Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems

A fuzzy logic controller equipped with a training algorithm is developed such that the H^∞ tracking performance should be satisfied for a model-free nonlinear multiple-input multiple-output (MIMO) system, with external disturbances. Due to universal approximation theorem, fuzzy control provides nonlinear controller, i.e., fuzzy logic controllers, to perform the unknown nonlinear control actions and the tracking error, because of the matching error and external disturbance is attenuated to arbitrary desired level by using H^∞ tracking design technique. In this paper, a new direct adaptive interval type-2 fuzzy controller is developed to handle the training data corrupted by noise or rule uncertainties for nonlinear MIMO systems involving external disturbances. Therefore, linguistic fuzzy control rules can be directly incorporated into the controller and combine the H^∞ attenuation technique. Simulation results show that the interval type-2 fuzzy logic system can handle unpredicted internal disturbance, data uncertainties, very well, but the adaptive type-1 fuzzy controller must spend more control effort in order to deal with noisy training data. Furthermore, the adaptive interval type-2 fuzzy controller can perform successful control and guarantee the global stability of the resulting closed-loop system and the tracking performance can be achieved.     

Interval type 2 hierarchical FNN with the H-infinity condition for MIMO non-affine systems

To develop a controller that deals with noise-corrupted training data and rule uncertainties for interconnected multi-input–multi-output (MIMO) non-affine nonlinear systems with unmeasured states, an interval type-2 fuzzy system is integrated with an observer-based hierarchical fuzzy neural controller (IT2HFNC) in this paper. Also, an H_∞ control technique and a strictly positive real Lyapunov (SPR-Lyapunov) design approach are employed for attenuating the influence of both external disturbances and fuzzy logic approximation error on the tracking of errors. Moreover, the proposed hierarchical fuzzy structure can greatly reduce the number of adjusted parameters of the IT2HFNC, and then, the problem of online computational burden can be solved. According to the design of the interval type-2 fuzzy neural network and H_∞ control technique, the IT2HFNN controller can improve its robustness to noise, uncertainties, approximation errors, and external disturbances. Simulation results are reported to show the performance of the proposed control system mode and algorithms.     

Synchronization of uncertain chaotic systems based on adaptive type-2 fuzzy sliding mode control

A novel direct adaptive interval type-2 fuzzy neural network (FNN) controller in which linguistic fuzzy control rules can be directly incorporated into the controller is developed to synchronize chaotic systems with training data corrupted by noise or rule uncertainties involving external disturbances, in this paper. By incorporating direct adaptive interval type-2 FNN control scheme and sliding mode approach, two non-identical chaotic systems can be synchronized based on Lyapunov stability criterion. Moreover, the chattering phenomena of the control efforts can be reduced and the external disturbance on the synchronization error can be attenuated. The stability of the proposed overall adaptive control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded. From the simulation example, to synchronize two non-identical Chua’s chaotic circuits, it has been shown that type-2 FNN controllers have the potential to overcome the limitations of tpe-1 FNN controllers when training data is corrupted by high levels of uncertainty.     

A robust adaptive fuzzy variable structure tracking control for the wheeled mobile robot: Simulation and experimental results

In this paper an adaptive fuzzy variable structure control (kinematic control) integrated with a proportional plus derivative control (dynamic control) is proposed as a robust solution to the trajectory tracking control problem for a differential wheeled mobile robot. The variable structure controller, based on the sliding mode theory, is a well known, proven control method, fit to deal with uncertainties and disturbances (e.g., structural and parameter uncertainties, external disturbances and operating limitations). To minimize the problems found in practical implementations of the classical variable structure controllers, an adaptive fuzzy logic controller replaces the discontinuous portion of the control signals (avoiding the chattering), causing the loss of invariance, but still ensuring the robustness to uncertainties and disturbances without having any a priori knowledge of their boundaries. Moreover, the adaptive fuzzy logic controller is a feasible tool to approximate any real continuous nonlinear system to arbitrary accuracy, and has a simple structure by using triangular membership functions, a low number of rules that must be evaluated, resulting in a lower computational load for execution, making it feasible for real time implementation. Stability analysis and the convergence of tracking errors as well as the adaptation laws are guaranteed with basis on the Lyapunov theory. Simulation and experimental results are explored to show the verification and validation of the proposed control strategy.     

Fire-rule-based direct adaptive type-2 fuzzy H tracking control

This paper presents a novel H^∞ tracking-based direct adaptive fuzzy controller (HDAFC) for a class of perturbed uncertain affine nonlinear systems involving external disturbances and measurement noise. A practical interval type-2 (IT2) fuzzy logic system (FLS) is introduced to approximate the ideal control law. To eliminate the tradeoff between H^∞ tracking performance and high gain at the control input, a modified output tracking error is introduced. Based on the proposed fired-rule-determination algorithm, a practical average defuzzifier expressed in parameterized and closed formula is developed for the IT2 FLS. Without the restriction that the control gain function is exactly known, the IT2 HDAFC is constructed and its adaptive law is derived by virtue of the Lyapunov synthesis. To improve control performance under measurement noise, the recursive linear smoothed Newton predictor is further introduced as a delayless output filter. Simulated application of a single-link robot manipulator demonstrates the superiority of the proposed approach over the previous approach in terms of the settling time, tracking accuracy, energy consumption and smoothness of the control input.     

基于自适应模糊滑模控制的船舶航向控制器设计

针对船舶运动系统中固有的非线性、模型不确定性和风、浪、流等的干扰.提出了自适应模糊滑模控制(AFSMC)策略解决船舶的航向控制问题.通过采用模糊逻辑系统逼近系统未知函数,将滑模控制技术与自适应模糊控制技术相结合,设计了船舶航向AFSMC控制器.在滑模边界层内应用PI (proportional-integral)控制代替滑模控制中的切换项,削弱了滑模控制带来的抖振现象.借助李亚普诺夫函数证明了船舶运动系统中的信号都一致有界并利用Barbalat引理证明了跟踪误差渐近收敛到零.在参数摄动和外界干扰情况下进行了航向保持与改变仿真试验,采用AFSMC控制器得到了与无摄动和无干扰情况下相似的输出响应.实验结果表明,所提控制器能有效地处理系统不确定性和外界干扰,控制性能良好,具有很强的鲁棒性.     

Robust Control of an LUSM-Based $Xhbox{--}Yhbox{--}theta$ Motion Control Stage Using an Adaptive Interval Type-2 Fuzzy Neural Network

The robust control of a linear ultrasonic motor based $Xhbox{--}Yhbox{--}theta$ motion control stage to track various contours is achieved by using an adaptive interval type-2 fuzzy neural network (AIT2FNN) control system in this study. In the proposed AIT2FNN control system, an IT2FNN, which combines the merits of an interval type-2 fuzzy logic system and a neural network, is developed to approximate an unknown dynamic function. Moreover, adaptive learning algorithms are derived using the Lyapunov stability theorem to train the parameters of the IT2FNN online. Furthermore, a robust compensator is proposed to confront the uncertainties including the approximation error, optimal parameter vectors, and higher order terms in Taylor series. To relax the requirement for the value of lumped uncertainty in the robust compensator, an adaptive lumped uncertainty estimation law is also investigated. In addition, the circle and butterfly contours are planned using a nonuniform rational B-spline curve interpolator. The experimental results show that the contour tracking performance of the proposed AIT2FNN is significantly improved compared with the adaptive type-1 FNN. Additionally, the robustness to parameter variations, external disturbances, cross-coupled interference, and frictional force can also be obtained using the proposed AIT2FNN.      

Observer-based method for synchronization of uncertain fractional order chaotic systems by the use of a general type-2 fuzzy system

Synchronization of the fractional order chaotic systems is extensively studied in recent years due to its potential applications in many branches of science and engineering. The main problems in this field are that the dynamics of the system in hand are often uncertain and are perturbed by external disturbances. Also the unknown nonlinear functions in the system dynamics are generally complicated and in many practical applications we have measurement errors and unavailable states. In this paper, a novel robust and asymptotically stable controller is proposed to synchronize uncertain fractional order chaotic systems. Its design is based on linear matrix inequality (LMI) technique. Furthermore, an observer is presented to estimate the unavailable states. A general type-2 fuzzy system (GT2FS) based on α-plane representation with Gaussian secondary membership functions (MF) and type-2 non-singleton fuzzification is proposed to approximate the unknown complex nonlinear functions in the dynamics of system. The input uncertainties associated with the observer error and the malfunctioning of the input devices are modeled by interval type-2 fuzzy MFs instead of crisp numbers. To decrease the computational cost of the GT2FS, a simple type-reduction method is proposed. The antecedent parameters of GT2FS are tuned based on a modified form of social spider optimization (SSO) algorithm. The simulation examples show that the proposed control scheme gives high performance in the presence of unknown functions, external disturbances and unavailable states. The performance of GT2FS with different α-levels and different fuzzification methods are compared with type-1 and interval type-2 fuzzy systems in several examples.     

基于观测器的一类非线性系统的自适应模糊控制

针对一类有界的不确定非线性系统设计了模糊观测器和自适应控制器.该方法不需要系统状态完全可测的条件,而是通过模糊观测器估计系统的状态变量并且能保证观测误差是一致最终有界的.该自适应控制器取得了良好的控制效果并且保证了跟踪误差的一致最终有界性.仿真结果表明了本文所提出的方法有效性.     

自治飞艇直接自适应模糊路径跟踪控制

针对具有模型不确定和未知外部干扰的自治飞艇, 提出了直接自适应模糊路径跟踪控制方法. 该方法由路径跟踪控制和自适应模糊控制两部分组成. 首先基于飞艇的平面运动模型设计路径跟踪控制律, 包括制导律计算、偏航角跟踪和速度控制3 部分; 然后构造直接自适应模糊控制器逼近路径跟踪控制律中的不确定项. 稳定性分析证明所设计的控制律能使飞艇跟踪给定的期望路径, 跟踪误差收敛到原点的小邻域内. 仿真结果验证了所提出方法的有效性.

     

Robust adaptive fuzzy sliding mode trajectory tracking control for serial robotic manipulators

The ever increasingly stringent performance requirements of industrial robotic applications highlight significant importance of advanced robust control designs for serial robots that are generally subject to various uncertainties and external disturbances. Therefore, this paper proposes and investigates the design and implementation of a robust adaptive fuzzy sliding mode controller in the task space for uncertain serial robotic manipulators. The sliding mode control is well known for its robustness to system parameter variations and external disturbances, and is thus a highly desirable and cost-effective approach to achieve high precision control task for serial robots. The proposed controller is designed based on a fuzzy logic approximation to accomplish trajectory tracking with high accuracy and simultaneously attenuate effects from uncertainties. In the controller, the high-frequency uncertain term is approximated by using a fuzzy logic system while the low-frequency term is adaptively updated in real time based on a parametric adaption law. The control efficacy and effectiveness of the proposed control algorithm are comparatively verified against a recently proposed conventional controller. The test results demonstrate that the proposed controller has better trajectory tracking performances and is more robust against large disturbances than the conventional controller under the same operating conditions.     

Adaptive type-2 fuzzy sliding mode controller for SISO nonlinear systems subject to actuator faults

In this paper, an adaptive type-2 fuzzy sliding mode control to tolerate actuator faults of unknown nonlinear systems with external disturbances is presented. Based on a redundant actuation structure, a novel type-2 adaptive fuzzy fault tolerant control scheme is proposed using sliding mode control. Two adaptive type-2 fuzzy logic systems are used to approximate the unknown functions, whose adaptation laws are deduced from the stability analysis. The proposed approach allows to ensure good tracking performance despite the presence of actuator failures and external disturbances, as illustrated through a simulation example.     

Improved fuzzy sliding mode control for a class of MIMO nonlinear uncertain and perturbed systems

In this paper, a stable adaptive fuzzy sliding mode based tracking control is developed for a class of nonlinear MIMO systems that are represented by input output models involving system uncertainties and external disturbances. The main contribution of the proposed method is that the structure of the controller system is partially unknown and does not require the bounds of uncertainties and disturbance to be known. First, a fuzzy logic system is designed to estimate the unknown function. Secondly, in order to eliminate the chattering phenomenon brought by the conventional variable structure control, the signum function is replaced by an adaptive Proportional Derivative (PD) term in the proposed approach. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis, so that convergence to zero of tracking errors and boudedness of all signals in the closed-loop system can be guaranteed. Finally, a mass-spring-damper system is simulated to demonstrate the validity and the effectiveness of the proposed controller.     

Fuzzy approach-based optimal robust control for permanent magnet synchronous motor with experimental validation

This paper presents an optimal robust control for a permanent magnet synchronous motor (PMSM) with uncertainties and external disturbances which can be described by fuzzy approach. The fuzzy approach based on fuzzy set theory is distinguish from probability theory or fuzzy logic theory. Firstly, a dynamical model of the PMSM with uncertainties is established using a fuzzy approach. Then, a robust controller with an optimizable parameter is designed for PMSM to handle the uncertainties. The stability of the proposed control is proven using the Lyapunov theory. Furthermore, the controller gain is optimized by minimizing performance index, which contains the control performance and cost. Finally, the numerical simulations and experimental results are presented to validate the effectiveness of the proposed control with an optimal parameter.     

Adaptive sliding mode control for trajectory tracking of nonholonomic mobile robot with uncertain kinematics and dynamics

ABSTRACT

This article designs a novel adaptive trajectory tracking controller for nonholonomic wheeled mobile robot under kinematic and dynamic uncertainties. A new velocity controller, in which kinematic parameter is estimated, produces velocity command of the robot. The designed adaptive sliding mode dynamic controller incorporates an estimator term to compensate for the external disturbances and dynamic uncertainties and a feedback term to improve the closed-loop stability and account for the estimation error of external disturbances. The system stability is analyzed using Lyapunov theory. Computer simulations affirm the robustness of the designed control scheme.     

Interval type-2 fuzzy expert system for prediction of carbon monoxide concentration in mega-cities

This paper presents an indirect approach to interval type-2 fuzzy logic system modeling to forecaste the level of air pollutants. The type-2 fuzzy logic system permits us to model the uncertainties among rules and the parameters related to data analysis. In this paper, we propose an indirect method to create an interval type-2 fuzzy logic system from a historical data, where Footprint of Uncertainties of fuzzy sets are extracted by implementation of an interval type-2 FCM algorithm and based on an upper and lower value for the level of fuzziness m in FCM. Finally, the proposed model is applied for prediction of carbon monoxide concentration in Tehran air pollution. It is shown that the proposed type-2 fuzzy logic system is superior in comparison to type-1 fuzzy logic systems in terms of two performance indices.     

Semi-decentralized adaptive fuzzy control for cooperativemultirobot systems with H∞ motion/internal forcetracking performance

We present a semi-decentralized adaptive fuzzy control scheme for cooperative multirobot systems to achieve H(infinity) performance in motion and internal force tracking. First, we reformulate the overall system dynamics into a fully actuated system with constraints. To cope with both parametric and nonparametric uncertainties, the controller for each robot consists of two parts: 1) model-based adaptive controller; and 2) adaptive fuzzy logic controller (FLC). The model-based adaptive controller handles the nominal dynamics which results in both zero motion and internal force errors for a pure parametric uncertain system. The FLC part handles the unstructured dynamics and external disturbances. An H(infinity) tracking problem defined by a novel performance criterion is given and solved in the sequel. Hence, a robust controller satisfying the disturbance attenuation is derived being simple and singularity-free. Asymptotic convergence is obtained when the fuzzy approximation error is bounded with finite energy. Maintaining the same results, the proposed controller is further simplified for easier implementation. Finally, the numerical simulation results for two cooperative planar robots transporting an object illustrate the expected performance.     

基于FPSO的电力巡检机器人的广义二型模糊逻辑控制

针对电力巡检机器人(Power-line inspection robot, PLIR)的平衡调节问题, 设计了广义二型模糊逻辑控制器(General type-2 fuzzy logic controller, GT2FLC); 针对GT2FLC中隶属函数参数难以确定的问题, 通过模糊粒子群(Fuzzy particle swarm optimization, FPSO)算法来优化隶属函数参数. 将GT2FLC的控制性能与区间二型模糊逻辑控制器(Interval type-2 fuzzy logic controller, IT2FLC)和一型模糊逻辑控制器(Type-1 fuzzy logic controller, T1FLC) 的控制性能进行对比. 除此之外, 还考虑了外部干扰对三种控制器控制效果的影响. 仿真结果表明, GT2FLC具有更好的性能和处理不确定性的能力.     

An adaptive fuzzy sliding-mode controller design for walking control with functional electrical stimulation: A computer simulation study

A major challenge to developing neuroprostheses for walking and to widespread acceptance of these walking systems is the design of a robust control strategy that provides satisfactory tracking performance, to be robust against time-varying properties of neuromusculoskeletal dynamics, day-today variations, muscle fatigue, and external disturbances, and to be easy to apply without requiring offline identification during different experiment sessions. The lower extremities of human walking are a highly nonlinear, highly time-varying, multi-actuator, multi-segment with highly inter-segment coupling, and inherently unstable system. Moreover, there always exist severe structured and unstructured uncertainties such as spasticity, muscle fatigue, external disturbances, and unmodeled dynamics. Robust control design for such nonlinear uncertain multi-input multi-output system still remains as an open problem. In this paper we present a novel robust control strategy that is based on combination of adaptive fuzzy control with a new well-defined sliding-mode control (SMC) with strong reachability for control of walking in paraplegic subjects. Based on the universal approximation theorem, fuzzy logic systems are employed to approximate the neuromusculoskeletal dynamics and an adaptive fuzzy controller is designed by using Lyapunov stability theory to compensate for approximation errors. The proposed control strategy has been evaluated on a planar model of bipedal locomotion as a virtual patient. The results indicate that the proposed strategy provides accurate tracking control with fast convergence during different conditions of operation, and could generate control signals to compensate the effects of muscle fatigue, system parameter variations, and external disturbances. Interesting observation is that the controller generates muscle excitation that mimic those observed during normal walking.     

A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.