Fuzzy logic controllers have been implemented in various areas, from automatic control to expert systems, due to the ability of capturing the imprecise nature of human knowledge and reasoning processes. An adaptive-networks-based fuzzy inference system (ANFIS), a class of adaptive feedforward networks, is functionally equivalent to fuzzy inference systems and implements the learning process using neural networks. One of disadvantages of ANFIS is that it is an off-line learning process that may need a model of the plant to start the learning. This paper presents some initial work on a new ANFIS structure. The approach uses two fuzzy systems - one for training and tuning and the second for learning and control. Each fuzzy system is an adaptive network-based fuzzy inference system. The modified ANFIS uses a form of back propagation for the neural network part while the parameters of the fuzzy rule part uses a Kalman Filter estimator to assign its appropriate values. Stability issues are addressed for a single input, single output second-order example to illustrate the convergence properties and a nonlinear pendulum problem is investigated. Results show that the new two-stage ANFIS structure is a viable approach to control of uncertain systems.
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