Adaptive Fuzzy Controller for State-feedback Optimal Control

Whatever non-linear universal approximator, easy and fast to tune, robust enough and inherently parallel is of great interest for adaptive control as a additional way of identifying and controlling non-linear processes. Among them, fuzzy models present a singular Janus-faced: On one hand, they are knowledge-based software environments constructed from a collection of linguistic IF-THEN rules, and on the other hand, they realize nonlinear mappings which have interesting mathematical properties like “low-order and local interpolation” and “universal function approximation”. The locality inherent to the way fuzzy models decompose a problem into fuzzy regions makes the design of these models a time-consuming activity especially when facing multi-variables problems. This paper first discusses how to provide fuzzy models with the capacity to automatically self-tune their parameters by using wellknown gradient-based algorithms. Then the temporal extension of the gradient-based method which allows the automatic tuning of the fuzzy controller parameters over a temporal horizon will be presented and illustrated for an optimal control and a time-minimization simple problems.