A fuzzy decentralized variable structure tracking control with optimal and improved robustness designs: theory and applications

To begin with, each subsystem of a nonlinear interconnected system was approximated by a weighted combination of L linear pulse transfer function systems (LPTFSs). For every nominal LPTFS of the mth subsystem, a dead-beat to its switching surface was first designed. The output disturbance of the mth LPTFS included the interconnections coming from the other subsystems, the approximation error of the mth subsystem, and the interactions resulting from the other LPTFSs. In general, this output disturbance was not small and contains various frequencies. Under this circumstances, the H/sup /spl infin//-norm of the weighted sensitivity function between the mth switching surface and its corresponding output disturbance was minimized. In addition, an appropriate selection of the weighted function for the sensitivity could reject the corresponding mode of the output disturbance. Although the effect of the output disturbance is attenuated and partially rejected, a better performance could be enhanced by a switching control based on the Lyapunov redesign. In addition, the stability of the overall system was verified by Lyapunov stability theory. The simulations for the LPTFSs with different delays or nonminimum phases or unstable features were arranged to evaluate the effectiveness of the proposed control. Finally, the application to the trajectory tracking of the robot arm including the fuzzy modeling was carried out to confirm the practicality of the proposed control.     

Fuzzy linear pulse-transfer function-based sliding-mode control fornonlinear discrete-time systems

In this paper, a nonlinear discrete-time system in the presence of input disturbance and measurement noise is approximated by N subsystems described by the linear pulse-transfer functions. Although the input disturbance and the measurement noise are unknown, they are modeled as known pulse-transfer functions. The approximation error between the nonlinear discrete-time system and the fuzzy linear pulse-transfer function system is represented by the linear time-invariant dynamic system in every subsystem, whose degree can be larger than that of the corresponding subsystem. Besides the input disturbance and the measurement noise, uncertainties are caused by the approximation error of the fuzzy-model and the interconnected dynamics resulting from the other subsystems. Owing to the presence of input disturbance, measurement noise, or uncertainties, a disadvantageous response occurs. Based on Lyapunov redesign, the switching control in every subsystem is designed to reinforce the system performance. Due to the time-invariant feature for a constant reference input, the operating point can approach the sliding surface in the manner of finite-time steps. The stability of the overall system is verified by Lyapunov stability theory     

Fuzzy Mixed H2/H∞ Optimization-Based Decentralized Model Reference Control and Application to Piezo-Driven XY Table Systems

In this paper, a decentralized model reference control via fuzzy mixed H²/H^infin optimization design was developed. Each subsystem contained L linear pulse transfer function systems (LPTFSs). The reference model for every LPTFS was first designed to shape the response of the ith closed-loop subsystem. Then the H² -norm of the output error (i.e., the difference between the output of the reference model and the system) and weighted control input of the jth LPTFS was minimized to obtain a control such that smaller energy consumption with bounded tracking error of the jth LPTFS was achieved. However, an output disturbance of the jth LPTFS caused by the interactions among the LPTFSs, the interconnections among the subsystems, modeling errors, and external loads deteriorated system performance or even resulted in instability. In this situation, the H ^infin-norm of weighted sensitivity between output disturbance and output error of the jth LPTFS was minimized to attenuate its effect. A nonlinear control based on output error for every LPTFS was also established to improve robust performance. The stability of the overall system was then verified by Lyapunov stability criterion. The application to piezo-driven XY table system (PD-XY-TS) was carried out to confirm the usefulness of the proposed control     

Mixed H/sub 2//H/sub /spl infin// design for a decentralized discrete variable structure control with application to mobile robots

In this paper, a decentralized discrete variable structure control via mixed H/sub 2//H/sub /spl infin// design was developed. In the beginning, the H/sub 2/-norm of output error and weighted control input was minimized to obtain a control such that smaller energy consumption with bounded tracking error was assured. In addition, a suitable selection of this weighted function (connected with frequency) could reduce the effect of disturbance on the control input. However, an output disturbance caused by the interactions among subsystems, modeling error, and external load deteriorated system performance or even brought about instability. In this situation, the H/sub /spl infin//-norm of weighted sensitivity between output disturbance and output error was minimized to attenuate the effect of output disturbance. Moreover, an appropriate selection of this weighted function (related to frequency) could reject the corresponding output disturbance. No solution of Diophantine equation was required; the computational advantage was especially dominated for low-order system. For further improving system performance, a switching control for every subsystem was designed. The proposed control (mixed H/sub 2//H/sub /spl infin// DDVSC) was a three-step design method. The stability of the overall system was verified by Lyapunov stability criterion. The simulations and experiments of mobile robot were carried out to evaluate the usefulness of the proposed method.     

Mixed H2/H infinity design for a decentralized discrete variable structure control with application to mobile robots.

In this paper, a decentralized discrete variable structure control via mixed H2/H infinity design was developed. In the beginning, the H2-norm of output error and weighted control input was minimized to obtain a control such that smaller energy consumption with bounded tracking error was assured. In addition, a suitable selection of this weighted function (connected with frequency) could reduce the effect of disturbance on the control input. However, an output disturbance caused by the interactions among subsystems, modeling error, and external load deteriorated system performance or even brought about instability. In this situation, the H infinity-norm of weighted sensitivity between output disturbance and output error was minimized to attenuate the effect of output disturbance. Moreover, an appropriate selection of this weighted function (related to frequency) could reject the corresponding output disturbance. No solution of Diophantine equation was required; the computational advantage was especially dominated for low-order system. For further improving system performance, a switching control for every subsystem was designed. The proposed control (mixed H2/H infinity DDVSC) was a three-step design method. The stability of the overall system was verified by Lyapunov stability criterion. The simulations and experiments of mobile robot were carried out to evaluate the usefulness of the proposed method.     

Adaptive tracking H-infinity control for switched nonlinear systems with unknown control gain sign

This paper addresses the adaptive tracking control scheme for switched nonlinear systems with unknown control gain sign. The approach relaxes the hypothesis that the upper bound of function control gain is known constant and the bounds of external disturbance and approximation errors of neural networks are known. RBF neural networks (NNs) are used to approximate unknown functions and an H-infinity controller is introduced to enhance robustness. The adaptive updating laws and the admissible switching signals have been derived from switched multiple Lyapunov function method. It’s proved that the resulting closed loop system is asymptotically Lyapunov stable such that the output tracking error performance and H-infinity disturbance attenuation level are well obtained. Finally, a simulation example of Forced Duffing systems is given to illustrate the effectiveness of the proposed control scheme and improve significantly the transient performance.     

力矩输入有界的柔性关节机器人轨迹跟踪控制

为解决柔性关节机器人在关节驱动力矩输出受限情况下的轨迹跟踪控制问题,提出一种基于奇异摄动理论的有界控制器.首先,利用奇异摄动理论将柔性关节机器人动力学模型解耦成快、慢两个子系统.然后,引入一类平滑饱和函数和径向基函数神经网络非线性逼近手段,依据反步策略设计了针对慢子系统的有界控制器.在快子系统的有界控制器设计中,通过关节弹性力矩跟踪误差的滤波处理加速系统的收敛.同时,在快、慢子系统控制器中均采用模糊逻辑实现控制参数的在线动态自调整.此外,结合李雅普诺夫稳定理论给出了严格的系统稳定性证明.最后,通过仿真对比实验验证了所提出控制方法的有效性和优越性.     

Data-based iterative learning control for multiphase batch processes

In order to cope with the problem of the robustness conditions dependence on system parameters information, this paper investigates a data-based iteration learning control (ILC) for multiphase batch processes with different dimensions and system uncertainty. Firstly, by minimizing the residual between the actual subsystem output and the approximated subsystem output, a gradient-type approximation law is designed to approximate the system lower triangular parameters matrix and initial state. Secondly, by minimizing the approximated tracking error between the desired trajectory and the approximated output, a data-based ILC is constructed in an interactive mode with the approximation law. Finally, the boundedness of the approximation error of the real system parameters from the approximated parameters is derived by means of vector norm theory, while the unconditional robustness of the proposed data-based ILC is proved. Simulation results illustrate the effectiveness and practicability of the proposed data-based ILC.     

Circular Formation Flight Control for Unmanned Aerial Vehicles With Directed Network and External Disturbance

This paper proposes a new distributed formation flight protocol for unmanned aerial vehicles(UAVs)to perform coordinated circular tracking around a set of circles on a target sphere.Different from the previous results limited in bidirectional networks and disturbance-free motions,this paper handles the circular formation flight control problem with both directed network and spatiotemporal disturbance with the knowledge of its upper bound.Distinguishing from the design of a common Lyapunov fiunction for bidirectional cases,we separately design the control for the circular tracking subsystem and the formation keeping subsystem with the circular tracking error as input.Then the whole control system is regarded as a cascade connection of these two subsystems,which is proved to be stable by input-tostate stability(ISS)theory.For the purpose of encountering the external disturbance,the backstepping technology is introduced to design the control inputs of each UAV pointing to North and Down along the special sphere(say,the circular tracking control algorithm)with the help of the switching function.Meanwhile,the distributed linear consensus protocol integrated with anther switching anti-interference item is developed to construct the control input of each UAV pointing to east along the special sphere(say,the formation keeping control law)for formation keeping.The validity of the proposed control law is proved both in the rigorous theory and through numerical simulations.     

多模型主动容错滑模预测控制在太阳能热发电系统中的应用

针对太阳能热发电系统的随机性和干扰性强的特点,以解决太阳能热发电的平稳性问题,本文设计了多模型主动容错滑模预测控制器.对实测的数据进行模糊聚类,再用递推最小二乘法建立集热子系统的多模型;采用基于累计误差最小的切换策略在线选择最优控制模型;为降低在建立多模型的过程中数据的缺失、故障和强扰动引起的误差,建立太阳能集热系统的自适应预测模型;设计主动容错滑模预测控制器提高输出的跟踪精度和鲁棒性;最后,验证该算法应用的有效性和优势.     

Fuzzy neural-based control for nonlinear time-varying delay systems.

In this paper, a partially known nonlinear dynamic system with time-varying delays of the input and state is approximated by N fuzzy-based linear subsystems described by a state-space model with average delay. To shape the response of the closed-loop system, a set of fuzzy reference models is established. Similarly, the same fuzzy sets of the system rule are employed to design a fuzzy neural-based control. The proposed control contains a radial-basis function neural network to learn the uncertainties caused by the approximation error of the fuzzy model (e.g., time-varying delays and parameter variations) and the interactions resulting from the other subsystems. As the norm of the switching surface is inside of a defined set, the learning law starts; in this situation, the proposed method is an adaptive control possessing an extra compensation of uncertainties. As it is outside of the other set, which is smaller than the aforementioned set, the learning law stops; under this circumstance, the proposed method becomes a robust control without the compensation of uncertainties. A transition between robust control and adaptive control is also assigned to smooth the possible discontinuity of the control input. No assumption about the upper bound of the time-varying delays for the state and the input is required. However, two time-average delays are needed to simplify the controller design: 1) the stabilized conditions for every transformed delay-free subsystem must be satisfied; and 2) the learning uncertainties must be relatively bounded. The stability of the overall system is verified by Lyapunov stability theory. Simulations as compared with a linear transformed state feedback with integration control are also arranged to consolidate the usefulness of the proposed control.     

H ∞ output tracking control for discrete‐time switched systems via output feedback

This paper studies the problem of H _∞ output tracking control for a class of discrete‐time switched systems. Neither the measurability of the system state nor the solvability of the output tracking control problem for each individual subsystem is required. We design controllers for subsystems and a switching law to solve the H _∞ output tracking problem for the switched system. The designed controllers use only the measured output feedback, and the switching law is based on the measured output tracking error. In addition, the quadratic function corresponding to each subsystem is not required to be positive definite. A numerical example is provided to demonstrate the feasibility and validity of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

严格反馈互联系统分散式backstepping自适应迭代学习控制

基于Lyapunov分析方法,针对具有严格反馈形式的非线性互联系统,本文设计了一种分散式backstepping自适应迭代学习控制器.子系统之间的互联项为所有子系统输出项线性有界,为每个子系统设计的控制器仅采用该子系统的信息,不需要子系统之间相互传递信息.在控制器中,引入在时间轴和迭代轴上同时更新的自适应参数,以补偿子系统之间的互联项影响.通过采用本文给出的控制器,可使得每个子系统的输出跟踪相应的参考模型输出,仿真结果验证了本文算法的有效性.     

变负载机械手轨迹跟踪控制器设计

本文针对具有变负载的不确定刚性机械手系统,提出了一种依赖平均驻留时间的神经网络自适应切换控制策略.本控制方案将夹持不同负载的刚性机械手系统视为切换系统,即根据负载的不同将整个系统分为若干子系统,并基于平均驻留时间原则对每个子系统分别设计控制器.在各子系统中,分别采用径向基函数(RBF)神经网络逼近系统结构参数,以避免控制器对系统精确模型的依赖.同时,基于神经网络设计鲁棒补偿项,以抑制集总扰动对系统的影响.然后,利用多Lyapunov函数方法证明了轨迹跟踪误差的一致最终有界性.最后,通过仿真验证,所提出的控制方案不仅可实现变负载机械手期望轨迹的高精度跟踪,而且可有效削弱输入力矩的抖振.     

Quasi-ISS/ISDS observers for interconnected systems and applications

This paper considers interconnected nonlinear dynamical systems and studies observers for such systems. For single systems the notion of quasi-input-to-state dynamical stability (quasi-ISDS) for reduced-order observers is introduced and observers are investigated using error Lyapunov functions. It combines the main advantage of ISDS over input-to-state stability (ISS), namely the memory fading effect, with reduced-order observers to obtain quantitative information about the state estimate error. Considering interconnections quasi-ISS/ISDS reduced-order observers for each subsystem are derived, where suitable error Lyapunov functions for the subsystems are used. Furthermore, a quasi-ISS/ISDS reduced-order observer for the whole system is designed under a small-gain condition, where the observers for the subsystems are used. As an application, we prove that quantized output feedback stabilization for each subsystem and the overall system is achievable, when the systems possess a quasi-ISS/ISDS reduced-order observer and a state feedback law that yields ISS/ISDS for each subsystem and therefor the overall system with respect to measurement errors. Using dynamic quantizers it is shown that under the mentioned conditions asymptotic stability can be achieved for each subsystem and for the whole system.     

基于滑模观测器和广义观测器的故障估计方法

针对受未知干扰影响的一类非线性系统,提出一种基于滑模观测器和广义观测器的执行器故障和传感器故障估计方法.首先通过线性变换将原系统解耦为两个降阶的子系统,其中一个子系统受执行器故障和干扰的影响,另一个含有传感器故障和干扰,进一步将后一个子系统转化为广义系统.对两类子系统分别设计滑模观测器和广义观测器,给出估计误差一致最终有界的条件,得到系统状态和未知干扰的估计值.然后,利用等效输出控制原理重构执行器故障,引入干扰补偿保证重构算法的鲁棒性,再根据广义观测器的结果获得传感器故障的估计值.最后,通过计算机仿真验证了本文方法的有效性.     

Model-free Adaptive Dynamic Programming Based Near-optimal Decentralized Tracking Control of Reconfigurable Manipulators

In this paper, a model-free near-optimal decentralized tracking control (DTC) scheme is developed for reconfigurable manipulators via adaptive dynamic programming algorithm. The proposed controller can be divided into two parts, namely local desired controller and local tracking error controller. In order to remove the normboundedness assumption of interconnections, desired states of coupled subsystems are employed to substitute their actual states. Using the local input/output data, the unknown subsystem dynamics of reconfigurable manipulators can be identified by constructing local neural network (NN) identifiers. With the help of the identified dynamics, the local desired control can be derived directly with corresponding desired states. Then, for tracking error subsystems, the local tracking error control is investigated by the approximate improved local cost function via local critic NN and the identified input gain matrix. To overcome the overall error caused by the substitution, identification and critic NN approximation, a robust compensation is added to construct the improved local cost function that reflects the overall error, regulation and control simultaneously. Therefore, the closed-loop tracking system can be guaranteed to be asymptotically stable via Lyapunov stability theorem. Two 2-degree of freedom reconfigurable manipulators with different configurations are employed to demonstrate the effectiveness of the proposed modelfree near-optimal DTC scheme.     

Robust discrete variable structure control with finite-time approach to switching surface

By using a dead-beat control technique of discrete-time systems, a robust discrete variable structure control (DVSC) is developed for the linear discrete-time systems subject to input disturbance, measurement noise and uncertainty. The proposed control includes two parts: equivalent control and switching control. Based on the internal model principle, the input disturbance and the measurement noise modeled as pulse transfer functions, are rejected by the equivalent control. The unmatched uncertainty caused by the time-invariant parameter variations is also tackled by the equivalent control. If the inverse of stable characteristic polynomial of the real closed-loop system is a finite-degree polynomial, the trajectory reaches the switching surface in a finite-time step. Due to the subjection of input disturbance or measurement noise or uncertainty, a poor response occurs. Under these circumstances, a switching control based on Lyapunov redesign is employed to improve the system performance. The stability of the closed-loop system is then verified by Lyapunov stability theory. Simulations are also given to confirm the usefulness of the proposed controller.     

RBF neural networks-based robust adaptive tracking control for switched uncertain nonlinear systems

In this paper, a robust adaptive H∞ control scheme is presented for a class of switched uncertain nonlinear systems. Radical basis function neural networks (RBF NNs) are employed to approximate unknown nonlinear functions and uncertain terms. A robust H∞ controller is designed to enhance robustness due to the existence of the compound disturbance which consists of approximation errors of the neural networks and external disturbance. Adaptive neural updated laws and switching signals are deducted from multiple Lyapunov function approach. It is proved that with the proposed control scheme, the resulting closed-loop switched system is robustly stable and uniformly ultimately bounded (UUB) such that good capabilities of tracking performance is attained and H∞ tracking error performance index is achieved. A practical example shows the effectiveness of the proposed control scheme.     

Finding a stabilising switching law for switching nonlinear models

This paper considers the stabilisation of switching nonlinear models by switching between the subsystems. We assume that arbitrary switching between two subsystems is possible once a subsystem has been active for a predefined number of samples. We use a Takagi–Sugeno representation of the models and a switching Lyapunov function is employed to develop sufficient stability conditions. If the conditions are satisfied, we construct a switching law that stabilises the system. The application of the conditions is illustrated in several examples.