Fuzzy logic and soft computing.Technology development and by Bonissone P.P.

By Bonissone P.P.

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In the context of our paper we will only consider feedforward NNs. , 1993 we will further limit our discussion to multilayer feedforward nets. A feedforward multilayer NN is composed of a network of processing units or neurons. Each neuron performs the weighted sum of its input, using the resulting sum as the argument of a non-linear activation function. Originally the activation functions were sharp thresholds or Heavyside functions, which evolved to piecewise linear saturation functions, to di erentiable saturation functions or sigmoids, and to gaussian functions for RBFs.

Triangular norms T-norms and their dual T-conorms are two-place functions from 0,1 x 0,1 to 0,1 that are monotonic, commutative and associative. They are the most general families of binary functions that satisfy the requirements of the conjunction and disjunction operators, respectively. Their corresponding boundary conditions satisfy the truth tables of the Boolean AND and OR operators. Any triangular norm T A; B falls in the interval Tw A; B  TA; B  MinA; B, where B if maxA; B = 1, Tw A; B = minA; 21 0 otherwise The corresponding DeMorgan dual T-conorm, denoted by SA; B, is de ned as SA; B = 1 , T1 , A; 1 , B 22 Tw A; B is referred to as the drastic T-norm to re ect its extreme behavior and is clearly non-continuous.

Some proposed control methods su er from undesirable oscillatory behavior under certain operating conditions. An example is ADSTIC control Schwarz, 1975 . This method monitors the average current in the resonant inductor against a reference signal. The control problem arise when the instantaneous inductor current changes much faster than the control system can compensate. , 1982 , diode conduction control King and Stuart, 1983 , and many others. 2 Solution Description Control Strategy. To determine the basic control law for this circuit, consider the case where the control frequency, or Fc , is restricted to values above the circuit's resonant frequency.

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