Petri Type 2 Fuzzy Neural Networks (PT2FNN) for Identification and Control of Dynamic Systems—A New Structure and a Comparative Study

The techniques and theories used for identification and control of uncertain dynamic systems based on the universal approximators are diverse, but can mainly be divided into two categories, some are basic universal approximators as fuzzy systems (FS), neural networks (NN) and wavelet neural networks (WNN). And other hybrid approximators which are combinations between two basic approximators as fuzzy neural wavelet networks (FWNN) and petri fuzzy systems (PFS). These approximators can be used to estimate the dynamic of system in an aim to construct a controller, as we can use it directly to estimate the control law using specific learning algorithms. In this paper, a hybrid structure between type 2 fuzzy logic and petri networks (PT2FNN) is proposed as a new approximator to alleviate the problem of uncertainties with an optimal cost. By incorporating Petri layers, the number of rules is optimized. Moreover, the time consumed is reduced using a new inference type 2 method. The parameter update algorithms are derived based on the gradient method. This hybrid structure is tested for the identification and the control of uncertain dynamic plants. The simulation results showed that the proposed structure performs better compared with other approximators.