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**Towards a paradigm for fuzzy logic control.**
*(English)*
Zbl 0845.93048

Although fuzzy logic controllers (FLC) are suitable for a wide range of control applications and show good performance, there are still problems which are expected to be solved. Till now, little has been done to study mathematically the stability of FLC and to provide repeatable algorithms for designing FLC. Also while designing FLC, there are so many parameters that it is difficult to make a choice for them. The present paper is intended to lay a foundation for fuzzy logic control design, constructing a class of FLC that is suitable for a broad range of applications. Some scalar definitions relevant to FLC are extended to the multidimensional case, including such concepts as vector numbers and membership vectors. A rigorous mathematical definition for the function \(g(x)\) synthesized by a fuzzy associative memory is given. It is shown that for the existence and uniqueness of solutions in a closed-loop system with a fuzzy logic controller, the fuzzy associative memory function \(g(x)\) must be Lipschitz. An algorithm for designing a FLC is proposed in the paper. Also the scalar and the two-dimensional cases are studied in detail.

Reviewer: A.N.Karkishchenko (Taganrog)

### MSC:

93C42 | Fuzzy control/observation systems |

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93C35 | Multivariable systems, multidimensional control systems |

### Keywords:

nonlinear; fuzzy logic controllers; design; multidimensional; membership vectors; fuzzy associative memory
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\textit{F. L. Lewis} and \textit{K. Liu}, Automatica 32, No. 2, 167--181 (1996; Zbl 0845.93048)

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