T–S fuzzy control for dithered nonlinear singularly perturbed systems with multiple time delays

This paper is concerned with the stability problem of nonlinear multiple time-delay singularly perturbed (NDSP) systems. To overcome the effect of modeling error between the reduced-order model of the NDSP plant and Takagi–Sugeno (T–S) fuzzy models, a robustness design of model-based fuzzy control is proposed in this study. A stability criterion in terms of Lyapunov’s direct method is derived to guarantee the asymptotic stability of NDSP systems. According to this criterion, a model-based fuzzy controller is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the NDSP system. If the designed fuzzy controller cannot stabilize the NDSP system, a high-frequency signal, commonly referred to as dither, is simultaneously introduced to stabilize it. Based on the relaxed method, the NDSP system can be stabilized by regulating appropriately the parameters of dither. If the dither’s frequency is high enough, the output of the dithered reduced system and that of its corresponding mathematical model – the relaxed reduced system – can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered reduced system based on the one of the relaxed reduced system.     

Optimal H fuzzy control for nonlinear multiple time-delay interconnected systems: Using dithers as auxiliaries

This paper presents an effective approach to stabilize nonlinear multiple time-delay (NMTD) interconnected systems via a composite of fuzzy controllers and dithers. First, a neural-network (NN) model is employed to approximate each subsystem. Then, the dynamics of the NN model is converted into a linear differential inclusion (LDI) state-space representation. Next, in terms of Lyapunov?s direct method, a delay-dependent stability criterion is derived to guarantee the exponential stability of the NMTD interconnected system. Subsequently, the stability conditions of this criterion are reformulated into a linear matrix inequality (LMI). Based on the LMI, a robustness design of fuzzy control is synthesized not only to stabilize the NMTD interconnected system but also to achieve the optimal H^∞ performance by minimizing the disturbance attenuation level. A set of high-frequency signals (commonly referred to as dithers) is simultaneously injected to stabilize the NMTD interconnected system when the designed fuzzy controllers cannot stabilize it. If the dithers’ frequencies 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 get a rigorous prediction of the stability of the dithered interconnected system by establishing the stability of the relaxed interconnected system. Finally, a numerical example with simulations is given to illustrate the feasibility of our approach.     

Chaos control of the permanent magnet synchronous motor with time-varying delay by using adaptive sliding mode control based on DSC

This paper focuses on the problem of chaos control for the permanent magnet synchronous motor with chaotic oscillation, unknown dynamics and time-varying delay by using adaptive sliding mode control based on dynamic surface control. To reveal the mechanism of motor system and facilitate controller design, the dynamic behavior of the system is investigated. Nonlinear items of system model, upper bounds of time delays and their derivatives are taken as unknown in the overall process. A RBF neural network with an adaptive law, which eliminates restrictions on accurate model and parameters, is employed to cope with unknown dynamics. In order to solve issues such as chaotic oscillation, ‘explosion of complexity’ of backstepping, and chattering associated with sliding mode control, a sliding mode controller is developed within the framework of dynamic surface control by the hybrid of adaptive technology and RBF neural network. In addition, an appropriate Lyapunov function is employed to demonstrate the system stability. Finally, the feasibility of the proposed scheme is testified by simulation.     

Nonlinear modeling and robust LMI fuzzy control of overhead crane systems

Overhead cranes are widely used structures for lifting and conveying heavy loads. The development of feedback control systems for such equipment is important due to the large number of potential applications and advantages over manual operation concerning stability and robustness. This paper aims to represent the key nonlinear dynamics of crane systems by means of a state-space fuzzy model with compact rule-base structure. The fuzzy model is useful to assist the design of a fuzzy controller based on the concept of parallel compensation. A well-posed conservative linear-matrix-inequality (LMI) feasibility problem is formulated so that a solution guarantees closed-loop Lyapunov stability, bounded control inputs, quick positioning of the supporting cart, and suppression of load oscillations and collisions. The fuzzy controller is composed by rules with linear control laws derived from local state-space models. The controller warrants asymptotic convergence of the states. Due to the nonlinear nature of the fuzzy model and controller, Jacobian linearization is avoided. The proposed fuzzy control approach for cranes has shown to be more effective and robust than an optimal quadratic controller, and able to move cargo smoothly and safely to a destination. Particularly, constrained and smoother control inputs avoid actuator saturation, and tend to increase its lifetime. Laboratory experiments using the LMI fuzzy controller and actual data validates the approach for cranes in actual scenario.     

混沌的非线性控制

基于逆系统方法设计了控制混沌的非线性控制器，以呈现混沌性态的虫口模型映射和Ｈｅｎｏｎ映射为例给出了控制算例，最后讨论了可能的推广和发展     

Design of digital controllers for uncertain chaotic systems using fuzzy logic

A new and systematic method to design digital controllers for uncertain chaotic systems with structured uncertainties is presented in this paper. Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system, while the uncertainties are decomposed such that the uncertain chaotic system can be rewritten as a set of local linear models with an additional disturbed input. Conventional control techniques are utilized to develop the continuous-time controllers first. Then, the digital controllers are obtained as the digital redesign of the continuous-time controllers using the state-matching approach. The performance of the proposed controller design is illustrated through numerical examples.     

Gray-fuzzy control of a nonlinear two-mass system

This study presents application of a fuzzy controller to a nonlinear two-mass system control. The proposed controller structure is strengthened with a gray estimator. Firstly, a complete state-space mathematical model for a nonlinear two-mass system is developed and numerically simulated. Then, a fuzzy controller is designed to regulate the speed of the system. In order to perform a dynamic and powerful control action, future error values are estimated by gray modeling technique. The gray estimators of the torsional torque and the load machine speed are tested with open-loop and closed-loop control structures to test the robustness of the proposed method for step changes in input parameters. It is observed that the tracking ability of the gray estimators is not influenced for different operation modes. The performances of the control structures, which are supported with gray estimators, are given and no additional feedbacks are required for robust control action. The simulation results are confirmed by experimental results and conclusions are given.     

Nonlinear dynamic analysis for a Francis hydro-turbine governing system and its control

In this paper, we introduce a novel model of a hydro-turbine system with the effect of surge tank based on state-space equations to study the nonlinear dynamical behaviors of the hydro-turbine system. The critical points of Hopf bifurcation and the relationship of the stability satisfying with the adjustment coefficients are obtained from direct algebraic criterion. Furthermore, the bifurcation diagrams and Lyapunov exponents are presented and analyzed. The dynamical behaviors of the points with representative characteristics are identified and studied in detail. Both theoretical analysis and numerical simulations show that chaotic oscillations, which cannot stabilize the system, may occur with the changes of adjustment coefficients. To control the undesirable chaotic behaviors in this system, fuzzy sliding mode governor based on the sliding mode control (SMC) and the fuzzy logic are designed, and considering the bounded disturbance. Finally, series of numerical simulations are presented to verify the effectiveness of the proposed governor, which prove that the hydro-turbine governing system can maintain a better operation station under the designed governor.     

Interval fuzzy robust non-fragile finite frequency control for active suspension of in-wheel motor driven electric vehicles with time delay

This paper proposes a fuzzy non-fragile finite frequency H_∞ control algorithm for the active suspension system (ASS) of the electric vehicles driven by in-wheel motors with an advanced dynamic vibration absorber (DVA). Firstly, an interval type-2 Takagi-Sugeno (T-S) fuzzy model is established to formulate the nonlinear time-delay ASS with the uncertainties of sprung mass, unsprung mass, suspension stiffness, and tire stiffness. Secondly, a differential evolution (DE) algorithm is adopted to optimize the parameters of vehicle suspension and DVA. Thirdly, a non-fragile finite frequency H_∞ control controller is developed under the consideration of controller perturbation and input delay to improve the comprehensive performance of the chassis under the finite frequency external disturbances. Finally, simulation tests are carried out to verify the effectiveness of the proposed controller.     

Network-based synchronization of T–S fuzzy chaotic systems with asynchronous samplings

In this paper, we study the problem of network-based synchronization of chaotic systems in Takagi–Sugeno (T–S) fuzzy form, in which the master and slave fuzzy chaotic systems are connected with a continuous-time controller through a network. In all communication channels, asynchronous samplings and external disturbances are considered. The asynchronously sampled state information of the master and slave systems received in the controller is treated by designing an observer for estimating the states of the master system. Then, based on the observation result, the problem of asynchronous samplings between the slave-controller and controller-slave channels is solved in two different cases. Sufficient conditions for the existence of the desired observer and controllers for each asynchronous cases are presented in the form of linear matrix inequalities. An numerical example is given to illustrate the validity and potential of the proposed new design techniques.     

Logistic映射混沌行为的动力学原因

Logistic映射是最具代表性的混沌系统,我们利用matlab程序计算了Logistic映射的迭代行为．并绘出了它的李亚普诺夫指数图,并从数学角度解释了混沌行为产生的动力学原因。     

PDC and Non-PDC fuzzy control with relaxed stability conditions for contintuous-time multiplicative noised fuzzy systems

This paper presents a relaxed scheme of fuzzy controller design for continuous-time nonlinear stochastic systems that are constructed by the Takagi–Sugeno (T–S) fuzzy models with multiplicative noises. Through Nonquadratic Lyapunov Functions (NQLF) and Non-Parallel Distributed Compensation (Non-PDC) control law, the less conservative Linear Matrix Inequality (LMI) stabilization conditions on solving fuzzy controllers are derived. Furthermore, in order to study the effects of stochastic behaviors on dynamic systems in real environments, the multiplicative noise term is introduced in the consequent part of fuzzy systems. For decreasing the conservatism of the conventional PDC-based fuzzy control, the NQLF stability synthesis approach is developed in this paper to obtain relaxed stability conditions for T–S fuzzy models with multiplicative noises. Finally, some simulation examples are provided to demonstrate the validity and applicability of the proposed fuzzy controller design approach.     

Master–slave chaos synchronization using adaptive TSK-type CMAC neural control

In this paper, an adaptive TSK-type CMAC neural control (ATCNC) system via sliding-mode approach is proposed for the chaotic symmetric gyro. The proposed ATCNC system is composed of a neural controller and a supervisory compensator. The neural controller uses a TSK-type CMAC neural network (TCNN) to approximate an ideal controller and the supervisory compensator is designed to guarantee system stable in the Lyapunov stability theorem. The developed TCNN provides more powerful representation than the traditional CMAC neural network. Moreover, all the control parameters of the proposed ATCNC system are evolved in the Lyapunov sense to ensure the system stability with a proportional–integral (PI) type adaptation tuning mechanism. Some simulations are presented to confirm the validity of the proposed ATCNC scheme without the occurrence of chattering phenomena. Further, the proposed PI type adaptation laws can achieve faster convergence of the tracking error than that using integral type adaptation laws in previous published papers.     

Observer-based output-feedback control of large-scale networked fuzzy systems with two-channel event-triggering

This paper concerns data transmissions for large-scale T–S fuzzy systems with event-triggering control, where each subsystem communicates its information via a two-channel network. We propose an event-triggering scheme in which two event-triggering mechanisms are used to verify the data transmissions. At first, a novel model transformation is presented, where the event-triggered control system is reconstructed as a constant-delay system with extra inputs and outputs. By using a relaxed Lyapunov–Krasovskii functional (LKF) without the requirement of positive definiteness for all Lyapunov matrices, and the scaled small gain (SSG) theorem, the co-design problem of desired observer and controller gains, event-triggering parameters, and the sampling period is resolved in the form of linear matrix inequalities (LMIs). It will be shown that the solution guarantees the stability of closed-loop fuzzy control system and the reductions of data communications in both the sensor-to-controller and controller-to-actuator channels. The proposed method is validated by using a numerical example.     

基于混沌动力学的知识创新演化规律分析

 知识创新是一个复杂的、隐含规律与秩序的演化过程,文中运用混沌理论进行了知识创新的演化趋势和规律探讨。将知识创新系统看作复杂系统,分析知识创新的混沌特性,建立基于创新能力的知识创新的混沌动力学模型。在模型建立的基础上,进行知识创新的模拟和动态演变规律的分析,以创新的状态和系统的演化为依据,将知识创新分为非时间连续的四类阶段：创新匮乏阶段、初步创新阶段、规律创新阶段和混沌创新阶段,与渐进性创新和突破性创新进行了对应分析,并基于本文的模型从知识创新角度分析了知识创新系统中渐进性创新与突破性创新的统一。     

An adaptive compensator for a vehicle driven by DC motors

A vehicle system driven by two independent DC motors is presented here, one of which is used for the right wheel and the other is used for the left wheel. An adaptive compensator using Takagi-Sugeno fuzzy systems is proposed to control the vehicle system. The compensator includes an adaptive model identifier and adaptive controller. An online method is used to adjust the parameters of the identifier model to match the behavior model of the vehicle system. Then, the parameters of the identifier model are employed in a standard parallel-distributed compensator to provide asymptotically stable equilibrium for the closed-loop vehicle drive system, in which the velocity and direction angle of the vehicle are controlled. Results demonstrate that the proposed controller structure is robust to load changes and follows different trajectories very well.     

Design of PID controller based on a self-adaptive state-space predictive functional control using extremal optimization method

In proportional-integral-derivative (PID) controller design, obtaining high stability and desired closed-loop response are of great importance for system engineers. Most existing methodologies, which have validated their excellent control performance on the accurate mathematical model, face significant difficulties in the unavoidable model mismatches and disturbance. To overcome these drawbacks, this paper proposes a self-adaptive state-space predictive functional control (APFC) based on extremal optimization method to design PID controller called EO-APFC-PID, wherein, the self-adaptive means, i.e., a forgetting factor recursive least squares (FFRLS) mechanism is embedded into state-space predictive functional control (PFC), and the proposed EO is exploited to alleviate the challenging problem that the elements in weighting factors of APFC technique are lacking analytical knowledge. The performance of the proposed EO-APFC-PID control scheme is demonstrated and compared with one classic PID tuning method and two state-of-the-art control strategies on the chamber pressure control for a coke furnace. The experimental results fully illustrate that the proposed method is more effective and efficient than other existing control strategies for achieving a desired behavior on the most test cases considered in this paper in terms of set point tracking, input disturbance rejection and output disturbance rejection.     

Exponential stability analysis and controller design of fuzzy systems with time-delay

Takagi-Sugeno (T-S) fuzzy models can provide an effective representation of complex nonlinear systems with a series of linear input/output submodels in terms of fuzzy sets and fuzzy reasoning. In this paper, the T-S fuzzy model approach is extended to the stability analysis and controller design for nonlinear systems with time delays. An improved stability condition is proposed by introducing adjustable parameters into the Lyapunov-Krasovskii functional. Stabilization approach for fuzzy state feedback is also presented. Sufficient conditions for the existence of fuzzy feedback gain are derived through the numerical solution of a set of obtained linear matrix inequalities (LMIs). Compared with the existing methods in the literature, the proposed approach has less conservatism and both the sizes of delay and its derivative are involved in the criterion. The dynamical performance of the system can be adjusted by changing the adjustable parameters. Finally, two examples are given to show the effectiveness of the proposed approach.     

Fuzzy adaptive event-triggered control for uncertain nonlinear system with prescribed performance: A combinational measurement approach

This paper addresses the adaptive fuzzy event-triggered control (ETC) problem for a class of nonlinear uncertain systems with unknown nonlinear functions. A novel ETC approach that exhibits a combinational triggering (CT) behavior is proposed to update the controller and fuzzy weight vectors, achieving the non-periodic control input signals for nonlinear systems. A CT-based fuzzy adaptive observer is firstly constructed to estimate the unmeasurable states. Based on this, an output feedback ETC is proposed following the backstepping and error transformation methods, which ensures the prescribed dynamic tracking (PDT) performance. The PDT performance indicates that the transient bounds, over-shooting and ultimate values of tracking errors are fully determined by the control parameters and functions chosen by users. The closed-loop stability is guaranteed under the framework of impulsive dynamic system. Besides, the Zeno phenomenon is circumvented. The theoretical analysis indicates that the proposed scheme guarantees control performance while considerably reducing the communication resource utilization and controller updating frequency. Finally, the numerical simulations are conducted to verify the theoretical findings.