A Fuzzy Control Heuristic Applied to Non-linear Dynamic System Using a Fuzzy Knowledge Representation

This paper presents the design of a fuzzy control heuristic that can be applied for modeling nonlinear dynamic systems using a fuzzy knowledge representation. Nonlinear dynamic systems have been modeled traditionally on the basis of connections between the subsystems that compose it. Never- theless, this model design does not consider some of the following problems: existing dynamics between the subsystems; order and priority of the connec- tion between subsystems; degrees of influence or causality between subsystems; particular state of each subsystem and state of the system on the basis of the combination of the diverse states of the subsystems; positive or negative influ- ences between subsystems. In this context, the main objective of this proposal is to manage the whole system state by managing the state combination of the subsystems involved. In the proposed design the diverse states of subsystems at different levels are represented by a knowledge base matrix of fuzzy intervals (KBMFI). This type of structure is a fuzzy hypercube that provides facilities operations like: insert, delete, and switching. It also allows Boolean opera- tions between different KBMFI and inferences. Each subsystem in a specific level and its connectors are characterized by factors with fuzzy attributes rep- resented by membership functions. Existing measures the degree of influence among the different levels are obtained (negatives, positives). In addition, the system state is determined based on the combination of the statements of the subsystems (stable, oscillatory, attractor, chaos). It allows introducing the dy- namic effects in the calculation of each output level. The control and search of knowledge patterns are made by means of a fuzzy control heuristic. Finally, an application to the co-ordination of the activities among different levels of the operation of an underground mine is developed and discussed.