In this paper a concise overview of the work that has been done by various researchers in the area of type-2 fuzzy logic is analyzed and discussed. Type-2 fuzzy systems have been widely applied in ...the fields of intelligent control, pattern recognition and classification, among others. The overview mainly focuses on past, present and future trends of type-2 fuzzy logic applications. Of utmost importance is the last part, outlining possible areas of applied research in type-2 FL in the future. The major contribution of the paper is briefing of the most relevant work in the area of type-2 fuzzy logic, including its theoretical and practical implications. As well as envisioning possible future works and trends in this area of research. We believe that this paper will provide a good platform for people interested in this area for their future research work.
This article providesa systematic approach for the design of an interval type-3 (IT3) Takagi-Sugeno (T-S) fuzzy logic system (FLS) using <inline-formula><tex-math notation="LaTeX">\alpha ...</tex-math></inline-formula>- plane representation. An IT3 FLS is designed with the baseline of the general type-2 (GT2) FLS in a similar manner as an IT2 FLS was designed from the baseline of type-1 FLS. Hence, IT3 FLS evolved as a successor of GT2 FLS, where secondary membership function is an interval type-2 fuzzy set (FS), and values of tertiary membership are unity over the footprint of uncertainty of secondary membership. This extra degree of freedom in IT3 FLS provides better modeling capability as compared to GT2 FLS in the presence of a high degree of uncertainty and vagueness. The proposed system will be more appealing while dealing with uncertain information or data, which is supposed to be generated from uncertain sources; i.e., there exist uncertainties even in the presence of uncertainty. The computations needed for the design of IT3 FLS are derived using IT2 FS and GT2 FS mathematics. The design algorithms adopted for the baseline IT2 T-S fuzzy system are as per the modified interval type-2 fuzzy c-regression model clustering algorithm and hyper-plane-shaped membership function. The proposed methodology is applied to several benchmark examples and obtained results are compared with recently developed fuzzy modeling methods having a comparable number of rule bases. The proposed IT3 T-S FLS shows good performance in terms of accuracy when data is corrupted by noise and uncertainties related to missing or unvarying data exist. The computational cost is linear with design parameters and by optimum choice of <inline-formula><tex-math notation="LaTeX">\alpha </tex-math></inline-formula>-planes, it is still bearable considering advantages and nature of applications.
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.
This article investigates an adaptive practical fixed-time control strategy for the output tracking control of a class of strict feedback nonlinear systems. By utilizing a backstepping algorithm, ...finite-time Lyapunov stable theory, and fuzzy logic control, a novel adaptive practical fixed-time controller is constructed. Fuzzy logic systems are introduced to approximate the unknown items of the system. Theoretical analysis proves that under the presented control strategy, the closed-loop system is practically fixed-time stable, and the tracking error converges to a small neighborhood of the origin within a fixed-time interval, in which the convergence time has no connection with the initial states of the system. In the meantime, all the signals of the closed-loop system are bounded. Finally, a numerical example is presented to indicate the feasibility and effectiveness of the proposed method.
The adaptive fuzzy identification and control problems are considered for a class of multi-input multi-output nonlinear systems with unknown functions and unknown dead-zone inputs. The main ...characteristics of the considered systems are that 1) they are composed of n subsystems and each subsystem is in nested lower triangular form, 2) dead-zone inputs are in nonsymmetric nonlinear form, and 3) dead-zone inputs appear nonlinearly in the systems and their parameters are not required to be known. The controller design for this class of systems is a difficult and complicated task because of the existences of unknown functions, the couplings among the nested subsystems, and the dead-zone inputs. In the controller design, the fuzzy logic systems are employed to approximate the unknown functions and the differential mean value theorem is used to separate dead-zone inputs. To compensate for dead-zone inputs, the compensative terms are designed in the controllers. The stability of the closed-loop system is proved via the Lyapunov stability theorem. A simulation example is provided to validate the feasibility of the approach.
The purpose of this tutorial paper is to make general type-2 fuzzy logic systems (GT2 FLSs) more accessible to fuzzy logic researchers and practitioners, and to expedite their research, designs, and ...use. To accomplish this, the paper 1) explains four different mathematical representations for general type-2 fuzzy sets (GT2 FSs); 2) demonstrates that for the optimal design of a GT2 FLS, one should use the vertical-slice representation of its GT2 FSs because it is the only one of the four mathematical representations that is parsimonious; 3) shows how to obtain set theoretic and other operations for GT2 FSs using type-1 (T1) FS mathematics (α- cuts play a central role); 4) reviews Mamdani and TSK interval type-2 (IT2) FLSs so that their mathematical operations can be easily used in a GT2 FLS; 5) provides all of the formulas that describe both Mamdani and TSK GT2 FLSs; 6) explains why center-of sets type-reduction should be favored for a GT2 FLS over centroid type-reduction; 7) provides three simplified GT2 FLSs (two are for Mamdani GT2 FLSs and one is for a TSK GT2 FLS), all of which bypass type reduction and are generalizations from their IT2 FLS counterparts to GT2 FLSs; 8) explains why gradient-based optimization should not be used to optimally design a GT2 FLS; 9) explains how derivative-free optimization algorithms can be used to optimally design a GT2 FLS; and 10) provides a three-step approach for optimally designing FLSs in a progressive manner, from T1 to IT2 to GT2, each of which uses a quantum particle swarm optimization algorithm, by virtue of which the performance for the IT2 FLS cannot be worse than that of the T1 FLS, and the performance for the GT2 FLS cannot be worse than that of the IT2 FLS.
This paper investigates the problem of fuzzy adaptive asymptotic tracking control for a third-order heterogeneous vehicular platoon system (HVPS) with input saturation. The unknown nonlinear ...functions are approximated using fuzzy logic systems (FLSs). To address the issue of input saturation, a control scheme with an auxiliary design system is proposed. A spacing error is created to reduce the inter-vehicle spacing. The proposed adaptive asymptotic tracking control design scheme employs the barrier Lyapunov functions (BLFs) to impose distance restrictions, ensuring collision avoidance and maintaining communication connections. The scheme guarantees asymptotic convergence with zero spacing error and proves the individual and string stability (SS) of the entire heterogeneous vehicular platoon. Simulations are conducted to demonstrate the effectiveness of the proposed results.
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