一类非线性系统的全局渐近稳定和有限时间镇定

针对一类全矩阵形式的非线性系统, 研究其全局稳定性及有限时间镇定问题. 首先, 全矩阵形式非线性系统被分成上三角形式和下三角形式非线性系统的加和, 并针对下三角形式非线性系统, 利用加幂积分方法, 自上而下地设计系统的全局稳定控制器; 其次, 在上面控制器作用下, 证明全矩阵形式系统在一个给定领域内是局部渐近稳定的; 最后, 运用自下而上的顺序, 一种嵌套饱和方法被用到上述控制器中, 通过调节饱和度, 使得闭环系统全局渐近稳定. 此外, 在适当的条件下, 可以得到全矩阵形式非线性系统的全局有限时间稳定性.     

基于输出反馈和滑模控制的一类二阶非线性系统 有限时间镇定方法

本文研究了一类具有不确定非线性动力学和未知外部扰动的二阶非线性系统的全局有限时间输出镇定问 题. 首先, 提出了一种全局状态反馈有限时间控制器, 实现了二阶非线性系统的有限时间镇定. 为了解决只有系统输 出可用这种更有挑战性的情况, 采用了一种新颖的设计思想, 即非分离原理. 构造了一个有限时间收敛的状态观测 器来估计未知状态. 在此观测器的基础上, 提出了一种基于输出的有限时间复合控制器. 基于李雅普诺夫方法, 证明 了整个闭环系统的全局有限时间稳定性. 仿真结果表明了理论的有效性.     

输入饱和约束下多智能体的有限时间一致

为解决多智能体系统在有限时间跟踪控制过程中受输入饱和影响的问题, 本文研究了输入饱和约束下的 二阶线性多智能体系统的有限时间一致和跟踪控制. 首先在无向通信拓扑下, 利用齐次函数, 设计了基于单饱和函 数的有限时间一致和跟踪控制器. 然后, 应用李雅普诺夫稳定性理论和代数图论等方法证明了控制算法的稳定性. 最后, 给出了能够使多智能体系统实现有限时间一致和跟踪的充分条件. 仿真结果验证了当系统存在输入饱和约束 时, 控制器能使多智能体在有限时间内完成跟踪任务.     

多变量非线性动态系统的全局稳定化控制器

对可化为Bymes-Isidori正规型的多变量非线性系统,仅利用线性组成部分的状态设计了全局稳定化控制器。引入了有限时间滑动模态的概念,其优点是线性部分的状态在有限时间内趋近于零。当非线性系统是最小相位时,所设计的控制器保证了系统的全局稳定性。     

含模型不确定性的上三角非线性系统的全局镇定

本文针对一类具有模型不确定性的上三角非线性系统,利用嵌套饱和函数方法研究其全局镇定问题.首先,对系统中存在的未知幂指数、未知控制参数和不确定性非线性函数施加适当假设,并基于Lyapunov稳定性定理利用已知的参数设计局部镇定控制器.然后,将设计的控制器与饱和函数结合得到饱和控制器.通过适当选取饱和度,可以证明只要不确定参数在限定的范围内,该控制器都能够使得闭环系统全局渐近稳定.最后,选取不同的系统幂指数搭建数值仿真算例.在相同的控制器作用下,系统状态和控制轨迹渐近收敛至原点,从而验证了所提控制算法的有效性和鲁棒性.     

无领航者的多Euler-Lagrange系统有限时间一致性算法

本文针对无领航者的多Euler-Lagrange系统,设计了一种分布式有限时间一致性控制算法.该算法只利用相邻个体的位置信息和自身的速度信息作为输入,使得网络化Euler-Lagrange系统在有限时间内达到一致性.考虑到闭环Euler-Lagrange系统的非自主性,运用Matrosov定理、Lyapunov稳定性定理和有限时间稳定性定理等对所设计的控制器的稳定性进行了证明,并进行了数值仿真实验,验证了控制器的有效性.     

多自由度机械臂的饱和输出反馈有限时间同步位置控制EI北大核心CSCD

针对输入受限的多自由度机械臂高精度位置控制问题,本文充分考虑驱动器饱和非线性的影响,提出了多自由度机械臂输出反馈饱和有限时间比例–微分(PD)+同步位置控制策略,应用Lyapunov稳定性理论和几何齐次性技术证明了闭环系统的全局有限时间稳定性.非线性饱和函数的恰当引入,使得所提出的控制器具有清晰明确的上界,可以通过预先选择满足特定条件的控制器参数有效避免驱动器饱和问题;同步控制项的恰当引入,使得所提出的控制器兼顾了多自由度机械臂各轴间的同步协调性,从而获得更快的收敛速度和更好的系统整体性能,满足工程实际对机械臂的高精度要求.本文的数值仿真结果验证了所提出的控制方法的有效性和可行性.     

输入饱和下非线性系统的事件触发控制器设计

本文研究了具有输入饱和的非线性系统事件触发控制策略设计问题.首先,针对输入饱和下非线性系统,建立混杂系统模型.其次,当非线性函数满足Lipschitz条件下,给出闭环混杂系统局部一致渐近稳定性的稳定判据,并设计了事件触发饱和控制器.然后,当非线性函数满足扇区条件时,给出闭环混杂系统框架下满足局部一致渐近稳定性的LMI条件,并设计了事件触发饱和控制器.进一步地,在事件触发饱和控制器作用下,分析了非线性系统的半全局鲁棒镇定性.最后,结合两个仿真实例说明了所提出事件触发控制策略的有效性.     

基于采样控制的一类本质非线性系统的全局镇定

针对一类含不确定参数的本质非线性系统,基于非光滑控制技术,提出了 一种基于采样控制的全局非光滑镇定方案. 首先,基于加幂积分技术和递归设计方法,提出了一类采样状态反馈控制器构造性设计方法.然后,通过合理地构造Lyapunvo泛函,严格地证明了存在一个最大采样周期 可以保证闭环系统的全局渐近稳定性. 由于控制器是离散形式的,所以在实际中易于用计算机来实现. 仿真结果验证了该方法的有效 性.     

输入饱和情况下农用拖拉机的直线导航控制

本文以农用拖拉机为研究对象, 提出了一种基于饱和方法的直线路径跟踪导航算法. 该算法可以为农用拖拉机导航中普遍存在的输入饱和控制问题提供一种有效的解决办法. 首先, 基于直线导航系统运动学模型, 将其线性化得到易于控制设计的线性系统模型. 其次, 设计非饱和控制器, 使得系统在该非饱和控制器作用下全局镇定. 最后, 结合饱和函数和非饱和控制器, 构造出饱和控制器, 并证明在该饱和控制器作用下系统全局渐近稳定. 该控制方案的优点在于: 控制器结构较为简单, 且饱和控制器中从外到内的饱和度并不需要按照递减顺序选取, 从而提高了闭环系统的收敛性能. 仿真结果验证了上述方法的有效性.     

Finite-time output feedback stabilisation for a class of feedforward nonlinear systems with input saturation

This paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.     

PID control for global finite-time regulation of robotic manipulators

This paper addresses the global finite-time regulation problem of robotic manipulators. A simple nonlinear proportional-integral-derivative (PID) control is proposed by adding a nonlinear proportional and derivative term to the commonly used PID controller. Lyapunov's stability theory and geometric homogeneity technique are employed to prove global finite-time stability. Advantages of the proposed control include the absence of modelling information in the control law formulation and the global finite-time stability featuring fast transient and high-precision positioning. Explicit conditions on the controller parameters to ensure global finite-time regulation stability are obtained. Simulations are presented to demonstrate the effectiveness and the improved performances of the proposed approach.     

Robust finite-time consensus tracking for second-order multi-agent systems with input saturation under general directed communication graphs

In this paper, we study the global finite-time consensus tracking problem for uncertain second-order multi-agent systems subject to input saturation. The communication graphs are allowed to be general directed graphs. Sliding-mode observer-based distributed controllers are proposed such that global finite-time consensus tracking is achieved with bounded control inputs. Only relative state or output measurements are used in the proposed controller which reduces the communication requirement on the agents. Simulation examples are given to illustrate the effectiveness of the proposed control strategies.     

Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems

This article considers the problem of global finite-time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field. To solve the problem, we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities. Then, using the homogeneous domination approach, we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite-time stable. Due to the use of a reduced-order observer, the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators.     

Global finite-time attitude regulation using bounded feedback for a rigid spacecraft

This paper investigates the problem of global attitude regulation control for a rigid spacecraft under input saturation. Based on the technique of finite-time control and the switching control method, a novel global bounded finite-time attitude regulation controller is proposed. Under the proposed controller, it is shown that the spacecraft attitude can reach the desired attitude in a finite time. In addition, the bound of a proposed attitude controller can be adjusted to any small level to accommodate the actuation bound in practical implementation.     

The finite-time almost disturbance decoupling for nonlinear systems

The finite-time almost disturbance decoupling problem is investigated for nonlinear systems in strict feedback form using backstepping. A recursive design algorithm is proposed to construct a continuous stabilising feedback controller so that the corresponding closed-loop system is finite-time stable when there is no external disturbances and the influence of the external disturbances on the output is attenuated to a given degree. This paper is the first to solve the finite-time almost disturbance decoupling problem. Two examples are given to show the feasibility of the proposed design method.     

输入饱和受限下的刚体飞行器姿态系统的有限时间镇定

研究存在输入饱和受限下的飞行器姿态控制问题, 提出一种有限时间姿态镇定方案. 针对基于修改的Rodriguez 参数模型的飞行器姿态控制系统, 基于齐次性理论和饱和控制器设计方法, 并充分利用系统的模型结构特征, 设计一类饱和的有限时间姿态控制器, 使得姿态可以在有限时间内被镇定到平衡点. 仿真结果验证了所设计姿态控制器的有效性.

     

Global finite-time stabilisation for a class of stochastic nonlinear systems by output feedback

In this paper, the problem of global finite-time stabilisation by output feedback is considered for a class of stochastic nonlinear systems. First, based on homogeneous systems theory and the adding a power integrator technique, a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system. Then, the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms; it is shown that the proposed output-feedback control law can guarantee that the closed-loop system is global finite-time stable in probability. Finally, simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme.