Interval Type-2 Fuzzy Controller Research Articles

Self-Learning in Aerial Robotics Using Type-2 Fuzzy Systems: Case Study in Hovering Quadrotor Flight Control

This paper aims to design an enhanced self-adaptive interval type-2 fuzzy control system (ESAF2C) for stabilization of a quadcopter drone under external disturbances. Due to the ability to accommodate the footprint-of-uncertainty (FoU), an interval type-2 Takagi-Sugeno fuzzy scheme is employed to directly address the uncertainties in the nonlinear system. Sliding mode control (SMC) is utilized to optimize the upper and lower parameters of our proposed ESAF2C system using a self-tuning technique. The ‘Enhanced Iterative Algorithm with Stop Condition’ type-reducer is accommodated in the proposed design for its suitability to real-time implementation. To handle external disturbances and the ground effect in the closed-loop flight control system, a robustness term is added to the control effort. Lyapunov theory is applied to prove the stability of our closed loop control system. Moreover, we study the measurement noise effect for different levels of noise powers using our proposed technique. The efficacy of the proposed controller is investigated in a hovering quadcopter drone through numerical simulations and real-time flight tests in the presence of external disturbances. We highlight the disturbance rejection capability of our proposed control system with respect to type-1 fuzzy and conventional PID controllers.

Artificial potential field neuro-fuzzy controller for autonomous navigation of mobile robots

Some autonomous navigation methods, when implemented alone, can lead to poor performance, whereas their combinations, when well thought out, can yield exceptional performances. We have demonstrated this by combining the artificial potential field and fuzzy logic methods in the framework of mobile robots’ autonomous navigation. In this article, we investigate a possible combination of three methods widely used in the autonomous navigation of mobile robots, and whose individual implementation still does not yield the expected performances. These are as follows: the artificial potential field, which is quick and easy to implement but faces local minima and robustness problems. Fuzzy logic is robust but computationally intensive. Finally, neural networks have an exceptional generalization capacity, but face data collection problems for the learning base and robustness. This article aims to exploit the advantages offered by each of these approaches to design a robust, intelligent, and computationally efficient controller. The combination of the artificial potential field and interval type-2 fuzzy logic resulted in an interval type-2 fuzzy logic controller whose advantage over the classical interval type-2 fuzzy logic controller was the small size of the rule base. However, it kept all the classical interval type-2 fuzzy logic controller characteristics, with the major disadvantage that type-reduction remains the main cause of high computation time. In this article, the type-reduction process is replaced with two layers of neural networks. The resulting controller is an interval type-2 fuzzy neural network controller with the artificial potential field controller’s outputs as auxiliary inputs. The results obtained by performing a series of experiments on a mobile platform demonstrate the proposed navigation system’s efficiency.

Ride Comfort-Road Holding Trade-off Improvement of Full Vehicle Active Suspension System by Interval Type-2 Fuzzy Control

This paper presents a hybrid fuzzy controller structure to improve ride comfort-road holding trade-off characteristics of a full vehicle active suspension system. The controller includes two interval type-2 fuzzy logic controllers, optimized for ride comfort and road holding, for each tire. Type C random road profiles according to ISO 8608 are applied to each tire in the model and ride index, road holding, crest factor, and RMS acceleration values are evaluated. Stability of the overall closed loop system is presented by phase plane analysis. The simulation results reveal that simultaneous improvement of ride index and road holding can be made possible with the proposed controller.

Optimization of Type-2 Fuzzy Logic Controller Design Using the GSO and FA Algorithms

This paper presents a comparative study between the firefly algorithm (FA) and the galactic swarm optimization (GSO) method, where the performance of both methods is observed and tested in the optimization of a fuzzy controller for path tracking of an autonomous mobile robot. The main contribution of this work is finding the best method that generates an optimal vector of values for the membership function optimization of the fuzzy controller. This with the goal of improving the performance of the controller and thus the trajectory generated by the autonomous robot is closer to the desired trajectory. It should be noted that the fuzzy controller that is optimized is an interval type-2 fuzzy controller, which has a greater capability for managing uncertainty than a type-1 fuzzy controller. In this case, the limiting membership functions in the interval type-2 fuzzy sets are themselves type-1 fuzzy sets that define the footprint of uncertainty. Type-2 fuzzy controllers have been shown in previous works to handle better the control of robotic systems under noisy and dynamic conditions and this is why their optimal design is very important. Simulation results show that GSO outperforms FA in the optimal design of interval type-2 fuzzy controllers.

A Robust Self-Adaptive Interval Type-2 TS Fuzzy Logic for Controlling Multi-Input–Multi-Output Nonlinear Uncertain Dynamical Systems

Recently, Type-2 fuzzy systems have become increasingly prominent as they have been applied to various nonlinear control applications. This article presents an adaptive fuzzy controller based on the sliding-mode control theory. The proposed self-adaptive interval Type-2 fuzzy controller (SAF2C) is based on the Takagi–Sugeno (TS) fuzzy model and it accommodates the “enhanced iterative algorithm with stop condition” type-reducer, which is more computationally efficient than the “Kernel–Mendel” type-reduction algorithm. We developed an integrated multi-input–multi-output (MIMO) SAF2C-controller to reduce the computation time so that we can expedite the learning process of our control algorithm by 80% compared to separate single-input–single-output (SISO) controllers. The stability of our controller is proven using the Lyapunov technique. To ensure the applicability of the presented control scheme, we implemented our controller on various nonlinear systems, including a hexacopter unmanned aerial vehicle (UAV). We also compare the accuracy of our controller with a conventional proportional–integral–derivative autopilot system. Our research indicates around 20% improvement in its transient response, in addition to achieving a better noise rejection capability with respect to a Type-1 fuzzy counterpart.

Model-free adaptive control for the PEMFC air supply system based on interval type-2 fuzzy logic systems

Control aims to avoid oxygen starvation and maximize the net power output by maintaining the optimal oxygen excess ratio (OER), which varies between 1.8 and 2.5. Because of the nonlinearity of the proton exchange membrane fuel cell (PEMFC) air supply system and the different conditions, ensuring an optimal OER is still a challenge. In this study, a model-free adaptive controller is presented for the PEMFC air supply system based on feedback linearization and interval type-2 fuzzy logic systems (IT2 FLSs). Theoretical analysis and experimental results verify the effectiveness of the proposed control scheme. For the theoretical analysis, first, the PEMFC air supply system is transformed into a canonical form with the feedback linearization technique. Then, zero-dynamics stability is discussed in detail to determine the stability of the internal dynamics. Finally, an adaptive interval type-2 fuzzy logic system controller (AIT2FLSC) is designed on the basis of the Lyapunov stability theory, which does not require complete a priori knowledge of the system dynamics. For the experimental results, the root mean square error (RMSE), variance, and standard deviation (SD) of the tracking error are used as tracking performance metrics to evaluate the control accuracy of the proposed AIT2FLSC, which are 0.0968, 0.0093, and 0.0962, respectively. Compared with the traditional proportion integration differentiation controller (RMSE 0.1119, variance 0.0122, and SD 0.1105), this proposed algorithm obtains better adaptability and the RMSE of the tracking error improves 13.48%. Compared with the adaptive type-1 fuzzy logic system controller (AT1FLSC) (RMSE 0.1076, variance 0.0113, and SD 0.1063), this AT2FLSC has a stronger ability to deal with uncertainty and the RMSE of the tracking error improves 10% when the stack temperature is fixed (353.15 K). Furthermore, when the stack temperature is time-varying, the RMSE, variance, and SD of the tracking error under the AIT2FLSC are 0.0966, 0.0092, and 0.0960, respectively, which is less than AT1FLSC (0.1085, 0.0115, and 0.1073) and the RMSE of the tracking error improves 10.99%.

Interval Type-2 Fuzzy Logic PID Controller Based on Differential Evolution with Better and Nearest Option for Hydraulic Serial Elastic Actuator

Interval type-2 fuzzy logic controller (IT2FLC) owns good performance under uncertainty and nonlinearity environments while its optimization is hard and complicated. In this work, we propose an optimization method based on differential evolution with better and nearest option (NbDE) for interval type-2 fuzzy logic PID controller (IT2FL-PID-C) in order to control the position of hydraulic serial elastic actuator (SEA). Firstly, a simplified IT2FL-PID-C structure with fewer parameters is proposed to reduce the difficulty of the optimization of IT2FL-PID-C. To balance its frequency and step performance, an objective function with weighted integral time absolute error and integral square error is given. Secondly, to investigate the performance of NbDE based IT2FL-PID-C, three experiments are conducted. A set of experiments is taken to determine the weight for fitness function. Then we compare NbDE with other algorithms. In addition, NbDE-IT2FL-PID-C is also compared with other optimization methods. At last, NbDE-IT2FL-PID-C is applied to hydraulic SEA and compared with PID. And a range for the weight of fitness function is given. The results have shown the superiority of NbDE with proposed fitness function to optimize IT2FL-PID-C and the superiority of NbDE-IT2FL-PID-C to control the position of hydraulic SEA.

Adaptive Type-2 Fuzzy Neural-Network Control for Teleoperation Systems With Delay and Uncertainties

Interacting with human operators, remote environment, and communication networks, teleoperation systems are considerably suffering from complexities and uncertainties. Managing these is of paramount importance for safe and smooth performance of teleoperation systems. Among the countless solutions developed by researchers, type-2 fuzzy (T2F) algorithms have shown an outstanding performance in modeling complex systems and tackling uncertainties. Moreover, artificial neural networks (NNs) are well known for their adaptive learning potentials. This article proposes an adaptive interval type-2 fuzzy neural-network control scheme for teleoperation systems with time-varying delays and uncertainties. The T2F models are developed based on the experimental data collected from a teleoperation setup over a local computer network. However, the resulted controller is evaluated on an intercontinental communication network through the Internet between Australia and Scotland. Moreover, the slave robot and the remote workspace are completely different and unforeseen. Stability and performance of the proposed control is analyzed by Lyapunov–Krasovskii method. Comprehensive comparative studies demonstrate that the proposed controller outperforms traditional techniques in experimental evaluations.

One wheel vehicle real world control based on interval type 2 fuzzy controller

In this study, a novel adaptive interval type-2 fuzzy controller (AIT2FC) is used for a single-wheel vehicle (SWV) control problem. A control technique for use by a person riding on an SWV that enables real-world balance control of electric unicycles is proposed. The proposed SWV can keep balance and move around. Moreover, it can also stand up stably in any position when a person rides on it without touching the ground. AIT2FC is an advanced version of the traditional Mamdani-like fuzzy controller. The AIT2FC parameters are adjusted online using an intelligent dynamic tuning method. Moreover, the parameter learning rates of the adaptive laws are determined using a stability algorithm to guarantee the system error convergence. Furthermore, an SWV based on a microcontroller with some handmade hardware circuits is implemented. Finally, the efficiency of the AIT2FC is proved by real-time control of SWVs.

Design of the footprints of uncertainty for a class of typical interval type-2 fuzzy PI and PD controllers

The Footprint of Uncertainty (FOU) for an Interval type-2 (IT2) input fuzzy set is a key parameter of IT2 fuzzy PI and PD (FPI and FPD) controllers because it provides additional options to handle uncertainties. Because the effects of FOUs on IT2 FPI and FPD controller are still unclear, it is necessary to provide a guideline for designing the FOUs. In this study, from the input–output relationship of IT2 FPI and FPD controllers using typical and popular configuration, the variation trend of variable gains, in relation to the increase of FOUs, was analyzed. It is mathematically proven that variable gains of typical controllers decrease or not increase as the FOUs increase. These theoretical results can be extended to provide a guideline for designing FOUs of typical IT2 FPI and FPD controllers. Real-time response of linear voice coil motor is used to show the effectiveness of our results.

An Optimal Interval Type-2 Fuzzy Logic Controller for Maximum Power Capture of Point Absorbers

An optimal interval Type-2 Fuzzy logic controller is proposed for maximum power capture from point absorbers. First, based on an introduced point absorber, a model-based feedback-simplifier is proposed to reduce the complexity of the nonlinear part of the model. Then, two interval Type-2 Fuzzy systems are designed for finding the optimal values of damping and stiffness coefficients so that the maximum power absorption is realised. A black hole optimisation algorithm is then introduced to find the optimal values of the parameters of the Fuzzy system. Finally, the high performance of the proposed scheme is confirmed using simulations. The contributions of this paper are: (1) designing a model-based feedback simplifier for point absorbers, (2) introducing a state space of the final closed-loop system, (3) designing an interval Type-2 Fuzzy controller for the final system, (4) training the Fuzzy controller parameters using a black hole optimisation algorithm.

Interval type-2 and type-1 Fuzzy Logic Controllers for congestion avoidance in internet routers

Active queue management (AQM) scheme is an important research area in congestion control. The AQM mechanism attains the congestion controller by regularize the length of queue from evaluation or dropping the packets at the moderate routers. In this paper the interval type-2 and type-1 fuzzy logic controller are designed to desist the congestion in the networks. Several evolutionary optimization algorithms are used to select the parameters of two controllers as particle swarm optimization (PSO), social spider optimization (SSO) and ant colony Optimization (ACO). The simulation of linearized model of TCP/AQM are introduced in MATLAB (R2018a). Results of the PID like fuzzy type-1controller is compared with PID like interval type-2 fuzzy controller (IT2-FLC) based on optimization algorithms in each controller and shows that IT2-FLC with SSO has been given the best result.

Nature-inspired and hybrid optimization algorithms on interval Type-2 fuzzy controller for servo processes: a comparative performance study

In this paper, performance evaluations of six well-known nature-inspired algorithms have been reported containing genetic algorithm, cuckoo search, particle swarm optimization, differential evolution, bee colony, and combined particle swarm optimization and differential evolution (CPSODE) algorithms. Based on these optimization algorithms, input and output scaling factors of an interval Type-2 fuzzy PID controller (IT2-FLC) are chosen for closed-loop servo tracking. Optimal values of the scaling factors are chosen by minimization of the objective function which is defined based on the closed-loop controller performance criteria. A detailed comparative analysis is reported based on the simulation and experimental results. Performance analysis reveals that improved performance, reliability, robustness, and lesser noise sensitivity are reported by IT2-FLC with the optimal values obtained by the hybrid algorithm CPSODE.

Dynamic Event-Triggered Control for Interval Type-2 Fuzzy Systems Under Fading Channel.

This article is to tackle the event-based state-feedback control problem for interval type-2 (IT2) fuzzy systems subject to the fading channel. For saving communication resources, a dynamic event-triggered (ET) mechanism is utilized to decide the data transmission from sensors to the controller. A time-varying random process is employed to characterize the fading phenomenon in the unpredictable communication network. By considering the effect of channel fading, a nonparallel distribution compensation (non-PDC) IT2 fuzzy controller is synthesized and its number of rules and membership functions (MFs) can be freely selected. As a consequence, the closed-loop fuzzy system possesses imperfectly matched MFs. By taking the global membership boundary information into stability analysis, the membership-function-dependent analysis method is employed to handle these imperfectly matched MFs and to obtain relaxed criteria. Besides, sufficient criteria are obtained so that the resulting closed-loop IT2 fuzzy system can achieve stochastic stability despite fading measurements. The effectiveness of the proposed method is illustrated by a mass-spring-damper system and a numerical example.

Fuzzy Control for Uncertain Electric Vehicle Systems with Sensor Failures and Actuator Saturation

This paper considers the yaw-moment control issue for uncertain electric vehicle systems with sensor failures and actuator saturation. By employing the interval type-2 (IT2) fuzzy approach, the uncertain electric vehicle systems are constructed as an IT2 fuzzy model. In this model, the parameter uncertainties are described through the membership functions (MFs) with lower and upper bounds. Then, an IT2 fuzzy state-feedback controller, which can share different MFs with the IT2 fuzzy model, is designed. The sensor failures can be quantified by a variable varying in a given interval. Meanwhile, the saturation nonlinearities can be handled by employing a norm-bounded strategy. By means of the Lyapunov stability approach, sufficient conditions of the controller design are derived to achieve the desired performance. Finally, simulation results based on the electric vehicle systems are presented to demonstrate the effectiveness of the proposed control scheme.

Sliding-Mode-Control-Theory-Based Adaptive General Type-2 Fuzzy Neural Network Control for Power-line Inspection Robots

In this paper, adaptive general type-2 fuzzy neural network control for motion balance adjusting of a power-line inspection robot is developed. It is used to enhance the anti-interference ability of the controlled plant. General type-2 fuzzy system is adopted because of its ability to more effectively handle uncertainties which may exist as external disturbances and parameter perturbations. The structure of general type-2 fuzzy system is designed by mimicking the neural network. The adaptive laws can be obtained based on the sliding mode control theory. This provides a kind of dynamic general type-2 fuzzy system whose membership functions and consequent parts are changing adaptively. The proposed controller is used to control an under-actuated non-linear power-line inspection (PLI) robot. Different simulation conditions are considered to test the anti-interference ability of the proposed controller. Simulation results indicate that the proposed method can strengthen the PLI robot’s anti-interference ability in a better way as compared to its interval type-2 fuzzy counterpart and PD controller.

Stability analysis of dynamic nonlinear interval type-2 TSK fuzzy control systems based on describing function

This paper focuses on the limit cycles prediction problem to discuss the stability analysis of dynamic nonlinear interval type-2 Takagi–Sugeno–Kang fuzzy control systems (NIT2 TSK FCSs) with adjustable parameters. First, in order to alleviate computational burden, a simple architecture of NIT2 TSK FCS using two embedded nonlinear type-1 TSK fuzzy control systems (NT1 TSK FCSs) is proposed. Then, describing function (DF) of NIT2 TSK FCS is obtained based on the DFs of embedded NT1 TSK FCSs. Subsequently, integrating the stability equation and parameter plane approaches provides a solution to identify the limit cycle and the asymptotically stable regions. Moreover, particle swarm optimization technique is applied to minimize the limit cycle region. Furthermore, for robust design, a gain-phase margin tester is utilized to specify the minimum gain margin ( $$\hbox {GM}_{\mathrm{min}}$$ ) and phase margin ( $$\hbox {PM}_{\mathrm{min}}$$ ) when limit cycles can arise. Finally, two simulation examples are considered to validate the advantages of the presented method.

Reliable Dissipative Interval Type-2 Fuzzy Control for Nonlinear Systems with Stochastic Incomplete Communication Route and Actuator Failure

This paper investigates the dissipative interval type-2 (IT2) fuzzy control issue for a group of uncertain nonlinear systems subject to randomly occurring sensor saturation and quantization. By utilizing the both lower and upper membership functions with relevant tradeoff moduli, uncertainties, which exist in the considered systems, can be captured effectively. During the design of the IT2 fuzzy controller, we take the actuator failure into consideration. Considering the randomicities for the occurrences of sensor saturation and quantization, two separate Bernoulli stochastic distributed courses are utilized to construct the corresponding complicated transmission route. In term of Lyapunov stability theory, sufficient criteria to design dissipative IT2 fuzzy controller are presented to assure the stochastic stability with strict dissipativity of resulting closed-loop systems. Finally, illustrative example verifies the effectiveness and merits of the control strategy proposed in this paper.

Using a Self‐Clustering Algorithm and Type‐2 Fuzzy Controller for Multi‐robot Deployment and Navigation in Dynamic Environments

AbstractThis study proposes a novel method for multi‐robot deployment and navigation under dynamic environments. To automatically determine the location deployment of multiple robots, a grid‐based method and self‐clustering algorithm (SCA) were used to simplify the environmental information and automatically deploy robot locations. In the navigation process, a behavior selector automatically turns on towards goal mode or wall‐following mode (WFM) depending on environmental conditions. WFM control adopts an interval type‐2 fuzzy controller (IT2FC). The parameters of the IT2FC are adjusted by using the dynamic group whale optimization algorithm (DGWOA). The proposed DGWOA uses a dynamic group and Lévy flight strategy to overcome the problem of falling into a local minimum solution. Experimental results reveal that the proposed method can successfully complete navigation tasks under dynamic environments.

A Fractional Order General Type-2 Fuzzy PID Controller Design Algorithm

Fractional order PID controller was received attentions in control problems for it had 2 freedom adjustable parameters. Practices had proved that better results could be obtained by introduction of fractional order PID in control problems. And in recently years, fractional order PID combined with fuzzy logic system was gradually got attention, the typical of which was fractional order type-1 fuzzy PID controller. For fractional order PID and fractional order type-1 fuzzy PID controller couldn't deal with the uncertainty of system, so fractional order interval type-2 fuzzy PID controller was applied to solve this problem. But interval type-2 fuzzy sets were a simplification of type-2 fuzzy sets, and there may be have the defect of information loss. A fractional order general type-2 fuzzy PID controller was proposed in this article. The proposed controller based on general type-2 fuzzy logic system, which can make full use of the advantages of general type-2 fuzzy logic system in describing the uncertainty of the system. The fractional order general type-2 fuzzy PID controller utilized a simplified type reduction called NT type reduction algorithm. The NT type reduction algorithm can get the defuzzification result directly and avoided iterative process as KM type reduction commonly used in interval type-2 fuzzy controller. The simulations of 3 processes and a practical inverted pendulum system show that fractional order general type-2 fuzzy PID controller can reduce overshoot, improve system response speed and accelerate system stability time in comparing with other controllers. Especially, when the system has disturbance, parameters uncertainty or structure uncertainty, the fractional order general type-2 fuzzy PID controller has better control effects than other compared controllers.