Interval Type-2 Fuzzy Logic Research Articles

An Intelligent Type-2 Fuzzy Stabilization of Multi-DC Nano Power Grids

This paper proposes a robust and intelligent droop control method to stabilize a cluster of DC nanogrids (DCNGs) with constant power loads (CPLs). Conventional droop methods suffer from voltage regulation in parallel converters due to the CPLs destructive effects, which cause instability in the DCNGs. To address the shortcomings of the conventional methodologies, this paper proposes a new droop-based single input interval type-2 fuzzy logic controller (SI-IT2-FLC), which enhances the transient response and improve the steady-state performance. The suggested method aims to boost the stability of the paralleled DCNGs in a cluster under the effect of the CPLs, which is inevitable in the practical applications. The efficacy of the suggested scheme is validated in different operating conditions. Moreover, real-time model-in-the-loop (MiL) results show the performance improvements in the transient and steady-state obtained by the novel suggested control approach.

A new fractional-order general type-2 fuzzy predictive control system and its application for glucose level regulation

In this paper a new robust fractional-order predictive controller is presented and employed to regulate the glucose level in type-1 diabetes. The dynamics of the system is fully unknown an it is online estimated by a fractional-order model using interval Type-2 (T2) fuzzy logic system. The proposed control system is composed of two main controllers which are the predictive General T2 Fuzzy Logic Controller (GT2-FLC) and compensator controller. In this structure, the main controller is the GT2-FLC which is optimized via the Biogeography-based Optimization (BBO) algorithm such that to minimize a cost function in a fixed prediction horizon. The compensator controller is designed to guarantee the closed-loop asymptotic stability. The performance of proposed control strategy is examined on the modified Bergman’s model of some patients with time-varying parameters, external noise perturbation and meal disturbances. The effectiveness of the proposed control scheme is verified and is compared with the other T2 fuzzy and well-known model predictive controllers. The results of the paper clearly show the superiority of the proposed T2 fuzzy logic control system.

Adaptive finite integral non-singular terminal synergetic control of nth-order nonlinear systems

This paper proposed a novel finite synergetic control scheme. This controller utilizes an integral non-singular terminal attractor technique that guarantees the finite-time convergence of the states, solves the singularity problem of a conventional terminal attractor manifold, and provides a chattering-free control signal. The principles of this controller are introduced and demonstrated for second and nth-order nonlinear systems. The stability of the controller is verified using Lyapunov stability theory. In addition, an interval type-2 fuzzy logic system is implemented to improve the overall performance of the controller. Analysis of a robotic manipulator and a servo-hydraulic actuator is used to illustrate the efficacy of the proposed Adaptive Finite Integral Non-singular Terminal Synergetic Control (AFINTSC).

Design of Interval Type-2 Fuzzy Controllers for Active Magnetic Bearing Systems

This article proposes an active levitation control system composed of an active magnetic bearing (AMB) rotor and an interval type-2 (IT2) model-based fuzzy logic controller (FLC). The controller aims to achieve fast and stable levitation by compensating for system uncertainties via proper design of IT2 membership functions. In particular, the complex nonlinear dynamics of the AMB are modeled as a set of local linear systems around multiple operating points, which can be stabilized by a parallel distributed compensation scheme. Sufficient conditions are derived to guarantee the asymptotical stability of the closed-loop system based on the linear matrix inequality approach and the Lyapunov stability theory. Moreover, input constraints are applied in an enhanced version of the controller. Experiments on a real AMB platform were conducted to demonstrate the effectiveness and superiority of the proposed IT2 FLC.

Observer-Based Interval Type-2 Fuzzy Logic Control for Nonlinear Networked Control Systems with Delays

One of the popular area of research for the past decade in the academia as well as in the industry is networked control systems (NCS). Variable time delays induced by the network and data packet dropout during transmission of data are among the problems encountered in these type of systems. Researchers proposed and developed various control strategies over the past years to deal with the above-mentioned problem. Fuzzy logic control (FLC) is a widely used technique for dealing with control problems, and the most commonly used one is type-1 FLC. However, the interval type-2 (IT2) is proven to be better at handling uncertainties compared to the type-1 FLC. In this paper, a nonlinear NCS with delays is considered, and an observer-based IT2 FLC is designed in order to improve the control of NCS due to the presence of uncertainties and delays. The developed scheme includes the design of a state feedback controller based on IT2 FLC, and an observer-based IT2 FLC using Lyapunov–Krasovskii theory. To investigate the effectiveness of the proposed scheme, simulations are performed considering various network delays. Firstly, the results of IT2 FLCs are compared with that of type-1 FLCs and improvement is observed. Secondly, the newly developed observer-based IT2 FLC is compared with the IT2 state feedback FLC developed in the literature. Results show faster and more effective response using the newly developed technique.

Robust design of type-2 fuzzy logic-based maximum power point tracking for photovoltaics

Photovoltaic (PV) power generation is uncertain and intermittent due to varying insolation and temperature. The Maximum Power Point Tracking (MPPT) algorithm implemented in a DC/DC converter ensures maximum PV power generation for a given insolation and temperature. This paper proposes a novel method to achieve this optimization under uncertainty: (1) An Interval Type-2 Fuzzy Logic System (IT2FLS) is used to tune the duty cycle of a DC/DC converter. The control gains and IT2 membership functions are tuned optimally using approximate gradient-descent algorithm. The so-called footprint of uncertainty (FOU) in the IT2 membership functions ensures that the IT2FLS is more powerful than traditional FLS in dealing with noise and uncertainty. (2) Taguchi’s orthogonal scenarios are used to evaluate the PV power generations by considering different meteorological conditions. Signal-to-noise ratios (SNR) obtained from Taguchi’s experiments are then analyzed by average effect of all control factor levels and main effect of each control factor to achieve the robust design of control gains and IT2 fuzzy membership functions. The proposed method is implemented using a DSP Chip-in-the-Loop (DIL) simulation through a real-time simulator OPAL-RT (OP5600) and TI DSP Chip (eZdsp TMS320F28335). A standalone PV system with a boost converter and load is used to demonstrate the practical applicability of the proposed method.

A Close Loop Multi-Area Brain Stimulation Control for Parkinson’s Patients Rehabilitation

In recent years, deep brain stimulation (DBS) has been one of the most effective methods for treating movement disorders, including hand tremor in advanced Parkinson’s disease (PD). In order to decrees the Parkinson’s tremor, a model of basal ganglia (BG) is often used to design a closed-loop control scheme for DBS. First, a feedback signal is provided using a sensor mounted to the patient’s finger to measure the tremor values. Then, a controller sends the appropriate control commands to the actuator, and finally, the BG areas of the brain actuator are simulated by the actuator. In the present paper, to control Parkinson’s tremor and reduce the value of stimulation intensity efficiently, two areas of BG such as subthalamic nucleus (STN) and globus pallidus internal (GPi) were controlled simultaneously. This strategy provides a reduction in the applied field and side-effects (e.g. muscle contraction and speech disorder) resulting from stimulation intensity. In particular, a new model-free scheme, called intelligent single input interval type-2 fuzzy logic (iSIT2-FL) combined with non-integer sliding mode control (SMC), is proposed to control two areas of BG. In the suggested strategy, an extended state observer (ESO) is established to approximate the unknown BG dynamics, whereas the non-integer SMC is applied to remove the ESO estimation error. Comparative simulation explorations are performed subsequently to ascertain the superior performance of the suggested intelligent control scheme over that of the state-of-the-art approaches.

Derivative-Based Learning of Interval Type-2 Intuitionistic Fuzzy Logic Systems for Noisy Regression Problems

This study presents a comparative evaluation of interval type-2 intuitionistic fuzzy logic system using three derivative-based learning algorithms on noisy regression problems. The motivation for this study is to manage uncertainty in noisy regression problems for the first time using both membership and non-membership functions that are fuzzy. The proposed models are able to handle ‘neither this nor that state’ in the noisy regression data with the aim of enabling hesitation and handling more uncertainty in the data. The gradient descent-backpropagation (first-order derivative), decoupled extended Kalman filter (second-order derivative) and hybrid approach (where the decoupled extended Kalman filter is used to learn the consequent parameters and gradient descent is used to optimise the antecedent parameters) are applied for the adaptation of the model parameters. The experiments are conducted using two artificially generated and one real-world datasets, namely Mackey–Glass time series, Lorenz time series and US stock datasets. Experimental analyses show that the extended Kalman filter-based learning approaches of interval type-2 intuitionistic fuzzy logic exhibit superior prediction accuracies to gradient descent approach especially at high noise level. The decoupled extended Kalman filter model however converges faster but incurs more computational overhead in terms of the running time.

A New Interval Type-2 Fuzzy Logic System Under Dynamic Environment: Application to Financial Investment

This paper proposes a new interval type-2 fuzzy logic system (IT2 FLS) for financial investment with time-varying parameters adaptive to real-time data streams by using an on-line learning method based on a state-space framework. Particularly, our state-space approach regards parameters of IT2 FLSs as state variables to sequentially learn by Bayesian filtering algorithms under dynamic environment, where time-series data are continuously observed with occasional structural changes. Moreover, our proposal is helpful for financial applications, which often involve various practical complex constraints, because general state-space model makes it possible to flexibly deal with non-linearities. In our empirical experiment with time-series data of financial assets, our approach is applied to on-line parameter learning of type-1 and type-2 FLSs for portfolio decision making. As a result, it is shown that the IT2 FLS holds its advantage against the type-1 FLS, even though the both type-1 and type-2 models have the adaptive time-varying parameters, which is an unexplored topic for empirical studies of this area.

A Novel Deep Reinforcement Learning Controller Based Type-II Fuzzy System: Frequency Regulation in Microgrids

The high-penetration of distributed generation technologies in the form of MicroGrids (MGs), in recent years, has increased the risk of frequency instability since their energy is supplied by renewable energy resources (RESs) with uncertain nature. Under such circumstances, providing an MG model with an efficient load frequency control (LFC) has a fundamental role in restoring the stability of the unstructured power system. In this study, a hybrid power system with the application of the Tidal Power Unit (TPU) and Vehicle-to-Grid (V2G) is effectively planed as an isolated MG. A new fractional gradient descent (FGD) based on a single-input interval type-2 fuzzy logic controller (SIT2-FLC) is suggested as the main LFC controller, where the footprint of uncertainty (FOU) coefficient of the SIT2-FLC is specifically adjusted to enhance the LFC performance. Additionally, a deep deterministic policy gradient (DDPG) with the actor-critic framework is considered to generate the supplementary control action, which is useful for the frequency stabilization by adapting to the randomness of load disturbances and RESs. Lastly, a model-in-the-loop (MiL) simulation is conducted to appraise the feasibility and applicability of the suggested design method from a systemic perspective.

Type-2 fuzzy logic based pitch angle controller for fixed speed wind energy system

In this paper, an interval Type-2 fuzzy logic based pitch angle controller is proposed for fixed speed wind energy system (WES) to maintain the aerodynamic power at its rated value. The pitch angle reference is generated by the proposed controller which can compensate the non-linear characteristics of the pitch angle to the wind speed. The presence of third dimension in the Type-2 fuzzy logic controller (FLC) membership function offers an additional degree-of-freedom in the design of the Type-2 FLC controller to improve the system performance. The applicability of the proposed controller is evaluated by considering a nonlinear simulation model of the WES which is developed and implemented using OPAL-RT real time digital simulator. The results show that the proposed controller offers better performance than the conventional PI and fuzzy logic controllers.

Interval Type-2 Intuitionistic Fuzzy Logic System for Time Series and Identification Problems - A Comparative Study

This paper proposes a sliding mode control-based learning of interval type-2 intuitionistic fuzzy logic system for time series and identification problems. Until now, derivative-based algorithms such as gradient descent back propagation, extended Kalman filter, decoupled extended Kalman filter and hybrid method of decoupled extended Kalman filter and gradient descent methods have been utilized for the optimization of the parameters of interval type-2 intuitionistic fuzzy logic systems. The proposed model is based on a Takagi-Sugeno-Kang inference system. The evaluations of the model are conducted using both real world and artificially generated datasets. Analysis of results reveals that the proposed interval type-2 intuitionistic fuzzy logic system trained with sliding mode control learning algorithm (derivative-free) do outperforms some existing models in terms of the test root mean squared error while competing favourable with other models in the literature. Moreover, the proposed model may stand as a good choice for real time applications where running time is paramount compared to the derivative-based models.

Multitasking Genetic Algorithm (MTGA) for Fuzzy System Optimization

Multi-task learning uses auxiliary data or knowledge from relevant tasks to facilitate the learning in a new task. Multi-task optimization applies multi-task learning to optimization to study how to effectively and efficiently tackle multiple optimization problems simultaneously. Evolutionary multi-tasking, or multi-factorial optimization, is an emerging subfield of multi-task optimization, which integrates evolutionary computation and multi-task learning. This paper proposes a novel and easy-to-implement multi-tasking genetic algorithm (MTGA), which copes well with significantly different optimization tasks by estimating and using the bias among them. Comparative studies with eight state-of-the-art single- and multi-task approaches in the literature on nine benchmarks demonstrated that on average the MTGA outperformed all of them, and had lower computational cost than six of them. Based on the MTGA, a simultaneous optimization strategy for fuzzy system design is also proposed. Experiments on simultaneous optimization of type-1 and interval type-2 fuzzy logic controllers for couple-tank water level control demonstrated that the MTGA can find better fuzzy logic controllers than other approaches.

Robust control of automatic voltage regulator (AVR) with real structured parametric uncertainties based on [formula omitted] and [formula omitted]-analysis

Within this work, a novel controller in terms of H infinity (H∞) and structured singular value decomposition has been presented to provide the robust performance of the Automatic Voltage Regulator (AVR) system Six real structured uncertainties in actuator, exciter and generator have been assumed for the linear transfer functions of the AVR system. Each uncertain parameter varies between a minimum and a maximum value due to the load variations in a period of time and aging effects over the life time. The efficiency of the presented design lies on two main reasons. The first is the simultaneous considering of the output disturbances, sensor noises and system uncertainties in the controller design approach. The second is the non-conservative modeling of all six structured parameters in the required μ-synthesis P−Δ−K configuration. By suboptimal H∞ control design technique and μ-analysis theorem, a single input single output (SISO) controller comprising a closed loop system with μ<1 is obtained. The offered controller’s supremacy is represented through comparison of its performance with some other optimized PID, PIDD fractional order PID (FOPID), fuzzy + PID and Interval Type-2 fuzzy logic controllers by heuristic optimization algorithms. The simulation outcomes indicate that the provided robust controller for the AVR system has the better performance than the other optimized and fuzzy controllers in a wide range of the uncertainties. Also, the better behavior of the intended robust controller was shown in two benchmarks: a single machine connected to a 230kV network, and a four-machine two-area test system.

Asymmetrical interval type-2 fuzzy logic control based MPPT tuning for PV system under partial shading condition

The conventional maximum power point tracking (MPPT) algorithm shows best performance under uniform insolation but when photovoltaic (PV) array is partially irradiated, the Power vs Voltage (P–V) plot consists of multiple local maxima power point (LMPP) and one global maxima power point (GMPP). The conventional MPPT algorithm may track local peak and fluctuate around it, resulting in lower power tracking. To eradicate this drawback of conventional algorithm, the solar PV system requires the synthesis of modified controller which is able to discriminate between local and global peak point. Along with implementing modified MPPT controller, to minimise the adverse effect of partial shading on PV system, different PV array arrangements like series-parallel (SP), honey comb (HC), total cross tied (TCT) etc. may be used. Author(s) in the present study, has proposed asymmetrical interval type-2 fuzzy logic control (IT-2 AFLC) based MPP algorithm for tracking global peak in partial shading condition (PSC) with different PV array arrangements. The presented algorithm has been compared with other approaches viz. perturb & observe (P&O) and type-1(T-1) FLC for GMPP tracking, fill factor, shading losses, mismatch loss and efficiency to establish its superiority. For evaluating the efficiency of different algorithms, the EN50530 MPPT efficiency test has been performed under dynamic condition. The proposed algorithm has been developed under MATLAB/Simulink environment.

Optimization of Interval Type-2 Fuzzy Logic System for Software Reliability Prediction

Since real world application is fraught with high amount of uncertainty, such as applicable to software reliability, there should be a method of handling the uncertainty. This paper presents a model to properly handle uncertainty in software data for effective prediction of the reliability of software at the early phase of software development process. In this paper we employed a Takagi-Sugeno-Kang (TSK)-based interval type 2 fuzzy logic systems with artificial neural network learning for the prediction of software reliability. The degree of membership grades of the interval type 2 fuzzy sets (IT2FSs) are obtained using interval type Gaussian membership function with fixed mean and uncertain standard deviation. The parameters of the IT2FLS membership functions are optimized using gradient descent (GD) back-propagation algorithm. As inputs to the system, reliability relevant software requirement metrics and the software size metrics are used. The proposed new approach makes use of qualitative data of requirement metrics of twenty three real software projects to examine its predictive ability. The performance of the model is evaluated using five performance metrics and found to provide better results when compared with existing approaches.

Interval Type-2 Intuitionistic Fuzzy Logic System for Forecasting the Electricity Load

A study on load forecasting prediction is important for efficient management of users' demands for any utility such as electricity and gas. Many computational intelligence approaches have been adopted for short term electricity load forecasts. For instance, artificial neural network, traditional fuzzy neural networks, support vector machines and other intelligent methods have been adopted in the literature. It is well known that load forecast is an important input for management decision systems in every power supply organization. Fuzzy logic systems (type-1 and type-2) have proven to be one of the effective tools for many load forecasting problems. In this study, interval type-2 intuitionistic fuzzy logic system equipped with membership functions, non-membership functions and hesitation indices is proposed for very short and short-term load forecasting for the first time. Gradient descent method is used to optimize the parameters of the developed model. The proposed model is compared with the traditional interval type-2 fuzzy logic and traditional neural network systems. Experimental analyses reveal that the proposed model outperform the two traditional systems in many load instances.

Movable Payload on Various Conditions of Two-Wheeled Double Links Wheelchair Stability Control Using Enhanced Interval Type-2 Fuzzy Logic

This paper presents investigations of control strategies for a two-wheeled wheelchair with a movable payload on various conditions using a double-link inverted pendulum concept. The wheelchair system is modeled in the SimWise 4D (SW4D) with its optimized control parameters determined using the Spiral Dynamic Algorithm (SDA) while being controlled by the proposed Interval Type-2 Fuzzy Logic Controller (IT2FLC). The robustness of the proposed controller in terms of maintaining the system’s stability while the wheelchair is standing in an upright position is tested under multiple circumstances. These included utilizing varying directions and applying magnitudes of external disturbances to the developed system with a movable payload (upward and downward) and testing the system’s forward and backward motions on a flat surface and the motions on an inclined surface. Ultimately, the two-wheeled wheelchair which adopts the proposed controller had shown a 68% and 77% reduction in the angular positions of Link1 and Link2, a 94% reduction in torques for both Link1 and Link2, and more than 98% reduction in traveling distance compared to the Fuzzy Logic Control Type-1 (FLCT1) controller which was used in the previous design. Moreover, the current work has taken into consideration the heightened nonlinearities and complexity of an additional moving payload on various conditions to represent more degree of freedom (DOF), compared to the fixed payload in the previous design with less DOF. This further rectifies that the enhanced IT2FLC had outperformed FLCT1 in handling nonlinearities and uncertainties, for the case of a two-wheeled wheelchair system with a movable payload.

An Unequal Clustering Algorithm for Wireless Sensor Networks Based on Interval Type-2 TSK Fuzzy Logic Theory

Clustering is an effective method for reducing energy consumption in wireless sensor networks (WSNs). In a multihop clustered network scenario, each sensor node transmits data to its own cluster head (CH), and the CH aggregates the data from its member nodes and forwards it to the base station (BS) via other CHs. However, the “hot spot” problem is prone to occur in clustered WSNs because CHs closer to the BS have heavier intercluster forwarding tasks. To address this problem, this paper proposes an unequal clustering algorithm based on interval type-2 TSK fuzzy logic theory (UCT2TSK). The relative distance to the BS (RDB), residual energy (RE), and node density (ND) are considered as the inputs of an interval type-2 fuzzy logic system (FLS). Through fuzzy reasoning, outputs are acquired that can be used to optimize the CHs and determine the cluster sizes. Simulation results verify that UCT2TSK can effectively balance energy consumption and enhance energy efficiency because it has better performance in network lifetime and network throughput than other classical and recent clustering algorithms.

Study on weighted-based noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

Interval type-2 fuzzy logic systems (IT2 FLSs) have been widely used in many areas. Among which, type-reduction (TR) is an important block for theoretical study. Noniterative algorithms do not involve the complicated iteration process and obtain the system output directly. By discovering the inner relations between discrete and continuous noniterative algorithms, this paper proposes three types of weighted-based noniterative according to the Newton-Cotes quadrature formulas in numerical integration techniques. Moreover, the continuous noniterative algorithms are considered as the benchmarks for computing. Four simulation experiments are provided to illustrate the performances of weighted-based noniterative algorithms for computing the defuzzified values of IT2 FLSs. Compared with the original noniterative algorithms, the proposed weighted-based algorithms can obtain smaller absolute errors and faster convergence speeds under the same sampling rate, which afford the potential values for designing T2 FLSs.