Model reference output feedback fuzzy tracking control design for nonlinear discrete-time systems with time-delay

In this study, a model reference fuzzy tracking control design for nonlinear discrete-time systems with time-delay is introduced. First, the Takagi and Sugeno (TS) fuzzy model is employed to approximate a nonlinear discrete-time system with time-delay. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple fuzzy observer-based controller is used in our approach without feedback linearization technique and complicated adaptive scheme. By the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be efficiently solved using the convex optimization techniques. Simulation example is given to illustrate the design procedures and tracking performance of the proposed method.     

Fuzzy tracking control design for nonlinear dynamic systems via T-Sfuzzy model

This study introduces a fuzzy control design method for nonlinear systems with a guaranteed H_∞ model reference tracking performance. First, the Takagi and Sugeno (TS) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple fuzzy controller is used in our approach without feedback linearization technique and complicated adaptive scheme. By the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be solved very efficiently using the convex optimization techniques. Simulation example is given to illustrate the design procedures and tracking performance of the proposed method     

H∞ decentralized fuzzy model reference tracking controldesign for nonlinear interconnected systems

In general, due to the interactions among subsystems, it is difficult to design an H_∞ decentralized controller for nonlinear interconnected systems. The model reference tracking control problem of nonlinear interconnected systems is studied via H_∞ decentralized fuzzy control method. First, the nonlinear interconnected system is represented by an equivalent Takagi-Sugeno type fuzzy model. A state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the H∞ model reference tracking performance is achieved. Furthermore, the stability of the nonlinear interconnected systems is also guaranteed. If states are not all available, a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control. Consequently, a fuzzy observer-based state feedback decentralized fuzzy controller is proposed to solve the H_∞ tracking control design problem for nonlinear interconnected systems. The problem of H _∞ decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP). The EVP can be solved very efficiently using convex optimization techniques. Finally, simulation examples are given to illustrate the tracking performance of the proposed methods     

一类非线性离散系统模糊控制器的分析和设计

针对一类非线性离散不确定系统,在系统状态不可测的情况下,以T-S模型描述不同状态空间的局部动态区域,并通过中心平均反模糊化、乘积推理、单点模糊化方法得到全局模糊系统模型.基于李亚普诺夫理论和线性矩阵不等式,设计了一种基于观测器的鲁棒控制器,并对离散状态下的此类系统进行了稳定分析.最后通过M ATLAB仿真,证明了该方法的有效性.     

一类离散非线性不确定互联系统的模糊分散控制

利用模糊控制方法研究一类离散非线性互联系统的分散控制问题.首先采用模糊(T-S)模型对离散非线性不确定互联系统进行模糊建模,应用并行分布补偿算法(PDC)给出状态反馈分散模糊控制方案,并基于李亚普诺夫函数方法证明了闭环系统的稳定性.然后当系统的状态不完全可测时,设计模糊分散观测器来估计各子系统的状态,从而给出基于观测器的状态反馈分散模糊控制设计的方法.因为该分散模糊控制设计问题是以线性矩阵不等式的形式给出,所以很容易用凸优化方法求解.仿真结果验证了所提出控制方法的有效性.     

Fuzzy adaptive output feedback control for a class of switched non-triangular structure nonlinear systems with time-varying delays

This paper investigates an adaptive fuzzy output feedback control design problem for switched nonlinear system in non-triangular structure form. The discussed system contains unknown nonlinear dynamics, unmeasured states and unknown time-varying delays under a batch of switching signals. Fuzzy logic systems are utilised to learn unknown nonlinear dynamics and construct a fuzzy switched nonlinear observer. By combining the property of fuzzy basis function with Lyapunov–Krasovskii functional and the command filter, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the closed-loop control system is proved via Lyapunov stability theory and average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme.     

Decentralized output feedback stabilization for a class of large‐scale feedforward nonlinear time‐delay systems

This paper is concerned with the decentralized stabilization problem for a class of large‐scale feedforward nonlinear time‐delay systems. The uncertain nonlinearities involved in the systems are assumed to be bounded by continuous functions of the inputs and delayed inputs multiplied by unmeasured states and delayed states. An observer‐based decentralized output feedback control scheme is proposed by using the dynamic gain control design approach. On the basis of the Lyapunov–Krasovskii stability theory, the global asymptotic stability of the closed‐loop control system is proved. Contrary to many existing control designs for feedforward nonlinear systems, the celebrated forwarding design and saturation design are not utilized here. An example is finally given to demonstrate the effectiveness of the proposed design procedure. Copyright © 2013 John Wiley & Sons, Ltd.     

一类严格反馈系统变比例增益精确微分补偿控制

针对包含不确定函数和未知外部扰动的一类严格反馈型非线性系统,提出基于精确扰动观测器的变比例增益自适应模糊控制器.系统中的未知不确定函数由模糊逻辑系统在线逼近,同时将模糊逻辑系统的逼近误差和未知外部扰动定义为总扰动,利用精确扰动观测器进行精确微分补偿控制. 将非线性函数应用于设计可调节的输出反馈增益,有效消除系统的稳态误差,使得系统跟踪误差可以控制在零的任意小邻域内.最后,通过Lyapunov定理证明闭环系统中所有信号均是有界的.数值仿真表明了所提出方案的有效性.     

Robust fuzzy control for uncertain discrete-time nonlinear Markovian jump systems without mode observations

This paper studies the robust fuzzy control problem of uncertain discrete-time nonlinear Markovian jump systems without mode observations. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a discrete-time nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. As a result, an uncertain Markovian jump fuzzy system (MJFS) is obtained. A stochastic fuzzy Lyapunov function (FLF) is employed to analyze the robust stability of the uncertain MJFS, which not only is dependent on the operation modes of the system, but also directly includes the membership functions. Then, based on this stochastic FLF and a non-parallel distributed compensation (non-PDC) scheme, a mode-independent state-feedback control design is developed to guarantee that the closed-loop MJFS is stochastically stable for all admissible parameter uncertainties. The proposed sufficient conditions for the robust stability and mode-independent robust stabilization are formulated as a set of coupled linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. Finally, it is also demonstrated, via a simulation example, that the proposed design method is effective.     

Event‐triggered practical finite‐time output feedback stabilization of a class of uncertain nonlinear systems

This paper studies the event‐triggered practical finite‐time output feedback stabilization problem for a class of uncertain nonlinear systems with unknown control gains. First, a reduced‐dimensional observer is employed to implement the reconstruction of the unavailable states. Furthermore, a novel event‐triggered output feedback control strategy is proposed based on the idea of backstepping design and sign function techniques. It is shown that the practical finite‐time stability of the closed‐loop systems is ensured by Lyapunov analysis and related stability criterion. Compared with the existing methods, the main advantage of this strategy is that the observer errors and event‐trigger errors can be processed simultaneously to achieve the practical finite‐time stability. Finally, an example is adopted to demonstrate the validity of the proposed scheme.     

DECENTRALIZED STABILIZATION OF H FUZZY CONTROL FOR NONLINEAR MULTIPLE TIME‐DELAY INTERCONNECTED SYSTEMS

A robustness design of fuzzy control is proposed in this paper to overcome the effect of modeling errors between nonlinear multiple time‐delay systems and fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the UUB (uniformly ultimately bounded) stability of nonlinear multiple time‐delay interconnected systems with disturbances. Based on this criterion and the decentralized control scheme, a set of fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time‐delay interconnected systems and the Hcontrol performance is achieved in the mean time.     

Observer-based hybrid adaptive fuzzy control for affine and nonaffine uncertain nonlinear systems

This paper presents a novel observer-based hybrid adaptive fuzzy controller for affine and nonaffine nonlinear systems with external disturbance. The suggested design is so easy and does not need a mathematical model for system under control and also it is very simple, efficient and robust. Based on the adaptive method and the system states observer, an observer-based adaptive fuzzy method is proposed to control an uncertain nonlinear system. Also, a supervisory controller term is employed to attenuate the residual error to a desired level and compensate the both uncertainties and observer errors. Although proposed control method needs the uncertainties to be bounded, it does not need this bound to be identified. Stability of the proposed method is shown based on Lyapunov theory and also the strictly positive real condition if all the implicated signals are uniformly bounded. Finally, in our simulation studies, to demonstrate the usefulness and efficiency of the suggested technique, an uncertain nonlinear system is employed.

     

Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large‐scale systems using DSC technique

In this paper, an adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large‐scale stochastic nonlinear systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. Using the designed fuzzy state observer, and by combining the adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy decentralized output feedback control approach is developed. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing appropriate design parameters. A simulation example is provided to show the effectiveness of the proposed approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

Design of fuzzy controllers for uncertain nonlinear systems using stability and robustness analyses

This paper analyzes the stability and robustness of uncertain nonlinear systems and shows that the analysis results provide an efficient technique for the design of fuzzy controllers. Based on a fuzzy plant model describing an uncertain nonlinear plant, this design involves the derivation of a stability criterion and a robust area in the uncertain parameter space in terms of some measures of the closed-loop control system matrices. An application example on balancing an inverted pendulum is given to illustrate the simple design methodology, the stability and the robustness of the feedback system incorporated with the proposed fuzzy controller.     

Adaptive fuzzy decentralised control for stochastic nonlinear large-scale systems in pure-feedback form

This paper is concerned with the problem of adaptive fuzzy decentralised output-feedback control for a class of uncertain stochastic nonlinear pure-feedback large-scale systems with completely unknown functions, the mismatched interconnections and without requiring the states being available for controller design. With the help of fuzzy logic systems approximating the unknown nonlinear functions, a fuzzy state observer is designed estimating the unmeasured states. Therefore, the nonlinear filtered signals are incorporated into the backstepping recursive design, and an adaptive fuzzy decentralised output-feedback control scheme is developed. It is proved that the filter system converges to a small neighbourhood of the origin based on appropriate choice of the design parameters. Simulation studies are included illustrating the effectiveness of the proposed approach.     

Output feedback control of large-scale nonlinear time-delay systems in lower triangular form

This paper is concerned with the stabilization problem for a class of large-scale nonlinear time-delay systems in lower triangular form. The uncertain nonlinearities are assumed to be bounded by continuous functions of the outputs or delayed outputs multiplied by unmeasured states or delayed states. An observer based output feedback control scheme is proposed using the dynamic gain control design approach. Based on Lyapunov stability theory, global asymptotic stability of the closed-loop control system is proved. Contrary to many existing control designs for lower triangular nonlinear systems, the celebrated backstepping method is not utilized here. An example is finally given to demonstrate the effectiveness of the proposed design procedure.     

Passive fuzzy controller design via observer feedback for stochastic Takagi-Sugeno fuzzy models with multiplicative noises

This paper investigates the fuzzy control problem of a class of nonlinear continuous-time stochastic systems with achieving the passivity performance. A model-based observer feedback fuzzy control utilizing the concept of so-called parallel distributed compensation (PDC) is employed to stabilize the class of nonlinear stochastic systems that are represented by the Takagi-Sugeno (T-S) fuzzy models. Based on the Lyapunov criteria, the Linear Matrix Inequality (LMI) technique is used to synthesize the observer feedback fuzzy controller design such that the closed-loop system satisfies stability and passivity constraints, simultaneously. Finally, a numerical example is given to demonstrate the applicability and effectiveness of the proposed design method.     

基于弹性能量函数的非线性不确定系统控制方法

针对非线性不确定系统的控制问题,提出一种基于弹性能量函数的扰动观测方法和弹性跟踪控制方法.该方法以弹性能量函数为核心,将其分别应用于扰动观测器、虚拟跟踪指令以及弹性跟踪控制器的设计.该控制方法的突出优势是只根据误差来消除误差,不涉及误差的微分运算,控制器增益参数完全根据积分步长来整定.理论研究表明,所提出的弹性跟踪控制方法不仅可从理论上保证各级子控制器的稳定性,有效解决高阶SISO非线性不确定系统的控制问题,而且可有效避免反步控制方法出现的微分爆炸问题.此外,每个子控制器只有一个由积分步长即可整定的增益参数,因而控制器结构简单、计算量较小.仿真结果表明:所提出的控制方法不仅具有快的响应速度、高的控制精度以及强的抗扰动能力,而且不依赖于被控对象模型,在非线性不确定系统控制领域具有广泛的应用前景.     

Robust H ∞ fuzzy control of nonlinear systems with multiple time delays

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and R_k of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ^∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.     

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

This paper investigates the problem of state observer design for a class of nonlinear uncertain dynamical systems with interval time‐varying delay and the one‐sided Lipschitz condition. By constructing the novel Lyapunov–Krasovskii functional while utilizing the free‐weighting matrices approach, the one‐sided Lipschitz condition and the quadratic inner‐bounded condition, novel sufficient conditions, which guarantee the observer error converge asymptotically to zero, are established for a class of nonlinear dynamical systems with interval time‐varying delay in terms of the linear matrix inequalities. The computing method for observer gain matrix is given. Finally, two examples illustrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.