Learning and Tuning Fuzzy Logic Controllers Through Reinforcement
Fuzzy Logic controller#
Step one: fuzzification(encoding)##
In coding the values from the sensors, one transforms the values of the sensors measurement by using the linguistic labels in the rule predictions. This process is commonly called fuzzification or encoding. The fuzzification stage requires matching the sensor measurement against the menbership functions of linguistic labels.
In modeling the hunman expert operator's knowledge, fuzzy control rules of the form
IF Error is small AND Change-in-error is small THEN
Force is small
can be used effectively when expert human operators can express the heuristics or the control knowledge that they use in controlling a process in terms of rules of the above form.
Conflict Resolution and Decision Making
As mentioned earlier, because of the partial matching attribute of fuzzy control rules and the fact that the preconditions of rules do overlap, more than one fuzzy control rule can fire at a time. The methology which is used in deciding which control action should be taken as the result of the firing of several rules can be referred to as conflict resolution. The following example, using two rules, illustrates this process. Assume that we have the following rules:
- Rule 1: IF X is \(A_{1]\) and Y is \(B_{1}\) THEN Z is \(C_{1}\)
- Rule 2: IF X is \(A_{2}\) and Y is \(B_{2}\) THEN Z is \(C_{2}\)
Each rule has an antecedent, of \(if\), part containing several preconditions, and a consequent, or \(then\), part which prescribes the value of one or more output actions. Now, if we have \(x_{0}\) and \(y_{0}\) as the sensor readings for fuzzy variables \(X\) and \(Y\), then their \(truth values\) are respesented by \(\mu_{A_{1}}(x_{0})\) and \(\mu_{B_{1}}(y_{0})\) respectively for rule 1, where \(\mu_{A_{1}}\) and \(\mu_{B_{1}}\) represent the membership function for \(A_{1}\) and \(B_{2}\), respectively. Similarly for rule 2, we have \(\mu_{A_{2}}(x_{0})\) and \(\mu_{B_{2}}(y_{0})\) as the truth values of the preconditions:
Similarly for rule 2
The control output of rule 1 is calculated by applying the matching strength of its precondtiontions on its conclusion. We assume that
and, for rule 2, that