Identification of MIMO systems using radial basis function networks with hybrid learning algorithm

When a radial basis function network (RBFN) is used for identification of a nonlinear multi-input multi-output (MIMO) system, the number of hidden layer nodes, the initial parameters of the kernel, and the initial weights of the network must be determined first. For this purpose, a systematic way that integrates the support vector regression (SVR) and the least squares regression (LSR) is proposed to construct the initial structure of the RBFN. The first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the SVR method. Then the weights of the RBFN are determined by solving a simple minimization problem based on the concept of LSR. After initialization, an annealing robust learning algorithm (ARLA) is then applied to train the RBFN. With the proposed initialization approach, one can find that the designed RBFN has few hidden layer nodes while maintaining good performance. To show the feasibility and superiority of the annealing robust radial basis function networks (ARRBFNs) for identification of MIMO systems, several illustrative examples are included.