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 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.     

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.     

Optimal and reinforced robustness designs of fuzzy variable structure tracking control for a piezoelectric actuator system

In this paper, a piezoelectric actuator (PEA) system is approximated by N subsystems, which are described by pulse transfer functions. The approximation error between the PEA system and the fuzzy linear pulse transfer function system is represented by additive nonlinear time-varying uncertainties in every subsystem. First, a dead-beat to the switching surface for every ideal subsystem is designed. It is called the "variable structure tracking control". The output disturbance of the ith subsystem is caused by the approximation error of fuzzy-model and the interaction dynamics resulting from other subsystems. In general, it is not small. Then, the H/sup /spl infin//-norm of the sensitivity function between the switching surface and the output disturbance is minimized. It is the "optimal robustness". Although the effect of the output disturbance is attenuated, a better performance can be reinforced by a switching control which is based on the Lyapunov redesign. This is the final step for the robustness design of control, which is "reinforced robustness". The stability of the overall system is verified by Lyapunov stability theory. Experimental work of a PEA system was carried out to confirm the validity 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     

一类脉冲切换系统的有限时间稳定性

针对一类具有脉冲现象的非线性切换系统,提出了一种基于有限时间稳定lyapunov函数技术和多Lyapunov函数技术相结合的有限时间稳定性分析方法。该方法首先将非线性系统的有限时间稳定性的概念推广到所考虑的脉冲切换系统。然后,利用有限时间Lyapunov函数技术,确保各个子系统达到有限时间稳定。进一步,给出一个有限时间稳定的非线性比较系统。通过多Lyapunov函数技术,保证原系统的Lyapunov函数值不超过比较系统的状态值,由此得到原脉冲非线性切换系统有限时间稳定的充分条件。最后,一个数值例子说明文中方法的有效性。本文所得的研究结果能应用于生产线控制,交通管理,网络控制等实际系统。     

不确定非线性切换系统的鲁棒H∞控制

讨论了一类不确定非线性切换系统的鲁棒H∞控制问题．首先,基于多Lyapunov函数方法,设计状态反馈控制器以及切换律,使得对于所有允许的不确定性．相应的闭环系统渐近稳定又具有指定的L2-增益．该问题可解的充分条件以一组含有纯量函数的偏微分不等式形式给出,此偏微分不等式较一般Hamilton-Jacobi不等式更具可解性．所提出的方法不要求任何一个子系统渐近稳定．接着作为应用,借助混杂状态反馈策略讨论了非切换不确定非线性系统的鲁棒H∞控制问题．最后通过一个简单例子说明了控制设计方法的可行性．     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.     

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.     

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.     

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.     

A multitask sliding mode control for mismatched uncertain large-scale systems

A new sliding mode control (SMC) approach, output variables only, single phase only and chattering phenomenon free, is presented for a class of mismatched uncertain large-scale systems. For a new multitask SMC, it is not required that the system states are available. Moreover, the sliding function in this study just depends on output variables. Using an exponential type sliding surface, the system states are always in the sliding mode at the beginning time t = 0. Using a newly appropriate linear matrix inequality stability conditions by the Lyapunov method are derived such that each subsystem in the new sliding mode is completely invariant to matched uncertainties. As a result, robustness of the mismatched uncertain large-scale systems can be assured throughout an entire response of the system starting from the initial time t = 0. In every subsystem, a scheme of decentralised control using only output states is proposed. In addition, a continuous controller is finally designed for chattering removal. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.     

Design of stabilizing switching control laws for discrete- and continuous-time linear systems using piecewise-linear Lyapunov functions

In this paper, the stability of switched linear systems is investigated using piecewise linear Lyapunov functions. In particular, we identify classes of switching sequences that result in stable trajectories. Given a switched linear system, we present a systematic methodology for computing switching laws that guarantee stability based on the matrices of the system. In the proposed approach, we assume that each individual subsystem is stable and admits a piecewise linear Lyapunov function. Based on these Lyapunov functions, we compose 'global' Lyapunov functions that guarantee stability of the switched linear system. A large class of stabilizing switching sequences for switched linear systems is characterized by computing conic partitions of the state space. The approach is applied to both discrete-time and continuous-time switched linear systems.     

Robust adaptive tracking control for a class of switched time-delay systems with application of vehicle roll dynamic control

The problems of stability and robust tracking control for a class of switched nonlinear systems with uncertain input and state delays are investigated in this study. In the presence of unknown functions and external disturbances, an adaptive fuzzy technique based on nonlinear disturbance observer is used to counteract the effects of external disturbances and approximate unknown functions. For this purpose, it is first assumed that a common Lyapunov function exists for the switched system, and then a new common Lyapunov–Krasovskii functional is built using the terms of the hypothetical common Lyapunov function. By employing this new function, the delay-dependent input-to-state stability (ISS) under an arbitrary switching signal is provided. The robust tracking control problem for this system is investigated next. Finally, to assure ISS and robust tracking performance, an adaptive control law is developed that ensures conditions of the aforementioned hypothetical common Lyapunov function. In addition, to demonstrate the efficiency of the proposed strategy, the aforesaid method is applied to a vehicle roll dynamic as well as a mass-spring system.     

基于干扰观测器的解耦快速终端滑模控制

针对一类欠驱动系统跟踪控制问题,提出了一种基于非线性干扰观测器的全局解耦快速终端滑模控制(NDODGFTSMC)策略。将欠驱动系统分解成两个子系统分别设计全局快速终端滑模面,利用其中一个子系统滑模面的符号函数来构造中间变量,并将该变量引入到另一个子系统的滑模面中,构造出整个系统的滑模面,采用等效控制法和模糊双幂次趋近律求解系统的控制律。同时为了消除系统扰动对控制效果的影响,设计了一种双曲正切非线性干扰观测器对系统干扰进行估计并补偿给控制器。利用Lyapunov稳定原理证明了系统滑模面的渐近稳定性。将该方法应用于小车倒立摆系统的控制中,仿真结果验证了其有效性及优越性。     

基于模型依赖驻留时间的异步切换控制

研究在模型依赖平均驻留时间切换策略下切换线性系统的异步切换控制问题,同时考虑模型依赖的控制器滞后时间的约束问题.在实际情况下,信号传输和系统检测等原因会导致控制器的切换滞后于子系统.基于这类情况,首先将子系统运行的区间划分为子系统与控制器相匹配的区间和非匹配的区间,根据模型依赖的驻留时间策略设计出各子系统的控制器;然后,结合模型依赖的控制器滞后时间、系统参数和Lyapunov稳定条件推导出合适的驻留时间设计参数,且使得异步切换系统全局一致指数稳定;最后通过数值仿真验证了所提出方法的有效性.     

Construction of Lyapunov–Krasovskii functionals for switched nonlinear systems with input delay

This paper studies the stability issue for switched nonlinear systems with input delay and disturbance. It is assumed that for the nominal system an exponential stabilizing controller is predesigned such that the switched system is stable under a certain switching signal, and a piecewise Lyapunov function for the corresponding closed-loop system is known. However, in the presence of input delay and disturbance, the system may be unstable under the same switching signal. For this case, a new Lyapunov–Krasovskii functional is firstly constructed based on the known Lyapunov function. Then, by employing this new functional, a new switching signal satisfying the new average dwell time conditions is constructed to guarantee the input-to-state stability of the system under a certain delay bound. The bound on the average dwell time is closely related to the bound on the input delay. Finally, numerical examples are given to illustrate the effectiveness of the proposed theory.     

Sliding mode control for uncertain switched systems subject to actuator nonlinearity

This paper considers the problem of sliding mode control for a class of uncertain switched systems subject to sector nonlinearities and dead-zone. In the control systems, each subsystem is not required to share the same input channel, which is usually assumed in the previous works. By employing a weighted sum of the input matrices, a common sliding surface is designed and the corresponding sliding mode dynamics is obtained. A switching signal based on the average dwell time strategy is further proposed to ensure the exponential stability of the sliding mode dynamics. Moreover, it is shown that the reachability of the specified sliding surface can be ensured despite the presence of actuator nonlinearity, parameter uncertainties and external disturbances. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.     

Hybrid control of synchronization of fractional order nonlinear systems

Under the existence of model uncertainties and external disturbance, finite‐time projective synchronization between two identical complex and two identical real fractional‐order (FO) chaotic systems are achieved by employing FO sliding mode control approach. In this paper, to ensure the occurrence of synchronization and asymptotic stability of the proposed methods, a sliding surface is designed and the Lyapunov direct method is used. By using integer and FO derivatives of a Lyapunov function, three different FO real and complex control laws are derived. A hybrid controller based on a switching law is designed. Its behavior is more efficient that if the individual controllers were designed based on the minimization of an appropriate cost function. Numerical simulations are implemented for verifying the effectiveness of the methods.