A Higher Order Online Lyapunov-Based Emotional Learning for Rough-Neural Identifiers

o enhance the performances of rough-neural networks (R-NNs) in the system identification‎, ‎on the base of emotional learning‎, ‎a new stable learning algorithm is developed for them‎. ‎This algorithm facilitates the error convergence by increasing the memory depth of R-NNs‎. ‎To this end‎, ‎an emotional signal as a linear combination of identification error and its differences is used to achieve the learning laws‎. ‎In addition‎, ‎the error convergence and the boundedness of predictions and parameters of the model are proved‎. ‎To illustrate the efficiency of proposed algorithm‎, ‎some nonlinear systems including the cement rotary kiln are identified using this method and the results are compared with some other models.