Backing control problem of a mobile robot with multiple trailers:fuzzy modeling and LMI-based design

The paper presents backing control of computer simulated mobile robots with multiple trailers by fuzzy modeling and control. We deal with two kinds of mobile robots: a mobile robot with five trailers and a mobile robot with ten trailers. To design fuzzy controllers, nonlinear models of the mobile robots with multiple trailers are represented by Takagi-Sugeno fuzzy models (TS fuzzy model). Before making TS fuzzy models, we simplify the nonlinear dynamics of the mobile robots. Under an assumption, TS fuzzy models are made from the simplified nonlinear models. The so-called parallel distributed compensation (PDC) is employed to design fuzzy controllers from the TS fuzzy models. Next, we derive a stability condition based on the Lyapunov approach. The stability condition of the designed fuzzy control system is cast in terms of linear matrix inequalities (LMI's) since it is reduced to a problem of finding a common Lyapunov function for a set of Lyapunov inequalities. Convex optimization techniques based on LMI's are utilized to solve the problem of finding stable feedback gains and a common Lyapunov function for the designed fuzzy control system. The simulation results show the effects of the fuzzy modeling, the controller design via the PDC, and the stability analysis based on LMIs     

Stochastic stability analysis of fuzzy hopfield neural networks with time-varying delays

The ordinary Takagi-Sugeno (TS) fuzzy models have provided an approach to represent complex nonlinear systems to a set of linear sub-models by using fuzzy sets and fuzzy reasoning. In this paper, stochastic fuzzy Hopfield neural networks with time-varying delays (SFVDHNNs) are studied. The model of SFVDHNN is first established as a modified TS fuzzy model in which the consequent parts are composed of a set of stochastic Hopfield neural networks with time-varying delays. Secondly, the global exponential stability in the mean square for SFVDHNN is studied by using the Lyapunov-Krasovskii approach. Stability criterion is derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages.     

Reliable $$H_{\infty }$$ Stabilization of Fuzzy Systems with Random Delay Via Nonlinear Retarded Control

In this paper, the robust reliable \(H_\infty \) control problem has been investigated for a class of nonlinear discrete-time TS fuzzy systems with random delay. In particular, the proposed fuzzy system consists of local nonlinear models with set of fuzzy rules, but the conventional TS fuzzy systems has local linear models. Our attention is focused on the design of a feedback reliable nonlinear retarded control law to ensure the robust asymptotic stability for nonlinear discrete-time TS fuzzy system with admissible uncertainties as well as actuator failure cases and random delay. In particular, by using an input delay approach, the random delay with stochastic parameters in the system matrices is introduced in the system model. Based on the Lyapunov approach, firstly, a sufficient condition for asymptotic stability is proposed for TS fuzzy systems in the presence of actuator failures. Then, a robust reliable \(H_\infty \) control is designed for the uncertain TS fuzzy system by solving a strict linear matrix inequalities using the available numerical software. Finally, a numerical example based on real-time ball and beam system is provided to validate the effectiveness of the proposed design technique.     

Impulsive Control for T-S Fuzzy Model Based Chaotic Systems Consisting of Van der Pol Oscillators Coupled to Linear Oscillators

This paper proposes an impulsive control scheme for chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators （VDPL） based on their Takagi-Sugeno （T-S） fuzzy models. A T-S fuzzy model is utilized to represent the chaotic VDPL system. By using comparison method, a general asymptotical stability criterion by means of linear matrix inequality （LMI） is derived for the T-S fuzzy model of VDPL system with impulsive effects. The simulation results demonstrate the effectiveness of the proposed scheme.     

AN H∞ FUZZY TRACKING CONTROL SCHEME FOR AFFINE COUPLED SPATIO-TEMPORAL CHAOS

Due to the interactions among coupled spatio-temporal subsystems and the constant bias term of affine chaos, it is difficult to achieve tracking control for the affine coupled spatiotemporal chaos. However, every subsystem of the affine coupled spatio-temporal chaos can be approximated by a set of fuzzy models; every fuzzy model represents a linearized model of the subsystem corresponding to the operating point of the controlled system. Because the consequent parts of the fuzzy models have a constant bias term, it is very difficult to achieve tracking control for the affine system. Based on these fuzzy models, considering the affine constant bias term, an H∞ fuzzy tracking control scheme is proposed. A linear matrix inequality is employed to represent the feedback controller, and parameters of the controller are achieved by convex optimization techniques. The tracking control for the affine coupled spatio-temporal chaos is achieved, and the stability of the system is also guaranteed. The tracking performances are testified by simulation examples.     

一类非线性互联系统的H∞模型参考跟踪分散输出反馈模糊控制

本文对一类不确定状态不可测非线性互联系统,给出了一种基于观测器的H_∞模型参考跟踪分散输出反馈模糊控制方法.设计中,首先采用模糊不确定T-S模型对非线性互联系统进行模糊建模,在此基础上,给出模糊分散观测器的H_∞设计和基于观测器的模型参考跟踪分散模糊控制的设计.应用李亚普诺夫和线性矩阵不等式方法给出了模糊分散系统稳定的充分条件.仿真结果进一步验证了所提出的模糊分散控制方法的有效性.     

T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays

This paper investigates the effectiveness of a passive tuned mass damper (TMD) and fuzzy controller in reducing the structural responses subject to the external force. In general, TMD is good for linear systems. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. To overcome the effect of modeling error between nonlinear multiple time-delay systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this paper. A stability criterion in terms of Lyapunov's direct method is derived to guarantee the stability of nonlinear multiple time-delay interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay interconnected system and the H/sup /spl infin// control performance is achieved at the same time. Finally, the proposed methodology is illustrated by an example of a nonlinear TMD system.     

Robust H ∞ Output Tracking Control for a Class of Nonlinear Systems with Time-Varying Delays

This paper addresses the H _∞ output tracking problem for a class of nonlinear systems subjected to model uncertainties and with interval time-varying delay. The stability of the nonlinear time-delay system is analyzed with a novel delay-interval-dependent Lyapunov–Krasovskii functional. Compared to state-of-the-art criteria for linear and nonlinear time-delay systems, less conservative stability conditions are derived with the introduction of new delay-interval-dependent terms and the exploitation of the delay subintervals size. The proposed analysis considers that the delay derivative is either upper and lower bounded, bounded above only, or unbounded, i.e., no restrictions are cast upon the derivative. Numerical examples are provided to enlighten the importance and advantages of the present criterion which outperforms previous criteria in time-delay systems literature. Also, an additional example is provided to highlight the effectiveness of the proposed H _∞ output tracking control design technique for complex nonlinear systems with time-varying delay.     

AN H∞ FUZZY TRACKING CONTROL SCHEME FOR AFFINE COUPLED SPATIO-TEMPORAL CHAOS

Due to the interactions among coupled spatio-temporal subsystems and the constant bias term of affine chaos, it is difficult to achieve tracking control for the affine coupled spatiotemporal chaos. However, every subsystem of the affine coupled spatio-temporal chaos can be approximated by a set of fuzzy models; every fuzzy model represents a linearized model of the subsystem corresponding to the operating point of the controlled system. Because the consequent parts of the fuzzy models have a constant bias term, it is very difficult to achieve tracking control for the affine system. Based on these fuzzy models, considering the affine constant bias term, an H∞ fuzzy tracking control scheme is proposed. A linear matrix inequality is employed to represent the feedback controller, and parameters of the controller are achieved by convex optimization techniques. The tracking control for the affine coupled spatio-temporal chaos is achieved, and the stability of the system is also guaranteed. The tracking performances are testified by simulation examples.     

Fuzzy Feedback Linearization Control for MIMO Nonlinear System and Its Application to Full-Vehicle Suspension System

The paper presents a novel fuzzy feedback linearization control of nonlinear multi-input multi-output (MIMO) systems for the tracking and almost disturbance decoupling (ADD) performances based on the fuzzy logic control (FLC). The main contribution of this study is to construct a controller, under appropriate conditions, such that the resulting closed-loop system is valid for any initial condition and bounded tracking signal with the following characteristics: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling. The feedback linearization control guarantees the almost disturbance decoupling performance and the uniform ultimate bounded stability of the tracking error system. As soon as the tracking errors are driven to touch the global final attractor with the desired radius, the fuzzy logic control immediately is applied via a human expert’s knowledge to improve the convergence rate. One example, which cannot be solved by the previous paper on the almost disturbance decoupling problem, is proposed in this paper to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by the proposed approach. In order to demonstrate the applicability, this paper has investigated a full-vehicle suspension system.     

Stability and Constrained Control of a Class of Discrete-Time Fuzzy Positive Systems with Time-Varying Delays

This paper deals with the stability of nonlinear discrete-time positive systems with time-varying delays represented by the Takagi–Sugeno (T–S) fuzzy model. The time-varying delays in the systems can be unbounded. Sufficient conditions of stability which are not relevant to the magnitude of delays are derived by a solution trajectory. Based on the stability results, the problems of controller design via the parallel distributed compensation (PDC) scheme are solved. The control is under the positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Constrained control is also considered, further requiring that the state trajectory of the closed-loop system be bounded by a prescribed boundary if the initial condition is bounded by the same boundary. The stability results and control laws are formulated as linear matrix inequalities (LMIs) and linear programs (LPs). A numerical example and a real plant are studied to demonstrate the application of the proposed methods.     

基于自适应模糊理论的某型无人机起飞控制方法

基于合理简化的无人机纵向模型,设计了一种自适应模糊控制器,该控制器将Takagi-Sugeno模糊系统与等效控制器相结合,以增强系统的鲁棒性.只要求预先知道系统的相对阶以及未知函数的上下界即可,不需要精确的数学模型.Lyapunov合成方法证明了跟踪误差能趋近于零且其余的控制信号均有界.最后,结合优先级按比例分配的控制分配器,给出了存在扰动情况下飞行控制系统的仿真结果,表明即使在模型部分未知的情况下,该系统仍然能够达到飞行控制的指标性能和品质要求,验证了该方法的有效性.     

Identification of pneumatic artificial muscle manipulators by a MGA-based nonlinear NARX fuzzy model

This study investigates the technique of modeling and identification of a new dynamic NARX fuzzy model by means of genetic algorithms. In conventional identification techniques, there are difficulties such as poor knowledge of the process, inaccurate process or complexity of the resulting mathematical model. All these factors deteriorate the identification performance when dealing with dynamic nonlinear industrial processes. To overcome these difficulties, this paper proposes a novel approach by using a modified genetic algorithm (MGA) combined with the predictive capability of nonlinear ARX (NARX) model for generating the dynamic NARX Takagi–Sugeno (TS) fuzzy model. The MGA algorithm processes the experimental input–output training data from the real system and optimizes the NARX fuzzy model parameters. This is referred to as fuzzy identification, which automatically generates the appropriate fuzzy if-then rules to characterize the dynamic nonlinear features of the real plant. The prototype pneumatic artificial muscle (PAM) manipulator, being a typical nonlinear and time-varying system, is used as a test system for this novel approach. This result shows that, with this MGA-based modeling and identification, the novel NARX fuzzy model identification approach to the PAM manipulator achieved highly outstanding performance and high precision as well. The accuracy of the proposed MGA-based NARX fuzzy model proves excellent in comparison with the MGA-based TS fuzzy model and the conventional GA-based TS fuzzy model.     

Finite-time tracking controller design for nonholonomic systems with extended chained form

A design scheme of the finite-time tracking controller is given for the nonholonomic systems with extended chained form. The relay switching technique and the terminal sliding mode control scheme with finite-time convergence are used to the design of the controller. The global stability is guaranteed and the system states accurately track the states of the reference model in finite time. The simulation results for two physical models of a knife-edge and a wheeled mobile robot have demonstrated the effectiveness of the proposed algorithm.     

Stabilization of Discrete-time Fuzzy Systems Via Delta Operators and its Application to Truck–Trailer Model

This paper addresses the problem of robust \(L_2{-}L_\infty \) control in delta domain for a class of Takagi–Sugeno (TS) fuzzy systems with interval time-varying delays and disturbance input. In particular, the system under study involves state time delay, uncertainties and fast sampling period \(\mathcal {T}\). The main aim of this work was to design a \(L_2{-}L_\infty \) controller such that the proposed TS fuzzy system is robustly asymptotically stable with a \(L_2{-}L_\infty \) prescribed performance level \(\gamma >0\). Based on the proper Lyapunov–Krasovskii functional (LKF) involving lower and upper bound of time delay and free-weighting technique, a new set of delay-dependent sufficient conditions in terms of linear matrix inequalities (LMIs) are established for obtaining the required result. The result reveals that the asymptotic stability is achieved quickly when the sampling frequency is high. Finally, a numerical example based on the truck–trailer model is given to demonstrate the effectiveness and potential of the proposed design technique.     

Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach

In this paper, a board class of uncertain fractional-order nonlinear systems is considered. A novel fractional-order sliding mode controller for output tracking of a time-varying reference signal is designed which can conquer the uncertainties and guarantees the asymptotic convergence of the system output toward the desired time-varying reference signal. For this purpose, an appropriate sliding surface is designed where maintaining the system’s states on this surface leads to asymptotic vanishing of error signal. Moreover, by tacking the fractional derivative of order α from the sliding surface, the convergence of system’s trajectories into the sliding surface in a finite time is proven. Finally, in order to verify the theoretical results, the proposed method is applied to a fractional-order gyroscope model and computer simulations show the efficiency of the proposed method in output tracking.     

Robust H ∞ Control of a Class of Switching Nonlinear Systems with Time-Varying Delay Via T–S Fuzzy Model

This paper considers H _∞ control of a class of switching nonlinear systems with time-varying delays via T–S fuzzy model based on piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs). The systems are switching among several nonlinear systems. The Takagi and Sugeno (T–S) fuzzy model is employed to approximate the sub-nonlinear dynamic systems. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a continuous-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T–S fuzzy systems. Average dwell-time approach and PFLKFs methods are utilized for the stability analysis and controller design, and with free fuzzy weighting matrix scheme. Switching and control laws are obtained such that the H _∞ performance is satisfied. The conditions of stability and the control laws are given in the form of LMIs which can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example and the control of an uncertain radio-controlled (R/C) hovercraft with time-varying delay are given to demonstrate the efficiency of the proposed method.     

Exponential H ∞ Output Tracking Control for Switched Neutral System with Time-Varying Delay and Nonlinear Perturbations

In this paper, the problem of exponential H _∞ output tracking control is addressed for a class of switched neutral system with time-varying delay and nonlinear perturbations. The considered system consists of different neutral and discrete delays. By resorting to the average dwell time approach, a new Lyapunov–Krasovskii functional is proposed to establish sufficient conditions for the exponential stability and H _∞ performance of switched neutral systems. Then, the problem of exponential H _∞ output tracking control is investigated, an explicit expression for the desired exponential tracking controller is also given. Finally, a numerical example is provided to demonstrate the potential effectiveness of the proposed method.     

A stable self-organizing fuzzy controller for robotic motioncontrol

It is well known that robotic manipulators are highly nonlinear coupling dynamic systems. It is difficult to establish an appropriate mathematical model for the design of a model-based controller. Although fuzzy logic control has a model-free feature, it still needs time-consuming work for the rules bank and fuzzy parameters adjustment. In this paper, a stable self-organizing fuzzy controller (SOFC) is proposed to manipulate the motion trajectory of a 5-degrees-of-freedom robot. This approach has a learning ability for responding to the time-varying characteristic of a robot. Its control rules bank can be established and modified continuously by online learning with zero initial fuzzy rules. In addition, this control strategy has effectively improved the stability problem of a previous SOFC. The experimental results show that this intelligent controller has a stable learning ability and good motion control capability     

空调房间温度复合模糊控制器研究

结合空调房间温度控制具有大滞后、非线性、时变的特点,设计了一种比例-模糊PID控制器。建立了空调温度的系统的模型,介绍了控制器实现原理以及结构,并详细叙述了各个参数的模糊控制规则。在MATLAB的Simulink中搭建系统模型并与传统PID比较,最后进行仿真。仿真结果表明,所设计的比例-模糊控制器比传统PID控制器有更好的动态性能和稳态性能。