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In this paper a new, generalized PSO (GPSO) algorithm is presented and analyzed, both theoretically and empirically. The new optimizer enables direct control over the properties of the search process. In addition, PSO is addressed in conceptually different manner, revealing further aspects of the algorithm behavior. GPSO is applied for training radial basis function neural network (RBF-NN) to identify dynamics of a nonlinear system. The target system is chosen to be of Lorenz type, known for its complex, chaotic behavior. Results presented in this paper clearly demonstrate effectiveness of the proposed algorithm.