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A review on interval type-2 fuzzy logic applications in intelligent control

A Generalized Type-2 Fuzzy Controller (GT2FC) was developed.Simulation of a GT2FC for a mobile robot is presented.Experiments support the notion that GT2FC handles more uncertainty. The aim of this paper is to show that a Generalized Type-2 Fuzzy Control System can outperform Type-1 and Interval Type-2 Fuzzy Control Systems when external perturbations are present. A Generalized Type-2 Fuzzy System can handle better uncertainty because of the nature of its membership functions, and as such, they are better tailored for situations where external noise is present. To test the noise resilience of Fuzzy Controllers, the design of a Fuzzy Controller for a mobile robot is presented in this paper, in conjunction with three types of external perturbations: band-limited white noise, pulse noise, and uniform random number noise. Noise resilience is measured through different performance indices, such as ITAE, ITSE, IAE, and ISE. Simulation results show that Generalized Type-2 Fuzzy Controllers outperform their Type-1 and Interval Type-2 Fuzzy Controller counterparts in the presence of external perturbations.

Generalized Type-2 Fuzzy Systems for controlling a mobile robot and a performance comparison with Interval Type-2 and Type-1 Fuzzy Systems

In this paper, the problem of fuzzy filter design is investigated for a class of nonlinear networked systems on the basis of the interval type-2 (IT2) fuzzy set theory. In the design process, two vital factors, intermittent data packet dropouts and quantization, are taken into consideration. The parameter uncertainties are handled effectively by the IT2 membership functions determined by lower and upper membership functions and relative weighting functions. A novel fuzzy filter is designed to guarantee the error system to be stochastically stable with $\boldsymbol {H_{\infty }}$ performance. Moreover, the filter does not need to share the same membership functions and number of fuzzy rules as those of the plant. Finally, illustrative examples are provided to illustrate the effectiveness of the method proposed in this paper.

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Filtering of Interval Type-2 Fuzzy Systems With Intermittent Measurements

System dynamics : Applications in management and policy 1

A survey on modern trainable activation functions.

Interval type-2 fuzzy neural networks &#x0028 IT2FNNs &#x0029 can be seen as the hybridization of interval type-2 fuzzy systems &#x0028 IT2FSs &#x0029 and neural networks &#x0028 NNs &#x0029. Thus, they naturally inherit the merits of both IT2FSs and NNs. Although IT2FNNs have more advantages in processing uncertain, incomplete, or imprecise information compared to their type-1 counterparts, a large number of parameters need to be tuned in the IT2FNNs, which increases the difficulties of their design. In this paper, big bang-big crunch &#x0028 BBBC &#x0029 optimization and particle swarm optimization &#x0028 PSO &#x0029 are applied in the parameter optimization for Takagi-Sugeno-Kang &#x0028 TSK &#x0029 type IT2FNNs. The employment of the BBBC and PSO strategies can eliminate the need of backpropagation computation. The computing problem is converted to a simple feed-forward IT2FNNs learning. The adoption of the BBBC or the PSO will not only simplify the design of the IT2FNNs, but will also increase identification accuracy when compared with present methods. The proposed optimization based strategies are tested with three types of interval type-2 fuzzy membership functions &#x0028 IT2FMFs &#x0029 and deployed on three typical identification models. Simulation results certify the effectiveness of the proposed parameter optimization methods for the IT2FNNs.

Parameter optimization of interval Type-2 fuzzy neural networks based on PSO and BBBC methods

Big Bang-Big Crunch optimization based interval type-2 fuzzy PID cascade controller design strategy

The interval type-2 fuzzy Proportional-Integral (PI) controller (IT2-FPI) might be able to handle high levels of uncertainties to produce a satisfactory control performance, which could be potentially due to the robust performance as a result of the smoother control surface around the steady state. However, the transient state and disturbance rejection performance of the IT2-FPI may degrade in comparison with the type-1 fuzzy PI (T1-FPI) counterpart. This drawback can be resolved via general type-2 fuzzy PI controllers which can provide a tradeoff between the robust control performance of the IT2-FPI and the acceptable transient and disturbance rejection performance of the type-1 PI controllers. In this paper, we will present a zSlices-based general type-2 fuzzy PI controller (zT2-FPI), where the secondary membership functions (SMFs) of the antecedent general type-2 fuzzy sets are adjusted in an online manner. We will examine the effect of the SMF on the closed-system control performance to investigate their induced performance improvements. This paper will focus on the case followed in conventional or self-tuning fuzzy controller design strategies, where the aim is to decrease the integral action sufficiently around the steady state to have robust system performance against noises and parameter variations. The zSlices approach will give the opportunity to construct the zT2-FPI controller as a collection of IT2-FPI and T1-FPI controllers. We will present a new way to design a zT2-FPI controller based on a single tuning parameter where the features of T1-FPI (speed) and IT2-FPI (robustness) are combined without increasing the computational complexity much when compared with the IT2-FPI structure. This will allow the proposed zT2-FPI controller to achieve the desired transient state response and provide an efficient disturbance rejection and robust control performance. We will present several simulation studies on benchmark systems, in addition to real-world experiments that were performed using the PIONEER 3-DX mobile robot that will act as a platform to evaluate the proposed systems. The results will show that the control performance of the self-tuning zT2-FPI control structure enhances both the transient state and disturbance rejection performances when compared with the type-1 and IT2-FPI counterparts. In addition, the self-tuning zT2-FPI is more robust to disturbances, noise, and uncertainties when compared with the type-1 and interval type-2 fuzzy counterparts.

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A Self-Tuning zSlices-Based General Type-2 Fuzzy PI Controller

Recent results on fuzzy control have shown that interval type-2 (IT2) fuzzy logic controllers (FLCs) might achieve better control performance due to the additional degree of freedom provided by the footprint of uncertainty (FOU) in their IT2 fuzzy sets. However, the design and robust stability analysis of the IT2-FLCs are still challenging problems due to their relatively more complex internal structure. In this paper, we will derive the explicitly fuzzy mapping (FM) of a single-input IT2-FLC (SIT2-FLC) to present design methods and investigate its robustness. The analytical information of the IT2-FM will give the opportunity to provide explanations on the roles of the FOU parameters by taking advantage of the well-developed framework of nonlinear control theory. Comparative theoretical explorations will be presented on the differences between the type-1 (T1) FM and IT2-FM to clearly show the role of the FOU on the robust control system performance. It will be proven that the robust stability of the IT2 fuzzy system is guaranteed with the aids of the well-known Popov–Lyapunov method. Moreover, analytical design methods are presented for SIT2-FLCs to generate commonly employed control curves by only tuning the size of the FOUs without a need of an optimization procedure. It will be theoretically shown that the FOU gives the opportunity to the SIT2-FLC to generate commonly employed nonlinear control curves while also providing a certain degree of robustness which cannot be accomplished by its T1 counterpart. The presented results provide theoretical explanations on the role of the FOU on the performance and robustness of the SIT2-FLC.

Robust Stability Analysis and Systematic Design of Single-Input Interval Type-2 Fuzzy Logic Controllers

In the last two decades, we have witnessed that Interval Type-2 Fuzzy Logic Systems (IT2-FLSs) have been successfully implemented in various engineering areas. In this paper, we will introduce a free open source Mat lab/Simulink toolbox for the development of IT2-FLSs for a wider accessibility to users beyond the type-2 fuzzy logic community. The presented IT2-FLS toolbox allows intuitive implementation of IT2-FLSs where it is capable to cover all the phases of its design. In order to allow users to easily construct IT2-FISs, a GUI is developed which is similar to that of Mat lab® Fuzzy Logic Toolbox. We have embedded various Type Reduction (TR) methods in the toolbox since the TR method is the most important operation that must be taken into consideration. This gives the opportunity to the user to examine the performance of his/her IT2-FLS design with respect to the TR methods. We have also developed an IT2-FLS Simulink library so that the designer can perform various simulation analyses and can also investigate the effect of TR method on the performance of the IT2-FLS. Moreover, the developed IT2-FLS Mat lab/Simulink toolbox contains an automatic connection between Mat lab and Simulink environments. Once the user has finished the design of the IT2-FLS via the GUI, it is possible to export his/her design directly to Simulink via an automatic Simulink file generation. We believe that the availability of the developed free and open-source IT2-FLS Mat lab/Simulink toolbox will be an important step for a wider deployment and development of IT2-FLSs.

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Tufan Kumbasar

Papers

Parameter optimization of interval Type-2 fuzzy neural networks based on PSO and BBBC methods

Big Bang-Big Crunch optimization based interval type-2 fuzzy PID cascade controller design strategy

A Self-Tuning zSlices-Based General Type-2 Fuzzy PI Controller

Robust Stability Analysis and Systematic Design of Single-Input Interval Type-2 Fuzzy Logic Controllers

An Open Source Matlab/Simulink Toolbox for Interval Type-2 Fuzzy Logic Systems