Evolution of Voronoi based Fuzzy Recurrent Controllers

TL;DR

This paper introduces the Recurrent Fuzzy Voronoi (RFV) model, an extension of Voronoi-based fuzzy controllers that incorporates temporal dynamics and memory, enabling better handling of time-dependent problems through evolutionary algorithms.

Contribution

The paper presents the RFV model, extending the FV model with internal units for temporal relations, and demonstrates its effectiveness in system identification and robotics tasks.

Findings

RFV effectively models temporal fuzzy systems.

The geometric evolution operators improve controller design.

Validated on system identification and robotics problems.

Abstract

A fuzzy controller is usually designed by formulating the knowledge of a human expert into a set of linguistic variables and fuzzy rules. Among the most successful methods to automate the fuzzy controllers development process are evolutionary algorithms. In this work, we propose the Recurrent Fuzzy Voronoi (RFV) model, a representation for recurrent fuzzy systems. It is an extension of the FV model proposed by Kavka and Schoenauer that extends the application domain to include temporal problems. The FV model is a representation for fuzzy controllers based on Voronoi diagrams that can represent fuzzy systems with synergistic rules, fulfilling the $\epsilon$-completeness property and providing a simple way to introduce a priory knowledge. In the proposed representation, the temporal relations are embedded by including internal units that provide feedback by connecting outputs to inputs. These internal units act as memory elements. In the RFV model, the semantic of the internal units can be specified together with the a priori rules. The geometric interpretation of the rules allows the use of geometric variational operators during the evolution. The representation and the algorithms are validated in two problems in the area of system identification and evolutionary robotics.