Fuzzy Constraint Networks for Process Control

One of the critisisms of rule-based fuzzy controllers has been their use of only shallow knowledge bases. This shallowness is primarily attributable to the expressiveness of rule-based systems, which is that of the Horn clause subset of rst-order predicate calculus (FOPC). We would argue that the language in which declarative knowledge is represented must be at least as expressive as the full FOPC. We propose using a constraint-based system which makes available the full FOPC and hence is richer in expressiveness than rule-based systems. In Sections 1 and 2 we introduce the notion of fuzzy constraint networks and compare them to fuzzy rule-based systems. The inference mechanism for such a fuzzy constraint-based system must ensure that the inferred knowledge is consistent with the constraints of the problem domain. We introduce one such inference mechanism , Fuzzy T-Local Propagation, in Section 3 and prove that this algorithm preserves consistency of a fuzzy constraint network. Finally , in Section 4 we illustrate the advantages of a fuzzy constraint-based control by comparing its inference with that of a fuzzy rule-based controller. 1 Constraint based problem solving Much of what we know about many real-world problems can be represented as sets of constraints. In engineering design, constraints represent the requirements that the artifact being designed must satisfy. The task of designing then becomes that of exploring design alternatives in a solution space bounded by these constraints. Similarly, in process control constraints can be used to model the controller and restrict the output to a desired state as speciied by the constraints. A constraint is a construct describing the relationship among one or more objects. A constraint network is a collection of objects interlinked by a set of constraints that specify relationships which must be sat-issed by the values that are assumed by these objects. Given values or domains of possible values for a (possibly empty) subset of its objects, a constraint network can be used: to infer values for the undetermined objects from the known object values, to reene the domains of possible values for the objects, or to test the consistency of the given values. In addition to these operations, constraint networks can also be used to support query answering, where the user may ask for the value of an object, or the truth-value of a proposition, based on the state of the network. As a simple illustration, consider the following. A temperature …