We describe the optimal design of type-3 fuzzy controllers with stability guaranteed by the fuzzy Lyapunov approach. The classical Lyapunov approach requires the Lyapunov candidate function derivative to be negative (numerically), however in the fuzzy Lyapunov approach the requirement is satisfied linguistically. In this approach, a fuzzy controller is established such that the fuzzy rules satisfy the requirement of negative derivative in a linguistic (fuzzy) way. Once the fuzzy rules are established, the membership functions are outlined and the parameters are found using metaheuristics. Results with a nonlinear plant (water tank) validate the approach.

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Optimal Design of Type-3 Fuzzy Controllers with Fuzzy Lyapunov Stability

  • Oscar Castillo,
  • Patricia Melin,
  • Cinthia Peraza,
  • Patricia Ochoa,
  • Leticia Amador

摘要

We describe the optimal design of type-3 fuzzy controllers with stability guaranteed by the fuzzy Lyapunov approach. The classical Lyapunov approach requires the Lyapunov candidate function derivative to be negative (numerically), however in the fuzzy Lyapunov approach the requirement is satisfied linguistically. In this approach, a fuzzy controller is established such that the fuzzy rules satisfy the requirement of negative derivative in a linguistic (fuzzy) way. Once the fuzzy rules are established, the membership functions are outlined and the parameters are found using metaheuristics. Results with a nonlinear plant (water tank) validate the approach.