Distributed fuzzy adaptive event-triggered finite-time consensus tracking control for uncertain nonlinear multi-agent systems with asymmetric output constraint

This article investigates the consensus problem for uncertain nonlinear multi-agent systems (MASs) with asymmetric output constraint. Different from BLF-based constraint consensus tracking control, a novel approach based on nonlinear state-dependent function is proposed to solve the asymmetric output constraint, which need not convert output constraint into tracking error bound. First-order sliding mode differentiator is incorporated into each step of backstepping control design to reduce computation burden. Further, in combination of proposed event-triggered mechanism based on time-varying threshold, a distributed fuzzy adaptive event-triggered finite-time consensus method is developed. It can ensure that the consensus tracking error tends to a small neighbor in a finite time and the asymmetric output constraint of each subsystem is not violated. Two simulations are given to demonstrate the effectiveness of control method.     

Asymptotic tracking control for constrained nonstrict‐feedback MIMO nonlinear systems via parameter compensations

This paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme.     

Event-triggered adaptive tracking control for nonlinear systems with input saturation and unknown control directions

This article is concerned with event-triggered adaptive tracking control design of strict-feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event-triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed-loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy.     

一种基于T-S模糊模型的自适应预测函数控制

针对离散时间非线性系统,提出了一种基于T-S模糊模型的自适应预测函数控制算法。该算法利用加权递推最小二乘法在线辨识T-S模糊模型后件参数,以克服模型失配对系统性能的影响。根据辨识得到的模型参数直接递推计算模型的预测输出,而不需要求解Diophantine方程,进而直接递推求解预测控制律,而不需要求解矩阵逆。仿真结果表明,该算法具有良好的跟踪性能和较强的鲁棒性。     

Event-triggered fuzzy adaptive control of incommensurate fractional order nonlinear systems

This paper focuses on the event-triggered control of nonstrict-feedback incommensurate fractional order systems with external disturbances. To release more communication resources and reduce the triggered time instant, we adopt the relative-threshold-based event-triggered strategy and prove that the Zeno behavior does not exist. We utilize the fuzzy systems to approximate the nonlinear systems and design an adaptive update law to estimate the approximation errors and external disturbances. To conquer the dimension explosion phenomenon in the backstepping process, we design a fractional order filter and apply the dynamic surface control technique. The closed-loop system is semiglobally stable and the tracking error converges to a small neighborhood of equilibrium point under the proposed control approach. Finally, the validity of the developed controller is verified by the simulation examples.     

随机非线性系统基于事件触发机制的自适应神经网络控制

针对一类具有严格反馈结构且控制方向未知的随机非线性系统，提出了基于事件触发机制的自适应神经网络（Adaptive neural network，ANN）输出反馈控制方法.利用径向基神经网络逼近系统中未知的非线性函数.通过引入Nussbaum增益函数并设计滤波器，解决了系统控制方向未知的问题.通过设计具有相对阈值的事件触发机制，保证了闭环随机非线性系统的有界性.最后给出数值仿真例子验证所提控制方法的有效性.     

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.     

Adaptive fuzzy control with smooth inverse for nonlinear systems preceded by non-symmetric dead-zone

In this study, the adaptive output feedback control problem of a class of nonlinear systems preceded by non-symmetric dead-zone is considered. To cope with the possible control signal chattering phenomenon which is caused by non-smooth dead-zone inverse, a new smooth inverse is proposed for non-symmetric dead-zone compensation. For the systematic design procedure of the adaptive fuzzy control algorithm, we combine the backstepping technique and small-gain approach. The Takagi–Sugeno fuzzy logic systems are used to approximate unknown system nonlinearities. The closed-loop stability is studied by using small gain theorem and the closed-loop system is proved to be semi-globally uniformly ultimately bounded. Simulation results indicate that, compared to the algorithm with the non-smooth inverse, the proposed control strategy can achieve better tracking performance and the chattering phenomenon can be avoided effectively.     

具有未建模动态的互联大系统事件触发自适应模糊控制

针对一类具有未建模动态及执行器故障的非严格反馈非线性互联大系统, 提出一种基于事件触发机制的模糊分散自适应输出反馈控制算法. 首先, 通过设计模糊状态观测器估计系统中不可测的状态, 并引入李雅普诺夫函数约束未建模动态. 然后, 提出一种基于事件触发机制的自适应容错控制器补偿多个执行器故障产生的影响. 最后, 利用障碍李雅普诺夫函数实现对系统输出的约束, 并证明闭环系统中所有信号均是半全局一致最终有界的, 且设计的事件触发机制可以避免Zeno行为. 数值仿真结果验证所提出设计方案的可行性及有效性.     

含执行器故障的切换非线性系统的事件触发自适应模糊容错控制

本文研究在平均驻留时间约束下,一类含有执行器故障的切换非线性系统输出反馈自适应模糊事件触发容错控制问题.首先,建立了一个模态依赖的状态观测器估计不可测量状态.利用模糊逻辑系统来逼近未知项.其次,构建自适应模糊容错事件触发控制方案能够节省网络资源和数据传输.然后,通过构造多Lyapunov函数和平均驻留时间法,证明闭环系统所有状态半全局一致最终有界的同时排除了Zeno现象.最后,通过数值仿真验证该方法的有效性.     

含执行器故障的切换非线性系统的事件触发自适应模糊容错控制

本文研究在平均驻留时间约束下,一类含有执行器故障的切换非线性系统输出反馈自适应模糊事件触发容错控制问题.首先,建立了一个模态依赖的状态观测器估计不可测量状态.利用模糊逻辑系统来逼近未知项.其次,构建自适应模糊容错事件触发控制方案能够节省网络资源和数据传输.然后,通过构造多Lyapunov函数和平均驻留时间法,证明闭环系统所有状态半全局一致最终有界的同时排除了Zeno现象.最后,通过数值仿真验证该方法的有效性.     

切换非线性系统的输出反馈周期事件触发控制

本文针对一类在任意切换信号作用下的切换非线性系统, 研究了其输出反馈周期事件触发控制问题. 所考 虑的非线性系统采用非严格反馈形式且含有未知时变控制系数. 在本文中, 仅利用采样时刻的系统输出. 为了估计 系统的不可量测的状态, 基于采样的系统输出构造了降维状态观测器. 为了减少通信资源的利用, 提出了一种新的 输出反馈周期事件触发策略, 该策略包含仅利用事件触发时刻的信息构造的输出反馈事件触发控制器以及仅在采 样时刻间歇性监测的离散事件触发机制. 通过选取可容许的采样周期及合适的公共Lyapunov函数, 证明了闭环系统 在任意切换下全局渐近稳定. 最后, 通过将本文中所给出的控制方案应用到数值算例中验证了其有效性.     

Adaptive fuzzy decentralized control for interconnected MIMO nonlinear subsystems

This paper describes an adaptive fuzzy control strategy for decentralized control for a class of interconnected nonlinear systems with MIMO subsystems. An adaptive robust tracking control schemes based on fuzzy basis function approach is developed such that all the states and signals are bounded. In addition, each subsystem is able to adaptively compensate for disturbances and interconnections with unknown bounds. The resultant adaptive fuzzy decentralized control with multi-controller architecture guarantees stability and convergence of the output errors to zero asymptotically by local output-feedback. An extensive application example of a three-machine power system is discussed in detail to verify the effectiveness of the proposed algorithm.     

Indirect adaptive fuzzy and impulsive control of nonlinear systems

The problem of indirect adaptive fuzzy and impulsive control for a class of nonlinear systems is investigated. Based on the approximation capability of fuzzy systems, a novel adaptive fuzzy and impulsive control strategy with supervisory controller is developed. With the help of a supervisory controller, global stability of the resulting closed-loop system is established in the sense that all signals involved are uniformly bounded. Furthermore, the adaptive compensation term of the upper bound function of the sum of residual and approximation error is adopted to reduce the effects of modeling error. By the generalized Barbalat's lemma, the tracking error between the output of the system and the reference signal is proved to be convergent to zero asymptotically. Simulation results illustrate the effectiveness of the proposed approach.     

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.     

模糊自适应在机器人行走平衡控制中的应用

针对多变量、非线性的两轮机器人系统的行走平衡控制问题,提出一种基于Backstepping（反推）方法和PID的控制策略。该策略在Backstepping控制器中加入模糊自适应部分,利用模糊系统逼近Backstepping设计过程中的未知非线性函数,模糊系统中的参数基于自适应律调整,解决了Backstepping控制器中因含有未知参数难以实现的困难,避免了两轮机器人系统不满足严格三角结构的问题。针对两轮机器人的仿真实验结果表明：采用设计的控制策略,可以实现两轮机器人的行走平衡控制任务。     

Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties

In this paper, an adaptive fuzzy output feedback control approach based on backstepping design is proposed for a class of SISO strict feedback nonlinear systems with unmeasured states, nonlinear uncertainties, unmodeled dynamics, and dynamical disturbances. Fuzzy logic systems are employed to approximate the nonlinear uncertainties, and an adaptive fuzzy state observer is designed for the states estimation. By combining backstepping technique with the fuzzy adaptive control approach, a stable adaptive fuzzy...     

Adaptive fuzzy backstepping output feedback control for strict feedback nonlinear systems with unknown sign of high-frequency gain

In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of SISO nonlinear strict-feedback systems with unknown sign of high-frequency gain and the unmeasured states. The nonlinear systems addressed in this paper are assumed to possess the unmodeled dynamics, dynamical disturbances and unknown nonlinear functions, where the unknown nonlinear functions are not linearly parameterized, and no prior knowledge of their bounds is available. In the recursive designing, fuzzy logic systems are used to approximate the unknown nonlinear functions, K-filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unmodeled dynamics and the unknown sign of the high-frequency gain, respectively. Based on Lyapunov function method, a stable adaptive fuzzy output feedback control scheme is developed. It is mathematically proved that the proposed adaptive fuzzy control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded, the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples.     

Adaptive Fuzzy Backstepping Tracking Control for Flexible Robotic Manipulator

In this paper, an adaptive fuzzy state feedback control method is proposed for the single-link robotic manipulator system. The considered system contains unknown nonlinear function and actuator saturation. Fuzzy logic systems (FLSs) and a smooth function are used to approximate the unknown nonlinearities and the actuator saturation, respectively. By combining the command-filter technique with the backstepping design algorithm, a novel adaptive fuzzy tracking backstepping control method is developed. It is proved that the adaptive fuzzy control scheme can guarantee that all the variables in the closed-loop system are bounded, and the system output can track the given reference signal as close as possible. Simulation results are provided to illustrate the effectiveness of the proposed approach.      

Event-triggered-based integral reinforcement learning output feedback optimal control for partially unknown constrained-input nonlinear systems

In this paper, an adaptive output feedback event-triggered optimal control algorithm is proposed for partially unknown constrained-input continuous-time nonlinear systems. First, a neural network observer is constructed to estimate unmeasurable state. Next, an event-triggered condition is established, and only when the event-triggered condition is violated will the event be triggered and the state be sampled. Then, an event-triggered-based synchronous integral reinforcement learning (ET-SIRL) control algorithm with critic-actor neural networks (NNs) architecture is proposed to solve the event-triggered Hamilton–Jacobi–Bellman equation under the established event-triggered condition. The critic and actor NNs are used to approximate cost function and optimal event-triggered optimal control law, respectively. Meanwhile, the event-triggered-based closed-loop system state and all the neural network weight estimation errors are uniformly ultimately bounded proved by Lyapunov stability theory, and there is no Zeno behavior. Finally, two numerical examples are presented to show the effectiveness of the proposed ET-SIRL control algorithm.