Property and evolution of the running-in attractor in an actual dynamic system

In this paper, the issue of adaptive neural tracking control for uncertain switched multi-input multi-output (MIMO) nonstrict-feedback nonlinear systems with average dwell time is studied. The system under consideration includes unknown dead-zone inputs and output constraints. The uncertain nonlinear functions are identified via neural networks. Also, neural networks-based switched observer is constructed to approximate all unmeasurable states. By means of the information for dead-zone slopes and barrier Lyapunov function (BLF), the problems of dead-zone inputs and output constraints are tackled. Furthermore, dynamic surface control (DSC) scheme is employed to ensure that the computation burden is greatly reduced. Then, an observer-based adaptive neural control strategy is developed on the basis of backstepping technique and multiple Lyapunov functions approach. Under the designed controller, all the signals existing in switched closed-loop system are bounded, and system outputs can track the target trajectories within small bounded errors. Finally, the feasibility of the presented control algorithm is proved via simulation results.

     

Event-triggered robust adaptive control for uncertain nonlinear systems preceded by actuator dead-zone

It is both theoretically and practically important to investigate the problem of event-triggered adaptive tracking control for a class of uncertain nonlinear systems subject to actuator dead-zone, which aims at reducing communication rate and compensating actuator nonlinearity simultaneously. In this paper, to handle such a problem, an event-trigger based adaptive compensation scheme is proposed for the system preceded by actuator dead-zone. The challenges of this work can be roughly classified into two categories: how to compensate the nonsmooth dead-zone nonlinearity and how to eliminate the quantization signal effects caused by event-triggered strategy. To resolve the first challenge, a new decomposition of dead-zone mathematical model is employed so that dead-zone nonlinearity can be successively compensated by using robust approach. In addition, an adaptive controller and its triggering event are co-designed based on the relative threshold strategy, such that an asymptotic tracking performance can be ensured. The proposed scheme is proved to guarantee the globally bounded of all closed-loop signals and the asymptotic convergence performance of tracking error toward zero. The simulation results illustrate the effectiveness of our proposed control scheme.     

Sliding mode control with adaptive fuzzy dead-zone compensation for uncertain chaotic systems

The dead-zone nonlinearity is frequently encountered in many industrial automation equipments and its presence can severely compromise control system performance. In this work, an adaptive variable structure controller is proposed to deal with a class of uncertain nonlinear systems subject to an unknown dead-zone input. The adopted approach is primarily based on the sliding mode control methodology but enhanced by an adaptive fuzzy algorithm to compensate the dead-zone. Using Lyapunov stability theory and Barbalat??s lemma, the convergence properties of the closed-loop system are analytically proven. In order to illustrate the controller design methodology, an application of the proposed scheme to a chaotic pendulum is introduced. A comparison between the stabilization of general orbits and unstable periodic orbits embedded in chaotic attractor is carried out showing that the chaos control can confer flexibility to the system by changing the response with low power consumption.     

Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation

This paper considers the problems of finite-time prescribed performance tracking control for a class of strict-feedback nonlinear systems with input dead-zone and saturation simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems and the unmeasurable states are estimated by designing a fuzzy state observer. In addition, a non-affine smooth function is used to approximate the non-smooth input dead-zone and saturated nonlinearity, and it is varied to the affine form via the mean value theorem. An adaptive fuzzy output feedback controller is developed by backstepping control method and Nussbaum gain method. It guarantees that the tracking error falls within a pre-set boundary at finite time and all the signals of the closed-loop system are bounded. The simulation results illustrate the feasibility of the design scheme.

     

Directly adaptive fuzzy control of discrete-time chaotic systems by least squares algorithm with dead-zone

A new design scheme of directly adaptive fuzzy control for a class of discrete-time chaotic systems is proposed in this paper. The T-S fuzzy model is employed to represent the discrete-time chaotic systems. Then a fuzzy controller is designed and the unknown coefficients of the controller are identified by least squares algorithm with dead-zone. By Lyapunov method, all the signals involved in the closed-loop systems are shown to be bounded and the error between the system output and the reference output is proved to converge to a small neighborhood of zero. Simulation results demonstrate the effectiveness of the theoretical results.     

Adaptive Neural Network Control for a DC Motor System with Dead-Zone

In this paper, an adaptive control strategy for tracking of a direct-current (DC) motor system with a dead-zone is developed. The main contribution of the developed scheme is that we successfully integrate an asymmetric barrier Lyapunov function approach to relax the requirements on the initial conditions. The unknown functions in the DC system are approximated by using the radial basis function neural networks (RBFNN). It is shown that the DC motor can follow a selected trajectory and all the signals are guaranteed to be bounded. Simulation results are provided to confirm the effectiveness of the proposed control.     

存在关节死区的空间机器人无扰快速终端滑模控制

针对机械臂一般操作过程中运动学的非完整特性进行运动规划时没有考虑机械臂与待抓取目标之间的关系与关节的实际特性, 研究了存在关节死区的漂浮基平面三连杆空间机械臂拦截目标前最后阶段的载体无扰动空间规划与控制. 首先根据拉格朗日第二类方程, 建立存在关节死区的载体位姿均不受控的漂浮基平面三连杆空间机械臂的动力学模型, 推导出三连杆空间机械臂反作用零空间的数学模型, 并对反作用零空间进行向量范数约束算法研究; 进而提出了一种具有抗干扰性与高收敛性的非奇异快速终端滑模控制算法实现系统的姿态无扰控制, 该方法采用变系数双幂次趋近率与非奇异快速终端滑模面相结合的方式, 提高系统状态收敛速度与抗干扰性. 为了消除机械臂关节存在的死区特性, 设计了自适应死区补偿器, 通过自适应控制来逼近死区特性的上界, 以消除关节死区对系统带来的影响, 确保跟踪控制的有效执行. 最后基于Lyapunov函数法证明了系统的稳定性, 并通过系统数值仿真结果验证了存在死区情况下机械臂的各关节角跟踪上无反应空间下的期望轨迹的同时载体的姿态处于稳定状态, 验证了所提方法的有效性.      

Adaptive fuzzy backstepping output feedback control of nonlinear uncertain time-delay systems based on high-gain filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO uncertain nonlinear strict-feedback systems. The considered nonlinear systems contain unknown nonlinear functions, unknown time-varying delays and unmeasured states. The fuzzy logic systems are first used to approximate the unknown nonlinear functions, and then a high-gain filter is designed to estimate the unmeasured states. Combining the backstepping recursive design technique and adaptive fuzzy control design, an adaptive fuzzy output feedback backstepping control method is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and both the observer error and tracking error converge to a small neighborhood of the origin. Two key advantages of our scheme are that (i) the high-gain filter is designed to estimate unmeasured states of time-delay nonlinear system, and (ii) the virtual control gains are functions. A simulation is included to illustrate the effectiveness of the proposed approach.     

Fuzzy adaptive high-gain-based observer backstepping control for SISO nonlinear systems with dynamical uncertainties

In this paper, a fuzzy adaptive output feedback control approach is developed for a class of SISO strict-feedback nonlinear systems with unmeasured states, unmodeled dynamics, and dynamical disturbances. In the backstepping recursive design, fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy adaptive high-gain observer is designed to estimate the unmeasured states; a dynamic signal is incorporated into the control scheme to dominate the dynamic uncertainties. Using the states estimates and combining the backstepping design technique, a fuzzy adaptive output feedback control is constructed recursively. It is proved that the proposed fuzzy adaptive output feedback control scheme can guarantee the all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SUUB), and the observer and tracking error converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated via an example.     

存在关节力矩输出死区及外部干扰的漂浮基空间机械臂积分滑模神经网络自适应控制

探讨了载体位置和姿态都不受控时,漂浮基空间机械臂在带有关节力矩输出死区及外部干扰情况下轨迹跟踪的控制算法设计问题。死区与外部干扰影响系统的跟踪精度与稳定性。为此引入积分型切换函数,减少外部干扰引起的稳态误差,并利用径向基函数神经网络逼近动力学方程的未知部分,设计了一种积分滑模神经网络控制方案。控制算法的优点是,在死区斜率与边界参数不确定及最优逼近误差上确界未知的条件下,可以利用最优逼近误差、死区及干扰的补偿项来消除影响。李亚普诺夫稳定性分析证明了闭环系统的稳定性,且轨迹跟踪误差将收敛到0的某个小邻域内。仿真算例证实了该控制算法的有效性,实现了空间机械臂的轨迹跟踪控制。     

Adaptive dynamic surface neural network control for nonstrict-feedback uncertain nonlinear systems with constraints

This paper presents an adaptive dynamic surface neural network control for a class of nonstrict-feedback uncertain nonlinear systems subjected to input saturation, dead zone and output constraint. The problem of input saturation is solved by designing an anti-windup compensator, and the issue of output constraint is addressed by introducing tan-type Barrier Lyapunov function. Furthermore, based on adaptive backstepping technique, a series of novel stabilizing functions are derived. First-order sliding mode differentiator is introduced into backstepping design to obtain the first-order derivative of virtual control. The real control input is obtained using dead-zone inverse method. It is proved that the proposed control scheme can achieve finite time convergence of the output tracking error into a small neighbor of the origin and guarantee all the closed-loop signals are bounded. Simulation results demonstrate the effectiveness of the proposed control scheme.     

Prescribed performance adaptive fuzzy output-feedback control of uncertain nonlinear systems with unmodeled dynamics

In this paper, an adaptive fuzzy output-feedback control approach is proposed for a class of uncertain nonlinear systems with unknown nonlinear functions, unmodeled dynamics, and 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. To solve the problem of unmodeled dynamics, the dynamical signal combined with changing supply function is incorporated into the backstepping recursive design technique. Under the framework of the backstepping control design technique and incorporated by the predefined performance technique, a new robust adaptive fuzzy output feedback control scheme is constructed. It is shown that all the signals of the resulting closed-loop system are bounded, and the system output remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example and comparison with the previous control methods are provided to show the effectiveness of the proposed control approach.     

Observer-based adaptive fuzzy backstepping control of MIMO stochastic nonlinear strict-feedback systems

In this paper, an adaptive fuzzy output feedback control approach is proposed for a class of multiinput and multioutput (MIMO) uncertain stochastic nonlinear strict-feedback 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. Utilizing the designed the fuzzy state observer and by combining the adaptive backstepping control design, an adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded (SUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. A simulation example is provided to show the effectiveness of the proposed approach.     

Decentralized adaptive neural network control for mechanical systems with dead-zone input

We propose a decentralized adaptive robust controller for trajectory tracking of mechanical systems with dead-zone input in this paper. The considered mechanical systems are with high-order interconnections and unknown non-symmetric nonlinear input. In each local controller, the neural network control is introduced to estimate the uncertainties and disturbances, meanwhile the siding mode control and adaptive technical are designed to compensate for the approximation errors. A nonlinear function is chosen to deal with the interconnections. Following, the stability and robustness are verified by using Lyapunov stability theorem. Finally, simulations are provided to support the theoretical results     

Adaptive terminal sliding mode control for anti-synchronization of uncertain chaotic systems

This paper presents an adaptive terminal sliding mode control method for anti-synchronization of uncertain chaotic systems. By fusion of the terminal sliding mode control and the adaptive control techniques, a robust controller is designed so that the states tracking error can reach the terminal sliding mode surface and converge to zero in a finite time. Finally, some simulation results are included to demonstrate the effectiveness and the feasibility of the proposed anti-synchronization scheme.     

Adaptive fuzzy output-feedback control of uncertain SISO nonlinear systems

The output-feedback control problem of a class of uncertain SISO nonlinear systems is investigated based on an indirect adaptive fuzzy approach. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. Compared with the existing results in the observer design, the main advantages of the proposed adaptive fuzzy output-feedback control approach are as follows: (1) It does not require to assume that the sign of the control gain coefficient is known and Nussbaum-gain technique is utilized to control the nonlinear systems with both the unknown control direction and the unmeasured states; (2) The observer in this paper is designed for the states rather than the tracking errors, then it is convenient to compute; (3) The controller singularity problem is perfectly avoided. The stability of the closed-loop system is analyzed by using Lyapunov method. A simulation example is given to verify the feasibility of the proposed approach.     

Decentralized sliding mode quantized feedback control for a class of uncertain large-scale systems with dead-zone input

This paper is concerned with the robust quantized feedback stabilization problem for a class of uncertain nonlinear large-scale systems with dead-zone nonlinearity in actuator devices. It is assumed that state signals of each subsystem are quantized and the quantized state signals are transmitted over a digital channel to the controller side. Combined with a proposed discrete on-line adjustment policy of quantization parameters, a decentralized sliding mode quantized feedback control scheme is developed to tackle parameter uncertainties and dead-zone input nonlinearity simultaneously, and ensure that the system trajectory of each subsystem converges to the corresponding desired sliding manifold. Finally, an example is given to verify the validity of the theoretical result.     

Adaptive fuzzy backstepping output feedback control for a class of MIMO time-delay nonlinear systems based on high-gain observer

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of multiinput and multioutput (MIMO) nonlinear systems with time delays and immeasurable states. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and an adaptive fuzzy high-gain observer is developed to estimate the unmeasured states. Using the designed high-gain observer, and combining the fuzzy adaptive control theory with the backstepping approach, an adaptive fuzzy output feedback control is constructed recursively. It is proved that all the signals of the closed-loop adaptive control system are semiglobally uniformly ultimately bounded (SUUB) and the tracking error converges to a small neighborhood of the origin.     

Fuzzy adaptive dynamic surface control for a single-link flexible-joint robot

In this paper, a fuzzy adaptive controller is proposed for a single-link flexible-joint robot. Fuzzy logic systems are used to approximate unknown nonlinearities, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping design with dynamic surface control (DSC) technique, a fuzzy adaptive output-feedback backstepping control approach is developed. It is proved that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and both the observer and tracking errors converge to a small neighborhood of the origin by appropriate choosing the design parameters. The simulation results are provided to demonstrate the effectiveness of the proposed controller. Two key advantages of our scheme are that (i)?the proposed control method does not require that the link velocity and actuator velocity of single-link flexible-joint robot be measured directly, and (ii)?the problem of ??explosion of complexity?? is avoided.