带有不确定性参数的多变量非线性系统的半全局实用镇定

研究一类含有零动态和不确定性参数的多输入多输出非线性系统的镇定问题,通过构造一个组合Lyapunov函数,对非线性动态部分设计了一个控制器可半全局实用镇定整个闭环系统的平衡点.仿真实例说明了所采用方法的有效性.     

一类非线性系统输出反馈的半全局实用镇定

研究了一类含有未知参数的非线性系统的半全局实用镇定问题,通过系统线性部分和零动态部分的Lyapunov函数构造了整个系统的Lyapunov函数,据此设计了使系统半全局实用稳定的状态反馈和动态输出反馈,且证明了只要未知参数不改变系统的相对阶,那么控制器是鲁棒的.仿真实例说明了所提出方法的有效性.     

基于混合观测器的混合反馈控制

对于一类混合动态系统,研究基于混合观测器的混合反馈控制问题．通过系统线性部分和离散事件部分的Lyapunov函数构造了整个混合系统的Lyapunov函数．据此设计了使整个系统稳定的混合反馈控制且证明了闭环系统的稳定性．仿真实例说明该方法的有效性．     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

非线性增益递归滑模动态面自适应NN控制

针对一类严反馈非线性不确定系统的跟踪控制问题,提出一种非线性增益递归滑模动态面 (Dynamic surface control, DSC)自适应控制方法. 通过设计一个新的非线性增益函数,并构造递归滑模动态面的控制策略和新的Lyapunov函数,同时利用神经网络在线逼近系统不确定项, 该方法有效解决了具有输入饱和约束条件下系统控制精度与动态品质间的矛盾,增强了控制器对其自身参数摄动的非脆弱性. 理论证明了闭环系统所有状态是半全局一致最终有界的,且跟踪误差可收敛至任意小.     

随机时滞系统的神经网络输出反馈动态面控制

针对一类具有未知控制方向的随机时滞系统设计自适应神经输出反馈控制器.首先,利用状态观测器估计不可测量的系统状态;其次,选择合适的Lyapunov-Krasovskii函数消除未知延迟项对系统的影响,利用Nussbaum-type函数处理系统的未知控制方向问题,通过神经网络逼近未知的非线性函数,以及用动态表面控制(DSC)解决控制器设计中出现的复杂性问题;最后,通过Lyapunov稳定性理论,构造一个鲁棒自适应神经网络输出反馈控制器,可以保证闭环系统中所有信号在二阶或四阶矩意义下一致最终有界,跟踪误差能收敛到零值小的领域内.仿真实例验证了所提出方法的有效性.     

一类具有未建模动态的非线性系统模糊自适应鲁棒控制

针对一类单输入单输出未建模动态不确定非线性系统,提出一种模糊自适应backstepping控制方法.设计中利用模糊逻辑系统逼近系统的未知函数,应用非线性阻尼项抵消系统的非线性不确定项,通过引入一个动态信号克服未建模动态.该模糊自适应控制方法保证了整个闭环系统的有界性,输出信号可调节到零的小邻域内.仿真结果进一步验证了该方法的有效性.     

欠驱动两杆机器人的统一控制策略和全局稳定性分析

针对包括 Acrobot 和 Pendubot 在内的欠驱动两杆机器人, 提出了一种统一的运动控制策略. 欠驱动两杆机器人的整个运动空间分为两个区域: 摇起区和平衡区, 并对这两个区域分别设计控制律. 首先, 在摇起区, 应用一种基于弱控制 Lyapunov 函数 (Weak-control Lyapunov function, WCLF) 的控制方法, 来增加系统能量和控制驱动杆的姿势. 其次, 为了避免奇异值的出现, 选择弱控制 Lyapunov 函数中的一个参数为系统状态空间的非线性函数. 然后, 通过系统状态调节基于弱控制 Lyapunov 函数的控制律中的另一个设计参数, 来改进系统控制效果. 使用弱控制 Lyapunov 设计的摇起区控制律, 可基于最大不变集原理保证其稳定性; 而机器人离开摇起区后, 利用非光滑 Lyapunov 函数 (Non-smooth Lyapunov function, NSLF) 来保证其稳定. 最后, 结合 WCLF 和 NSLF 保证了控制系统的全局稳定.     

输入饱和的一类切换系统神经网络跟踪控制

针对单输入单输出系统研究一种在任意切换下的跟踪控制问题,系统包含未知扰动和输入饱和特性.首先,利用高斯误差函数描述一个连续可导的非对称饱和模型.其次,利用径向基神经网络（Radial basis function neural network,RBF NN）逼近未知的系统动态.最后,基于公共的Lyapunov函数构造状态反馈控制器.设计的控制器避免过多参数调节从而减轻计算负荷.结果展示本文给出的状态反馈控制器可以保证闭环系统的所有信号是半全局一致有界的,并且跟踪误差可收敛到零值小的领域内.最后的仿真结果进一步验证提出方法的有效性.     

单输入线性系统的改进型动态抗饱和设计

本文基于状态重置的改进型动态抗饱和补偿方案, 研究了具有单输入的线性饱和系统的抗饱和控制问题. 相比较于传统的动态抗饱和补偿方案, 当执行器不饱和时, 改进的动态抗饱和补偿方案把动态抗饱和补偿器的状态重置为零. 所以当执行器不饱和时, 改进的动态抗饱和补偿器将不会对控制器进行补偿. 进一步的, 提出了一个时间依赖的Lyapunov函数来分析闭环系统的稳定性, 并以LMIs的形式给出了闭环系统的控制综合条件. 最后, 通过压电纳米运动平台验证了所提出的改进型动态抗饱和补偿方案的有效性。     

一类非线性系统控制Lyapunov函数的构造

The construction of control Lyapunov functions for a class of nonlinear systems is considered. We develop a method by which a control Lyapunov function for the feedback linearizable part can be constructed systematically via Lyapunov equation. Moreover, by a control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics, a control Lyapunov function for the overall nonlinear system is established.     

具有扰动输入的不确定性非线性系统的输出调节极限性能

本文研究了一类具有扰动输入的不确定性非线性系统的输出调节问题, 给出了该类系统在最差的不确定性参数和扰动输入情况下系统输出调节的极限性能. 所讨论的非线性系统是可镇定非最小相位系统, 并且该系统的零动态由“鲁棒输入对状态稳定(robust input-to-state stable)部分”和“不稳定但可镇定部分”组成. 假设系统的不确定性参数和扰动输入分别以非线性函数和仿射形式同时出现在系统零动态的鲁棒输入对状态稳定部分和系统的可线性化部分, 而且其可线性化部分的不确定性具有下三角形结构形式. 该系统输出调节问题的性能以其输出信号能量作为度量. 对于上述非线性系统, 在最差的不确定性参数和扰动输入情况下, 输出调节问题的极限性能只取决于镇定其零动态“不稳定部分”所需的最小能量.     

H-infinity control for cascade minimum-phase switched nonlinear systems

1Introduction H_∞control theory has become a powerful tool to solverobust stabilization or disturbance attenuation problems.Many results about linear H∞control have appeared,andlinear H∞theory has been generalized to nonlinear systems[1~5].Two major approaches have been used to providesolutions to nonlinear H∞control problems.One is basedon the dissipativity theory and differential games theory[2,6].The other is based on the nonlinear versionofclassical bounded real lemma[3~5].Both of th…     

Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control

In this paper, we focus on the problem of adaptive stabilization for a class of uncertain switched nonlinear systems, whose non-switching part consists of feedback linearizable dynamics. The main result is that we propose adaptive controllers such that the considered switched systems with unknown parameters can be stabilized under arbitrary switching signals. First, we design the adaptive state feedback controller based on tuning the estimations of the bounds on switching parameters in the transformed system, instead of estimating the switching parameters directly. Next, by incorporating some augmented design parameters, the adaptive output feedback controller is designed. The proposed approach allows us to construct a common Lyapunov function and thus the closed-loop system can be stabilized without the restriction on dwell-time, which is needed in most of the existing results considering output feedback control. A numerical example and computer simulations are provided to validate the proposed controllers.     

H-infinity control for cascade minimum-phase switched nonlinear systems

This paper is concerned wi th the H-infinity control problem for a class of cascade switched nonlinear systems.Each switched syste m in this class is composed of a zero-input asymptotically stable nonlinear part,which is also a switched system,and a linearizable part which i s controllable.Conditions under which the H-infinity con trol problem is solvable under arbitrary switching l aw and under some designed switching law are der ived respectively.The nonlinear state feedback and s witching law are designed.We exploit the structural characteristics of the switched nonlinear systems t o construct common Lyapunov functions for arbitrary switching and to find a single Lyapunov function for designed switching law.The proposed methods do not rely on the solutions of Hamilton-Jacobi in equalities.     

STABILIZATION OF A CLASS OF NONLINEAR NON‐MINIMUM PHASE SYSTEMS

This paper tackles the problem of stabilization of a class of non‐minimum phase nonlinear systems which have zero dynamics with an eigenvalue zero of multiplicity 2. By adding some new terms, called cross terms, we are able to generalize the concept of the Lyapunov function with a homogeneous derivative along the trajectory, which was introduced in [4], to produce a suitable Lyapunov function. The Lyapunov function assures that the stability of an approximate system, which consists of some lower order terms of a nonlinear system with an eigenvalue zero of multiplicity 2, implies the stability of the whole system. Applying these to non‐minimum phase zero dynamics of nonlinear systems with such a center, a sufficient condition and a design method of state feedback control are obtained for stabilizing the systems.     

State feedback stabilization for high-order stochastic nonlinear systems with zero dynamics

In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.     

Asymptotic Stabilisation of Multiple Input Nonlinear Systems via Sliding Modes

A dynamic feedback controller design method is proposed for multiple input systems. The method uses a novel choice of sliding surface to effect asymptotic linearisation of nonlinear differential input output systems and a class of state space systems. The stability of the overall system, that is a canonical state space form with a dynamic feedback, is analysed with a generalised Lyapunov approach plus an asymptotic analysis in a neighbourhood of the origin. The nonlinear system does not have to be expressed in regular form as is the case in many other sliding mode control approaches. A type of zero dynamics, which are the dynamics of the control, are involved. The resulting dynamic feedback is shown to provide chatter free control if the system is minimum phase with respect to the zero dynamics. The theoretical results are applied to Gas Jet systems with two controls.     

Maximal feedback linearization and its internal dynamics with applications to mechanical systems on

For systems that are not feedback linearizable, a natural question is: how to find the largest feedback linearizable subsystem and, if the partial linearization is not unique, what are the control‐theoretic properties of various partial linearizations. In this paper, we will consider the problem of how to choose a partially linearizing output that renders the zero dynamics asymptotically stable and when such an output exists. We will state general results solving completely the problem for systems whose linearizability defect is one by identifying and describing two classes of systems. For the first class, all maximal partial linearizations lead to the same zero dynamics. For the second class, any asymptotic behavior of the zero dynamics can be achieved by a suitable choice of a partially linearizing output. In the second part, we apply our results to mechanical systems with two‐degrees‐of‐freedom and provide a detailed study of their partial linearizations. We illustrate the obtained results by examples of Acrobot (which belongs to the second class) and Pendubot (which belongs to the first class).