Global finite-time stabilization design for a class of high-order uncertain nonlinear systems

The problem of finite-time stabilization for uncertain nonlinear systems is investigated.It is proved that a class of high-order nonlinear systems in the lower-triangular form is globally stabilized via non-Lipschitz continuous state feedback.By using the finite-time Lyapunov stability theorem and the method of non-smooth feedback design,a recursive design procedure is provided,which guarantees the finite-time stability of the closed-loop system.The simulation results show the effectiveness of the theoretical results.

Feedback Systems on a Reflexive Banach Space—Linearization

The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see [1] [2] [3]. We then consider a linear FS , and prove that, if ; , with the respective solutions of FS’s [A,B] and corresponding to the given (u,v) in . There exists,, positive real constants such that, . These results are the subject of theorems 3.1, ... , 3.3. The proofs of these theorems are based on our lemmas 3.2, ... , 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator I+BA and . The results obtained and demonstrated along this document, present an extension in general Banach space of those in [4] on a Hilbert space H and those in [5] on a extended Hilbert space .

基于非线性反馈方法的连续时间稳定线性系统的混沌反控制

提出了连续时闻线性稳定系统跟踪任意混沌系统实现混沌化的一般方法,该控制器通过非线性反馈取得,其中的反馈增益矩阵的求取与所跟踪的混沌系统无关,只与原连续时间线性稳定系统的状态矩阵有关。通过跟踪Rossler混沌系统和Lorenz混沌系统说明了该方法的设计过程.仿真结果表明了该方法的有效性和快速性。

基于输出反馈的一类Holder连续非线性系统的全局实际镇定

借助非线性系统实际观测器的概念,对一类Holder连续非线性系统进行了输出反馈控制器设计.通过对系统状态作线性变换,得到输出反馈控制器,当输出反馈控制律作用于该系统时,闭环系统是全局实际稳定的.仿真算例说明了所得结论的可行性和有效性.

基于输出反馈的一类大型互联Holder非线性系统的全局实际镇定

本文研究基于输出反馈的一类大型互联Holder连续非线性系统的全局实际镇定问题.通过构造每个子系统的状态观测器,并对观测器的状态作线性变换,得到分散输出反馈控制器.当输出反馈控制律作用于该系统时,闭环系统是全局实际稳定的.

基于干扰观测器的弹药传输机械臂非线性连续时变反馈控制

针对弹药传输机械臂在工作过程中由于受到基础振动干扰和负载不确定性的影响,存在定位精度低、定位速度慢的问题,以结构和工作原理相同的实验用原理样机为对象,提出一种基于干扰观测器扰动补偿的非线性连续时变反馈控制方法。该方法在控制律形式上类似比例微分(PD)控制,但其中比例和微分系数取决于系统Lyapunov函数,是系统误差变量的可微函数。为消除基础振动干扰和负载不确定性带来的非线性影响,采用一种有限时间非线性干扰观测器设计补偿环节。实验结果表明,基于观测器的扰动补偿可以将机械臂的定位时间由2.18 s缩短到1.32 s,缩短了39.4%;在所有基础振动干扰和不同负载的实验工况下,新控制方法都可以快速、稳定、精确地完成控制目标,验证了算法的有效性。

非线性连续时间系统L_1控制的非线性反馈(英文)

用集值分析方法研究了仿射非线性连续时间系统具λ 指数收敛率和 ρ 性能的L1 控制问题。首先 ,引入连续时间系统的受控λ 收缩集概念 ,并建立了与其Euler逼近的离散系统的受控收缩集之间的关系。然后 ,结合此概念 ,得到了这个问题有静态连续非线性解的充分条件。这推广了在稳定性意义下文献中的结果。

一类连续非线性系统的有限时间镇定问题

讨论了一类连续非光滑非线性系统的全局有限时间状态反馈镇定问题。利用有限时间Lyapunov稳定定理和加幂积分器的方法证明了这类系统在连续的状态反馈控制下是全局有限时间状态反馈镇定的,并给出了状态反馈控制器的设计方法。

微生物连续发酵过程线性反馈最优控制

研究了一类微生物连续发酵生产1,3-丙二醇的线性反馈最优控制策略.将稀释速率D和注入的甘油浓度C_(s0)作为控制变量,建立线性反馈控制器使得1,3-丙二醇的产量最大化.首先通过非线性动力系统模型,将最优化问题描述出来并引入线性反馈策略,使用精确罚方法找到这个半无限优化问题的近似问题.进而基于梯度优化,使用一种标准的非线性优化方法给出了近似问题的解,从而得到原优化问题的最优解并求得反馈控制参数.由于线性反馈控制策略可以实现闭环控制,很好地保证了鲁棒性,取得了一定的成效.

非线性反馈控制优化的Lyapunov函数模型

针对标准Lyapunov函数在工业复杂系统预测控制的应用中还存在控制约束力较差等问题,本文提出了一种基于非线性反馈控制优化的Lyapunov函数模型。首先采用GB公式引入Lyapunov函数,通过其变分方程来构造Lyapunov函数,同时可以将线性方程化为不同的等价系统,然后采用连续映射对原函数的反馈控制能力进行优化,将其转换为线性赋范空间,扩大非线性仿射控制系统的镇定问题,控制Ly Paunov函数的寻找范围,最后将改进算法对某工业复杂系统进行预测控制的实例仿真。仿真实验结果表明,本文提出的基于非线性反馈控制优化的Lyapunov函数具有更好的约束性,能很好地对复杂工业系统进行预测控制。

Consensus control of feedforward nonlinear multi-agent systems:a time-varying gain method

In this paper,the leader–follower consensus of feedforward nonlinear multi-agent systems is achieved by designing the distributed output feedback controllers with a time-varying gain.The agents dynamics are assumed to be in upper triangular structure and satisfy Lipschitz conditions with an unknown constant multiplied by a time-varying function.A time-varying gain,which increases monotonously and tends to infinity,is proposed to construct a compensator for each follower agent.Based on a directed communication topology,the distributed output feedback controller with a time-varying gain is designed for each follower agent by only using the output information of the follower and its neighbors.It is proved by the Lyapunov theorem that the leader–follower consensus of the multi-agent system is achieved by the proposed consensus protocol.The effectiveness of the proposed time-varying gain method is demonstrated by a circuit system.

H_∞ reference tracking control design for a class of nonlinear systems with time-varying delays

This paper investigates the H∞ trajectory tracking control for a class of nonlinear systems with time- varying delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality （LMI） technique. A unified model consisting of a linear delayed dynamic system and a bounded static nonlinear operator is introduced, which covers most of the nonlinear systems with bounded nonlinear terms, such as the one-link robotic manipulator, chaotic systems, complex networks, the continuous stirred tank reactor （CSTR）, and the standard genetic regulatory network （SCRN）. First, the definition of the tracking control is given. Second, the H∞ performance analysis of the closed-loop system including this unified model, reference model, and state feedback controller is presented. Then criteria on the tracking controller design are derived in terms of LMIs such that the output of the closed-loop system tracks the given reference signal in the H∞ sense. The reference model adopted here is modified to be more flexible. A scaling factor is introduced to deal with the disturbance such that the control precision is improved. Finally, a CSTR system is provided to demonstrate the effectiveness of the established control laws.