generate an empty net and data set structure

% Create training data
u = linspace(0,1,15)';
y = 1 ./ (0.1 + u);

% Assign training data
LMN.input = u;
LMN.output = y;

LMN.xRegressorDegree = 1;       % use 1st order polynoms for local models (default: 1)
LMN.maxNumberOfLM = 15;         % Termination criterion for maximal number of LLMs
LMN.minError = 0.05;            % Termination criterion for minimal error
LMN.kStepPrediction = 0;        % Static model
LMN.smoothness = 1;             % Less overlap between the validity functions
LMN.history.displayMode = true; % display information


% Train net
LMN = LMN.train;

% Generalization
uG = linspace(-0.05,1.2,270)';
yG = 1 ./ (0.1 + uG);

% Simulate net
yGModel = calculateModelOutput(LMN, uG, yG);
JG = calcGlobalLossFunction(LMN ,yG, yGModel);

figure
LMN.plotModel

figure
LMN.plotPartition
xInputDelay is empty, defaults are used: xInputDelay(1:p) = {0}
zInputDelay is empty, defaults are used: zInputDelay(1:p) = {0}
xOutputDelay is empty, defaults are used: xOutputDelay(1:p) = {[]}
zOutputDelay is empty, defaults are used: zOutputDelay(1:p) = {[]}

Initial net has 1 local linear model(s): J = 0.602127.


1. Iteration. Number of local linear models = 1. Checking for split of model 1 ...
   Testing split in dimension 1 with ratio 0.50: J = 0.390072.
-> Splitting in dimension 1 with ratio 0.50: J = 0.390072 and penalty = 0.580313.

2. Iteration. Number of local linear models = 2. Checking for split of model 2 ...
   Testing split in dimension 1 with ratio 0.50: J = 0.198680.
-> Splitting in dimension 1 with ratio 0.50: J = 0.198680 and penalty = 0.348564.

3. Iteration. Number of local linear models = 3. Checking for split of model 5 ...
   Split in dimension 1 with ratio 0.50 is forbidden!

3. Iteration. Model 5 can not be splitted. Try another model...

3. Iteration. Number of local linear models = 3. Checking for split of model 3 ...
   Testing split in dimension 1 with ratio 0.50: J = 0.198358.
-> Splitting in dimension 1 with ratio 0.50: J = 0.198358 and penalty = 0.434220.

4. Iteration. Number of local linear models = 4. Checking for split of model 7 ...
   Split in dimension 1 with ratio 0.50 is forbidden!

4. Iteration. Model 7 can not be splitted. Try another model...

All leaf models are locked. No further splitting possible. Training accomplished.


Final net has 4 local models and 8 parameters: J = 0.198358

Net 3 with 3 LMs and 6 parameters is suggested as the model with the best complexity trade-off.
Plot model for dimension 1.

ans =

  1×7 cell array

    []    []    [1×1 Line]    [1×1 Line]    [1×1 Line]    []    []