A javascript fuzzy logic controller implementation.
First create some input variables. The following code creates two variables 'i1' and 'i2'.
Each fuzzy variable consists of 1 or more fuzzy sets. A fuzzy set is a value like LOW (or L)
FuzzySet s = new FuzzySet(0.0,0.5,1.0);
This fuzzy set is a sawtooth function where the set value is zero outside [0.0 , 1.0] and increases linearly from 0.0 to 1.0 in the interval [0.0 , 0.5] and decreases linearly from 1 to 0 in the interval [0.5 , 1.0].
The following code defines the input fuzzy variable i1 for a input value over the range [0.0 , 1.0].
i1 = new FuzzyVariable();
i1.VL = new FuzzySet(-0.25,0.0,0.25);
i1.L = new FuzzySet(0.0,0.25,0.5);
i1.M = new FuzzySet(0.25,0.5,0.75);
i1.H = new FuzzySet(0.5,0.75,1.0);
i1.VH = new FuzzySet(0.75,1.0,1.25);
This variable has five fuzzy sets (VL,L,M,H,VH) that represents different fuzzy values.
Note that VL (very low) and VH (very high) overlap the [0.0 , 1.0] boundaries. Those values represent the 0.0 and 1.0 values of the input real value. The most important thing is that the fuzzy set values are 1.0 at points 0.0 and 1.0.
If the controller has another control input then define another fuzzy variable i2
i2= new FuzzyVariable();
i2.L = new FuzzySet(-0.5,0.0,0.5);
i2.M = new FuzzySet(0.0,0.5,1.0);
i2.H = new FuzzySet(0.5,1.0,1.5);
Note that this input fuzzy variable has only 3 fuzzy sets (L,M,H) for Low,Medium and High fuzzy values.
The output variable o for the controller is defined in the same manner.
o = new FuzzyVariable();
o.L = new FuzzySet(-0.5,0.0,0.5);
o.M = new FuzzySet(0.0,0.5,1.0);
o.H = new FuzzySet(0.5,1.0,1.5);
We must then define the fuzzy controller rules for each output set (L,M,H).
The table below shows all the possible output values in term of the input values i1 and i2. The input values for fuzzy variable i1 are listed in the top row in bold and the input values for the fuzzy variable i2 are shown in bold in the first columns.
| VL | L | M | H | VH | |
|---|---|---|---|---|---|
| L | L | M | M | H | H |
| M | M | M | H | H | H |
| H | M | H | H | H | H |
We can then construct the rules from the above matrix by first AND-ing all input values pairs for each row/column for each output value. The output value L for example is only triggered if i1 is VL and i2 is L. The rule is then
if (i1 is VL and i2 is L) then o = L
or in more compact form
o.L = i1.VL & i2.L
The rule for the output M is
o.M = i1.L & i2.L | i1.M & i2.L | i1.VL & i2.M | i1.L & i2.M | i1.VL & i2.H
where '&' represent the boolean operator AND and '|' represent the boolean operator OR.
The rule for output L
o.H = i1.H & i2.L | i1.VH & i1.H | i1.M & i2.M | i1.H & i2.M | i1.VH & i2.M | i1.L & i2.H | i1.M & i2.H | i1.H & i2.H | i1.VH & i2.H
We convert the above rules to code as
o.L.rule = new FuzzyRule();
o.L.rule.addExpr([i1.VL,i2.L]);
o.M.rule = new FuzzyRule();
o.M.rule.addExpr([i1.L,i2.L]);
o.M.rule.addExpr([i1.M,i2.L]);
o.M.rule.addExpr([i1.VL,i2.M]);
o.M.rule.addExpr([i1.L,i2.M]);
o.M.rule.addExpr([i1.VL,i2.H]);
...
Where each AND expression is added to the rule attribute with addExpr(list). In the example above we only have two input variables and therefore is the list, that is passed to addExpr(), has only two fuzzy sets/values. The AND terms are then internally ORed together.
The first step is to normalize the real input values (inputValue1 and inputValue2) so that their value lies in the interval [0,1]. That normalized value is then passed to the fuzzyfy() function of the respective fuzzy variable:
i1.fuzzyfy(inputValue1/maxInputValue1);
i2.fuzzyfy(inputValue2/maxInputValue2);
This will calculate internally the fuzzy set value for each fuzzy set defined by those variables.
When both input values have been fuzzyfied we can 'run' our fuzzy controller that has been defined by the rules in our output fuzzy variable 'o'.
o.fireRules();
This internally calculates all the output fuzzy sets values of the output fuzzy variable 'o'.
The real output value 'outputValue' is then calculated with the defuzzify() method :
var outputValue = o.defuzzify();
See FuzzyController.html to see example of a inverted pendulum controller that takes the normalized pendulum angle with vertical and angular velocity of the pendulum as inputs and outputs a normalized speed for a pendulum carriage. See inverted pendulum on Wikipedia