One of the major obstacles in using radial basis function (RBF) neural networks is the convergence toward local minima instead of the global minima. For this reason, an adaptive gradient multiobjective particle swarm optimization (AGMOPSO) algorithm is designed to optimize both the structure and parameters of RBF neural networks in this paper. First, the AGMOPSO algorithm, based on a multiobjective gradient method and a self-adaptive flight parameters mechanism, is developed to improve the computation performance. Second, the AGMOPSO-based self-organizing RBF neural network (AGMOPSO-SORBF) can optimize the parameters (centers, widths, and weights), as well as determine the network size. The goal of AGMOPSO-SORBF is to find a tradeoff between the accuracy and the complexity of RBF neural networks. Third, the convergence analysis of AGMOPSO-SORBF is detailed to ensure the prerequisite of any successful applications. Finally, the merits of our proposed approach are verified on multiple numerical examples. The results indicate that the proposed AGMOPSO-SORBF achieves much better generalization capability and compact network structure than some other existing methods.

Nonlinearity, uncertainties, and disturbances exist extensively in wastewater treatment processes (WWTPs), which result in control performance degradation and critical instability. To solve this problem, an efficient self-organizing sliding-mode controller (SOSMC) is proposed to achieve acceptable and stable control performance for WWTPs. The novelties of SOSMC involve: 1) a practical control strategy, combining advantages of sliding-mode control and fuzzy-neural network, was designed to suppress the disturbances and uncertainties of WWTPs; 2) a self-organizing mechanism, based on the tracking error and structure complexity, was developed to alleviate the chattering phenomenon of SOSMC and improve the control performance; and 3) the stability analysis, including the fixed and adaptive structures, was given to ensure the successful applications of SOSMC. Finally, experimental investigations on a real WWTP are employed to validate the merits of the proposed method.

Intelligent computing technologies are useful and important for online data modeling, where system dynamics may be nonstationary with some uncertainties. In this paper, an efficient learning mechanism is developed for building self-organizing fuzzy neural networks (SOFNNs), where a second-order algorithm (SOA) with adaptive learning rate is employed, the network size and the parameters can be determined simultaneously in the learning process. First, all parameters of SOFNN are adjusted by using the SOA strategy to achieve fast convergence through a powerful search scheme. Second, the structure of SOFNN can be self-organized using the relative importance index of each rule. The fuzzy rules used in SOFNN with SOA (SOA-SOFNN) are generated or pruned automatically to reduce the computational complexity and potentially improve the generalization power. Finally, a theoretical analysis on the learning convergence of the proposed SOA-SOFNN is given to show the computational efficiency. To demonstrate the merits of our proposed approach for data modeling, several benchmark datasets, and a real world application associated with nonlinear systems modeling problems are examined with comparisons against other existing methods. The results indicate that our proposed SOA-SOFNN performs favorably in terms of both learning speed and prediction accuracy for online data modeling.

Many nonlinear dynamical systems are usually lack of abundant datasets since the data acquiring process is time consuming. It is difficult to utilize the incomplete datasets to build an effective data-driven model to improve the industry productivity. To overcome this problem, a data-knowledge- based fuzzy neural network (DK-FNN) is developed in this paper. Compared with the existing methods, the proposed DK-FNN consists of the following obvious advantages. First, through the multilayered connectionist structure, this proposed DK-FNN can not only make full use of the data from the current scene, but also use the existing knowledge from the source scene to improve the learning performance. Second, an integrated-form transfer learning method is introduced to improve the learning performance of DK-FNN. This first reported integrated-form transfer learning method is able to integrate the internal information from the datasets in the source scene and the knowledge from the current scene to offset the data shortage in the learning process. Third, a mutual attraction strategy (MAS) is designed to balance the difference of data distributions to reduce the identification errors of DK-FNN, and thus the proposed DK-FNN can achieve the capability of improved identification for nonlinear dynamical systems. Finally, the effectiveness and the merit of DK-FNN are validated by applying it to several practical systems.

Interval type-2 fuzzy neural networks (IT2FNNs) usually stack adequate fuzzy rules to identify nonlinear systems with high-dimensional inputs, which may result in an explosion of fuzzy rules. To cope with this problem, a self-organizing IT2FNN, based on the information aggregation method (IA-SOIT2FNN), is developed to avoid the explosion of fuzzy rules in this article. First, a relation-aware strategy is proposed to construct rotatable type-2 fuzzy rules (RT2FRs). This strategy uses the individual RT2FR, instead of multiple standard fuzzy rules, to interpret interactive features of high-dimensional inputs. Second, a comprehensive information evaluation mechanism, associated with the interval information and rotation information of RT2FR, is developed to direct the structural adjustment of IA-SOIT2FNN. This mechanism can achieve a compact structure of IA-SOIT2FNN by growing and pruning RT2FRs. Third, a multicriteria-based optimization algorithm is designed to optimize the parameters of IA-SOIT2FNN. The algorithm can simultaneously update the rotatable parameters and the conventional parameters of RT2FR, and further maintain the accuracy of IA-SOIT2FNN. Finally, the experiments showcase that the proposed IA-SOIT2FNN can compete with the state-of-the-art approaches in terms of identification performance.

In this paper, a self-organizing intelligent controller (SOIC) is proposed for a class of nonlinear systems. The basic idea of this study is to use a self-organizing fuzzy neural network (SOFNN) to imitate control law directly, and then, appeal to obtain a compact structure of controller to further reduce the computational burden and enhance the control performance. Firstly, an effective criterion, using the tracking performance and structure risk of controller, is developed to self-organize the control rules online for SOIC to improve the tracking performance. Secondly, the structure and parameters of SOIC are updated by an adaptive projection-type algorithm to reduce the heavy computational burden to speed up the control response. Thirdly, the stability of SOIC is proved in the sense of Lyapunov and the guidelines for selecting the control parameters are given. Finally, the effectiveness of SOIC is illustrated with three nonlinear systems. It is shown that the proposed SOIC can achieve better control performance in comparison with some other control schemes.