Annealing Robust Radial Basis Function Networks with Support Vector Regression for Nonlinear Inverse System Identification with Outliers

In this paper, the proposed annealing robust radial basis function networks (RBFNs) based on support vector regression (SVR), RBFNs and annealing robust learning algorithm (ARLA) for the nonlinear inverse system identification with outliers. That is, a two-stage structure; namely, an identification stage and an inverse identification stage is proposed. Firstly, the ε or v SVR uses the quadratic programming optimization to determine the initial structure of the annealing robust RBFNs in each stage for the system identification and the inverse system identification with outliers. Then, the proposed annealing robust RBFNs are trained by the ARLA, which uses the annealing concept in the cost function of robust back-propagation learning algorithm, can overcome the error measurement caused by the outliers for each stage. Hence, the proposed method has the same capability of universal approximator with the traditional RBFNs, a faster learning speed than the traditional RBFNs and outlier noise rejection with the proposed neural network for the nonlinear inverse system identification with outliers. Finally, the proposed approach is applied to magneto-rheological damper systems. Simulation results show the superiority of the proposed method for the prototype magneto-rheological damper and the nonlinear inverse system identification with outliers.