Robustness design of fuzzy control for nonlinear multiple time-delay large-scale systems via neural-network-based approach

The stabilization problem is considered in this correspondence for a nonlinear multiple time-delay large-scale system. First, the neural-network (NN) model is employed to approximate each subsystem. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of each NN model. According to the LDI state-space representation, a robustness design of fuzzy control is proposed to overcome the effect of modeling errors between subsystems and NN models. Next, in terms of Lyapunov's direct method, a delay-dependent stability criterion is derived to guarantee the asymptotic stability of nonlinear multiple time-delay large-scale systems. Finally, based on this criterion and the decentralized control scheme, a set of fuzzy controllers is synthesized to stabilize the nonlinear multiple time-delay large-scale system.     

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.     

Stability analysis of T–S fuzzy models for nonlinear multiple time-delay interconnected systems

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for nonlinear interconnected systems with multiple time-delays using linear matrix inequality (LMI) theory. In terms of Lyapunov’s direct method for multiple time-delay fuzzy interconnected systems, a novel LMI-based stability criterion which can be solved numerically is proposed. Then, the common P matrix of the criterion is obtained by LMI optimization algorithms to guarantee the asymptotic stability of nonlinear interconnect systems with multiple time-delay. Finally, the proposed stability conditions are demonstrated with simulations throughout this paper.     

基于模糊模型和神经网络的多时滞不确定非线性系统的鲁棒H∞控制

针对一类具有多时滞的不确定非线性系统,提出了一种基于模糊模型和神经网络的组 合控制方法.利用具有多时滞的模糊T-S模型对系统进行近似建模并给出基于线性矩阵不等式 (LMI)的模糊H∞控制律.提出完全自适应RBF神经网络控制方法,通过在线自适应调整RBF 神经网络的权重、函数中心和宽度,来对消系统的未知不确定性和模糊建模误差的影响,不要求 系统的不确定项和模糊建模误差满足任何匹配条件或约束,并证明了闭环系统的稳定性.最后, 将所提出的方法应用到一具有多时滞的非线性混沌系统,仿真结果表明了该方法的有效性.     

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.     

Delay-dependent T–S fuzzy control for nonlinear interconnected systems: Using dithers as auxiliaries

In this study, a novel approach via the composite of fuzzy controllers and dithers is presented. According to this approach, we can synthesize a set of fuzzy controllers and find appropriate dithers to stabilize nonlinear multiple time-delay (NMTD) interconnected systems. A robustness design of model-based fuzzy control is first proposed to overcome the effect of modeling errors between the NMTD interconnected subsystems and Takagi–Sugeno (T–S) fuzzy models. In terms of Lyapunov's direct method, a delay-dependent stability criterion is then derived to guarantee the asymptotic stability of NMTD interconnected systems. Based on this criterion and the decentralized control scheme, a set of model-based fuzzy controllers is synthesized via the technique of parallel distributed compensation (PDC) to stabilize the NMTD interconnected system. When the designed fuzzy controllers cannot stabilize the NMTD interconnected systems, a batch of high-frequency signals (commonly referred to as dithers) is simultaneously introduced to stabilize it. If the frequencies of dithers are high enough, the outputs of the dithered interconnected system and those of its corresponding mathematical model–the relaxed interconnected system can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered interconnected system based on the one of the relaxed interconnected system. Finally, a numerical example is given to illustrate the feasibility of our approach.     

Stability and stabilization of fuzzy large-scale systems

This paper investigates the stability and stabilization problems for the fuzzy large-scale system in which the system is composed of a number of Takagi-Sugeno fuzzy model subsystems with interconnections. The stability criterion of the fuzzy large-scale system without control is derived first. Instead of fuzzy parallel distributed compensation design, linear state feedback control is used in the stabilization work. Each local control is obtained from Riccati equation of the corresponding subsystem and the interconnection terms are used to determine the local feedback gain determination. Based on Lyapunov criterion, some conditions are derived under which the whole fuzzy large-scale system is stabilized asymptotically. A numerical example is given to illustrate the control design procedure and its effectiveness.     

时滞大系统的Robust稳定性

在本文中考虑了由非线性扰动子系统组成的时滞大系统的鲁棒稳定性问题，利用Ｌｙａｐｕｎｏｖ稳定性准则，对角占优矩阵的方法和结合矩阵Ｒｉｃｃａｔｉ方程，获得了系统指数稳定的充分判据，本文的结果改进并推广了文（４，６）的结果。     

一类模糊时滞系统指定衰减度的鲁棒控制

研究了一类非线性时滞系统基于模糊T-S模型的鲁棒镇定问题,所考虑的不确定时滞系统含有时变未知但有界的状态时滞,首先利用Razumikhin定理和Lyapunov定理,得出了由模糊T-S模型描述的非线性时滞系统鲁棒稳定且具有指定衰减度的判据,其次得到了具有指定衰减度的无记忆状态反馈控制律存在的充分条件及相应的控制器设计方法,该条件被进一步等价地转化为一个线性矩阵不等式的可解性问题,所设计的控制器确保了闭环系统具有指定衰减度鲁棒稳定。     

前提不匹配的模糊时滞系统的稳定与控制

研究了基于Takagi-Sugeno（T-S）模糊模型描述的非线性时滞系统的稳定性与控制问题。选择一个最近提出的基于自由权矩阵的积分不等式,以线性矩阵不等式（LMIs）形式给出了保守性较小的时滞依赖的稳定性准则。基于前提不匹配策略,结合Finsler引理,提出了更为灵活的模糊状态反馈控制器的设计方法,该方法不要求控制器和系统分享共同的前提隶属函数和规则数目。最后,给出两个仿真算例,证明了所提理论的先进性和有效性。     

A novel criterion for nonlinear time-delay systems using LMI fuzzy Lyapunov method

This study presents a kind of fuzzy robustness design for nonlinear time-delay systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The basic idea of the proposed approach is to construct a fuzzy controller for nonlinear dynamic systems with disturbances in which the delay-independent robust stability criterion is derived in terms of the fuzzy Lyapunov method. Based on the robustness design and parallel distributed compensation (PDC) scheme, the problems of modeling errors between nonlinear dynamic systems and Takagi–Sugeno (T–S) fuzzy models are solved. Furthermore, the presented delay-independent condition is transformed into linear matrix inequalities (LMIs) so that the fuzzy state feedback gain and common solutions are numerically feasible with swarm intelligence algorithms. The proposed method is illustrated on a nonlinear inverted pendulum system and the simulation results show that the robustness controller cannot only stabilize the nonlinear inverted pendulum system, but has the robustness against external disturbance.     

An observer-based approach to controlling time-delay chaotic systems via Takagi-Sugeno fuzzy model

This study presents a fuzzy model-based control criterion for time-delay chaotic systems with uncertainty. The Takagi-Sugeno (T-S) fuzzy model is adopted for representing a chaotic system possessing a time delay. A unified approach for designing a fuzzy observer, which integrates parallel distributed compensation with an adaptive updating method, is first discussed. An observer-based fuzzy control scheme is then developed to deal with stabilization and tracking problems. Based on Lyapunov stability analysis, sufficient conditions that ensure robust control performance of time-delay chaotic systems are derived. These conditions are represented in terms of linear matrix inequalities and adaptive updating laws. Finally, the proposed approach is validated through numerical synchronization, stabilization, and model tracking control simulations.     

基于积分二次约束不确定时滞大系统的鲁棒容错控制

针对一类不确定时滞大系统,研究执行器或传感器失效情况下的鲁棒容错控制。通过运用积分二次约束、线性矩阵不等式及Lyapunov函数的新分析方法,得到无摄动时滞大系统具有鲁棒容错控制的时滞依赖稳定性判据。通过推导获得不确定时滞大系统的时滞依赖稳定性判据,设计鲁棒容错控制器。     

Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay

This paper is concerned with the problems of finite-time stability (FTS) and finite-time stabilisation for a class of nonlinear systems with time-varying delay, which can be represented by Takagi–Sugeno fuzzy system. Some new delay-dependent FTS conditions are provided and applied to the design problem of finite-time fuzzy controllers. First, based on an integral inequality and a fuzzy Lyapunov–Krasovskii functional, a delay-dependent FTS criterion is proposed for open-loop fuzzy system by introducing some free fuzzy weighting matrices, which are less conservative than other existing ones. Then, the parallel distributed compensation controller is designed to ensure FTS of the time-delay fuzzy system. Finally, an example is given to illustrate the effectiveness of the proposed design approach.     

Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method

In this study, we present a Takagi–Sugeno (T–S) fuzzy model for the modeling and stability analysis of oceanic structures. We design a nonlinear fuzzy controller based on a parallel distributed compensation (PDC) scheme and reformulate the controller design problem as a linear matrix inequalities (LMI) problem as derived from the fuzzy Lyapunov theory. The robustness design technique is adopted so as to overcome the modeling errors for nonlinear time-delay systems subject to external oceanic waves. The vibration of the oceanic structure, i.e., the mechanical motion caused by the force of the waves, is discussed analytically based on fuzzy logic theory and a mathematical framework. The end result is decay in the amplitude of the surge motion affecting the time-delay tension leg platform (TLP) system. The feedback gain of the fuzzy controller needed to stabilize the TLP system can be found using the Matlab LMI toolbox. This proposed method of fuzzy control is applicable to practical TLP systems. The simulation results show that not only can the proposed method stabilize the systems but that the controller design is also simplified. The effects of the amplitude damping of the surge motion on the structural response are obvious and work as expected due to the control force.     

模糊免疫PID算法在温度控制系统中的应用研究

该文针对温度控制系统非线性、大滞后、参数时变的特征,设计了模糊免疫PID控制器。该控制器结合了模糊逻辑、免疫机理以及PID调节的各种优点,既具有模糊控制的非线性作用,又具有免疫控制的自适应能力,同时还具有PID控制的广泛适用性。文章介绍了模糊免疫PID控制器的控制原理和设计方法,在Matlab中编写函数仿真,结果表明该控制器能够实现持续干扰情况下的闭环鲁棒稳定,并使系统呈现良好的动态和静态性能。     

Stabilization of nonlinear time-delay systems with input saturation via anti-windup fuzzy design

This investigation considers stability analysis and control design for nonlinear time-delay systems subject to input saturation. An anti-windup fuzzy control approach, based on fuzzy modeling of nonlinear systems, is developed to deal with the problems of stabilization of the closed-loop system and enlargement of the domain of attraction. To facilitate the designing work, the nonlinearity of saturation is first characterized by sector conditions, which provide a basis for analysis and synthesis of the anti-windup fuzzy control scheme. Then, the Lyapunov–Krasovskii delay-independent and delay-dependent functional approaches are applied to establish sufficient conditions that ensure convergence of all admissible initial states within the domain of attraction. These conditions are formulated as a convex optimization problem with constraints provided by a set of linear matrix inequalities. Finally, numeric examples are given to validate the proposed method.     

Robust Fuzzy Design for Nonlinear Uncertain Stochastic Systems via Sliding-Mode Control

This paper deals with the sliding-mode control (SMC) problem for nonlinear stochastic time-delay systems by means of fuzzy approach. The Takagi-Sugeno (T-S) fuzzy stochastic time-delay model with parametric uncertainties and unknown nonlinearities is presented. A sufficient condition for the exponential stability in mean square of the sliding motion is also derived. Moreover, it is shown that when the linear matrix inequalities (LMIs) with equality constraint are feasible, the designs of both sliding surface and sliding-mode controller can be easily obtained via convex optimization. A simulation example illustrating the proposed method is given.     

Analysis and synthesis of nonlinear time-delay systems via fuzzycontrol approach

Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller     

基于神经网络补偿的非线性时滞系统时滞正反馈控制

A new adaptive time-delay positive feedback controller (ATPFC) is presented for a class of nonlinear time-delay systems. The proposed control scheme consists of a neural networks-based identification and a time-delay positive feedback controller. Two high-order neural networks (HONN) incorporated with a special dynamic identification model are employed to identify the nonlinear system. Based on the identified model, local linearization compensation is used to deal with the unknown nonlinearity of the system. A time-delay-free inverse model of the linearized system and a desired reference model are utilized to constitute the feedback controller, which can lead the system output to track the trajectory of a reference model. Rigorous stability analysis for both the identification and the tracking error of the closed-loop control system is provided by means of Lyapunov stability criterion. Simulation results are included to demonstrate the effectiveness of the proposed scheme.