时变不确定非线性系统自适应滑模跟踪控制

针对一般的具有时变且界未知的非线性不确定性的单输入多输出非线性系统,提出一种自适应滑模跟踪控制器的框架.在该框架内,系统的时变且界未知的非线性不确定性可以通过函数逼近技术(FAT)表示成为一组正交基函数序列的组合,并通过滑模控制技术和直接Lyapunov方法获得基函数系数的更新律以及对不确定性逼近误差的在线自适应补偿,从而得到自适应的滑模控制律.所提出的基于函数逼近技术的自适应滑模跟踪控制策略在直流电机跟踪控制系统实验装置上进行了实际控制实验,并进行了性能的对比与分析.     

时变不确定非线性系统自适应滑模跟踪控制

针对一般的具有时变且界未知的非线性不确定性的单输入多输出非线性系统．提出一种自适应滑模跟踪控制器的框架。在该框架内,系统的时变且界未知的非线性不确定性可以通过函数逼近技术（FAT）表示成为一组正交基函数序列的组合,并通过滑模控制技术和直接Lyapunov方法获得基函数系数的更新律以及对不确定性逼近误差的在线自适应补偿,从而得到自适应的滑模控制律。所提出的基于函数逼近技术的自适应滑模跟踪控制策略在直流电机跟踪控制系统实验装置上进行了实际控制实验,并进行了性能的对比与分析。     

SCARA机器人模糊自适应滑模控制

为了提高SCARA机器人的轨迹跟踪控制性能,提出了一种基于非奇异终端滑模面和改进的快速趋近律的滑模控制策略。设计了一种非奇异的快速终端滑模面,可在任意初始状态下收敛到平衡点;改进滑模控制的趋近律,在保证快速趋近的同时可有效抑制抖振,并采用双曲正切函数代替传统的符号函数,有效地消除了高频抖振。采用模糊控制调节趋近律参数,改善初始状态误差过大时引起的力矩冲击问题;基于SCARA机器人模型仿真实验表明,实验结果跟踪性能良好,输出力矩平滑。     

具有初始状态不确定性的非线性系统脉冲补偿迭代学习控制

针对于具有初始状态不确定性的非线性时不变系统,采用矩形脉冲信号补偿传统的比例微分型一阶和二阶迭代学习控制律.在Lebesgue-p范数度量跟踪误差意义下,利用卷积的推广的Young不等式分析学习控制律的跟踪性能.分析表明,在适当选取比例学习增益,微分学习增益和非线性状态函数的Lipschitz常数以保证收敛因子小于1的前提下,渐近跟踪误差是由初始状态不确定性引起的,而且可通过调节补偿因子予以消减.数值仿真验证了补偿策略的有效性和理论分析的正确性.     

一类不确定切换模糊时滞系统的保性能控制

针对一类存在时滞的不确定切换模糊系统,研究系统的保性能控制问题.利用平行分布补偿算法(PDC)给出保性能控制器的设计方法,利用单Lyapunov函数方法和多Lyapunov函数方法,给出不确定切换模糊时滞系统保性能控制器存在的充分条件和切换律设计.使得闭环系统对所有允许的不确定,在所设计的控制器和切换律下实现保性能控制.仿真结果表明方法的有效性.     

非线性系统的自适应神经网络轨迹跟踪控制

文章讨论了一类非线性系统稳定自适应跟踪控制问题。为使非线性闭环系统的稳定及跟踪误差的收敛，对系统方程进行恒等变换，用径向基函数（RBF）神经网络逼近系统方程中的未知函数。在反步控制中构建控制律和更新律，并引入动态面控制（DSC）技术避免对虚拟控制变量求导出现奇异。通过Lyapunov泛函分析，推导出非线性系统镇定条件及所有闭环信号是半全局一致最终有界。最后由两个例子实现参考轨迹的有限时间跟踪，跟踪误差都能收敛到0的小邻域，验证了所提方案的有效性和鲁棒性。     

航天器位姿运动一体化直接自适应容错控制研究

针对航天器近距离操作过程中追踪航天器位姿控制系统执行器故障问题,提出了一种直接自适应容错控制方法,保证了追踪航天器在发生执行器故障下的自身稳定性和对目标航天器位姿状态的渐近跟踪性能.基于对偶四元数的航天器位姿一体化控制系统模型,首先,假设故障已知,设计标称控制信号;然后,设计自适应更新律对标称控制信号中的未知参数进行估计,构成自适应控制信号;最后,利用多Lyapunov函数对多故障模式下的系统性能进行分析.仿真结果表明了所提方法的有效性.     

基于扰动补偿的多源受扰系统反步控制设计

针对一类多源受扰系统的跟踪控制问题, 提出基于降阶广义扩张状态观测器(ROGESO)的指令滤波反步控制设计方法. 首先, 将各通道中的总扰动分别作为扩展状态变量, 通过构造ROGESO对其进行同步实时估计. 在此基础上, 利用反步法递归设计虚拟控制律, 实现各级子系统的镇定, 并将各通道的扰动估计值反馈至对应子系统的虚拟控制律中进行反向补偿, 提高系统的扰动抑制性能, 保证系统输出对参考输入信号的高精度跟踪. 然后, 应用Lyapunov函数分析闭环系统的稳定性. 最后, 通过数值仿真验证所提方法的有效性.     

滑动及侧滑影响下的移动机器人轨迹跟踪控制

对受滑动及侧滑影响的移动机器人轨迹跟踪控制问题进行研究。在动力学部分,通过模糊系统逼近系统中的未知非线性,H_∞控制对滑动和侧滑干扰因素的补偿,利用Lyapunov函数推导出模糊参数的自适应律,设计出基于动力学的自适应模糊控制器。在运动学部分,设计逆运动学控制器,处理移动机器人实际位置与期望位置的误差,得到移动机器人运动的期望速度。将逆运动学控制器与自适应模糊控制器级联,并通过Lyapunov方法证明控制系统的稳定性。与自适应动力学控制器进行比较。仿真结果表明:在滑动及侧滑的影响下提出的策略具有较好的轨迹跟踪性能。     

一类混沌系统的自适应控制(英文)

本文借助于功能函数研究了一类混沌系统的跟踪控制问题.首先,通过坐标变换将Chua's混沌系统转换为一种严格反馈控制系统的通用形式.其次,结合自适应鲁棒控制技术和Backstepping方法设计了参数自适应控制律,对存在的不确定性和未知干扰的非线性系统实现了输出跟踪控制.基于Lyapunov稳定性理论对每一步的虚拟控制进行分步设计,得到的控制器不仅使系统输出跟踪给定的期望输出,而且使得系统对于所允许的不确定系统状态全局一致有界.最后,严格地理论证明表示了所设计方法的有效性。     

非线性扩展结构大系统自适应神经网络跟踪控制

针对一类非线性关联大系统在结构扩展时的跟踪控制问题, 提出一种采用自适应神经网络的控制方法. 该方法要求在不改变原结构系统控制律的前提下设计新加入子系统的控制律和自适应律, 使扩展后所有子系统都具有很好的跟踪性能. 这里主要利用神经网络的逼近功能以及Backstepping 技术来设计自适应律和控制律, 通过Lyapunov 理论证明在该控制器的作用下闭环系统的所有信号均是有界的, 并可使系统准确跟踪. 仿真结果验证了所提出方法的有效性.

     

Robust adaptive control for a class of uncertain non-affine nonlinear systems using affine-type neural networks

A robust adaptive control is proposed for a class of single-input single-output non-affine nonlinear systems. In order to approximate the unknown nonlinear function, a novel affine-type neural network is used, and then to compensate the approximation error and external disturbance a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proved that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given out based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method.     

基于滤波反演法的参数不确定自动引导车的运动控制

针对参数不确定的自动引导车的运动控制问题,应用Backstepping方法设计自适应控制器,并运用Lyapunov稳定性理论与Barbalat定理证明了系统的稳定性;同时利用进化规划算法优化控制器参数,通过跟踪微分器对输入信号与虚拟控制信号进行滤波处理并提取微分信号,避免了对虚拟控制信号的解析求导,简化了控制器的设计过程。与传统PID控制的对比仿真结果表明,所提出的自适应控制策略能较好地补偿系统参数摄动的影响,提高了自动引导车的轨迹跟踪性能和鲁棒性。     

基于自适应RBF 网络补偿的智能车辆循迹控制

针对智能车辆这一复杂非线性时变系统的循迹控制问题,提出一种基于Lyapunov函数方法的RBF神经网络自适应补偿控制策略.首先建立了车辆循迹控制的动力学名义模型;然后利用RBF神经网络对车辆循迹控制名义模型的不精确部分进行自适应补偿;最后应用Lyapunov稳定性理论推导出RBF网络权值的训练规则并证明了控制系统的稳定性.仿真结果表明,该方法提高了循迹控制的精度,具有较高的可行性和实用性.     

Robust adaptive path-following control of underactuated marine vessel with off-track error constraint

In this paper, a new robust adaptive controller is investigated to force an underactuated surface marine vessel to follow a predefined parameterised path at a desired speed, despite actuator saturation and the presence of model uncertainties as well as environmental disturbances induced by waves, wind and sea-currents. To ensure robustness of the path-following controller, time-varying constraint on the off-track error (i.e. the maximal distance from the ship to the reference path) is considered. To address the off-track error constraint the tan-barrier Lyapunov function is incorporated with the control scheme, where the idea of auxiliary design system introduced in Chen, Sam, and Ren (2011) is adopted and its states are used in combination with backstepping and Lyapunov synthesis to adaptive tracking control design with guaranteed stability. Furthermore, the command filters are adopted to implement physical constraints on the virtual control laws so that analytic differentiation of the virtual control laws is avoided. We show that the proposed robust adaptive control law is able to guarantee semi-global uniform ultimate bounded stability of the closed-loop system. Numerical simulations and experimental results are carried out to demonstrate the effectiveness of the proposed algorithm.     

Tracking Control of Join-Free Timed Continuous Petri Net Systems under Infinite Servers Semantics

A new low-and-high gain algorithm is presented for tracking control of a subclass of timed continuous Petri Net (contPN) systems working under infinite servers semantics. The inherent properties of timed contPN determine that the control signals must be non-negative and upper bounded by functions of system states. In the proposed control approach, LQ theory is first used to design a low-gain controller such that the control signals satisfy the input constraints. Based on the low-gain controller, a high-gain term is further added to fully employ available control energy, and control performance can be improved consequently. In order to guarantee global tracking convergence and smoothness on the tracking target, a mixed trajectory (state step and ramp) is used instead of a pure step reference signal. The new tracking target is designed to ensure the existence of the low-gain controller and possible fast system response concurrently. Rigorous proof based on Lyapunov function is provided to guarantee that for a conservative and strongly connected Join-Free (JF) timed contPN system, the proposed algorithm can ensure the global asymptotical convergence of both system states and control signals.

带执行器饱和的N 连杆机械臂输出反馈动态面控制

针对带执行器饱和的多关节刚性机械臂系统,提出一种基于RBF神经网络补偿的输出反馈动态面控制.通过观测器实现角速度的观测,采用RBF网络实现执行器饱和的补偿;通过Lyapunov方法证明闭环系统的稳定性,实现高精度的角度和角速度跟踪.仿真结果表明,所提出的方法能够有效补偿系统存在的执行器饱和,显著减小跟踪误差,并且对于外界干扰具有一定的鲁棒性.     

An improved sum‐of‐squares based approach to fuzzy tracking control design of nonlinear systems

In this paper, using a more general Lyapunov function, less conservative sum‐of‐squares (SOS) stability conditions for polynomial‐fuzzy‐model‐based tracking control systems are derived. In tracking control problems the objective is to drive the system states of a nonlinear plant to follow the system states of a given reference model. A state feedback polynomial fuzzy controller is employed to achieve this goal. The tracking control design is formulated as an SOS optimization problem. Here, unlike previous SOS‐based tracking control approaches, a full‐state‐dependent Lyapunov matrix is used, which reduces the conservatism of the stability criteria. Furthermore, the SOS conditions are derived to guarantee the system stability subject to a given H_∞ performance. The proposed method is applied to the pitch‐axis autopilot design problem of a high‐agile tail‐controlled pursuit and another numerical example to demonstrate the effectiveness and benefits of the proposed method.     

From Trajectory Tracking Control to Leader–Follower Formation Control

Abstract

This work investigates the leader–follower formation control of multiple nonholonomic mobile robots. First, the formation control problem is converted into a trajectory tracking problem and a tracking controller based on the dynamic feedback linearization technique drives each follower robot toward its corresponding reference trajectory in order to achieve the formation. The desired orientation for each follower is selected such that the nonholonomic constraint of the robot is respected, and thus the tracking of the reference trajectory for each follower is feasible. An adaptive dynamic controller that considers the actuators dynamics in the design procedure is proposed. The dynamic model of the robots includes the actuators dynamics in order to obtain the velocities as control inputs instead of torques or voltages. Using Lyapunov control theory, the tracking errors are proven to be asymptotically stable and the formation is achieved despite the uncertainty of the dynamic model parameters. In order to assess the proposed control laws, a ROS-framework is developed to conduct real experiments using four ROS-enabled mobile robots TURTLEBOTs. Moreover, the leader fault problem, which is considered as the main drawback of the leader–follower approach, is solved under ROS. An experiment is conducted where in order to overcome this problem, the desired formation and the leader role are modified dynamically during the experiment.     

Entanglement classification via integer partitions

Quantum state engineering is a central task in Lyapunov-based quantum control. Given different initial states, better performance may be achieved if the control parameters, such as the Lyapunov function, are individually optimized for each initial state, however, at the expense of computing resources. To tackle this issue, we propose an initial-state-adaptive Lyapunov control strategy with machine learning. Specifically, artificial neural networks are used to learn the relationship between the optimal control parameters and initial states through supervised learning with samples. Two designs are presented where the feedforward neural network and the general regression neural network are used to select control schemes and design Lyapunov functions, respectively. We demonstrate the performance of the designs with a three-level quantum system for an eigenstate control problem. Since the sample generation and the training of neural networks are carried out in advance, the initial-state-adaptive Lyapunov control can be implemented for new initial states without much increase of computational resources.