This paper presents a fuzzy neural network system (FNNS) for implementing fuzzy inference systems. In the FNNS, a fuzzy similarity measure for fuzzy rules is proposed to eliminate redundant fuzzy logical rules, so that the number of rules in the resulting fuzzy inference system will be reduced. Moreover, a fuzzy similarity measure for fuzzy sets that indicates the degree to which two fuzzy sets are equal is applied to combine similar input linguistic term nodes. Thus we obtain a method for reducing the complexity of a fuzzy neural network. We also design a new and efficient on-line initialization method for choosing the initial parameters of the FNNS. A computer simulation is presented to illustrate the performance and applicability of the proposed FNNS. The result indicates that the FNNS still has desirable performance under fewer fuzzy logical rules and adjustable parameters.

This paper presents a new method for fine-tuning the Gaussian membership functions of a fuzzy neural network (FNN) to improve approximation accuracy. This method results in special shape membership functions without the convex property. We first recall that any continuous function can be represented by a linear combination of Gaussian functions with any standard deviation. Therefore, the Gaussian membership function in the second layer of the FNN can be replaced by several small Gaussian functions; the weighting vectors of this new network (called FNN 5 ) can then be updated using the backpropagation algorithm. The proposed method can adapt proper membership functions for any nonlinear input/output mapping to achieve highly accurate approximation. Convergence analysis shows that the weighting vectors of the FNN 5 eventually converge to the optimal values. Simulation results indicate that (a) this approach improves approximation accuracy, and (b) that the number of rules can be reduced for any given level of accuracy. For the purpose of illustrating the proposed method, the FNN 5 is also applied to tune PI controllers such that gain and phase margins of the closed-loop system achieve the desired specifications.

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In this paper, we propose a robust PID controller tuning method for parametric uncertainty systems (or interval plant family) using fuzzy neural networks (FNNs). This robust controller is based on robust gain and phase margin (GM/PM) specifications that satisfy user requirements. Here, the FNN system is used to identify the relation between the PID controller parameters and robust GM/PM. We can use the trained FNN system to determine the parameters of the PID controllers in order to satisfy robust GM/PM specifications that guarantee robustness and performance. Simulation results are shown to illustrate the effectiveness of the robust controller scheme.

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In this paper, robust sampled‐data control systems are analyzed in the frequency domain. Stability analysis of a sampled‐data control system using higher‐order integrators was proposed by Wang et al. in 1990 [1] and adopted in the approximate Z‐transform by Wang et al. in 1997 [2]. We further apply the approximate Z‐transform to analyze the stability boundary of a sampled‐data control system in which the plant transfer function has bounds prescribed on its parameters.

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