关于自适应非线性镇定的某些结果（英文）

不确定非线性系统的反馈控制一直是控制科学的中心问题之一,迄今已经取得很大进展.然而,目前现有大部分工作所研究的反馈控制规律,或是连续时间形式的,或是采样反馈形式但需要采样频率充分快,或是离散时间反馈形式,但需要被控离散时间系统的非线性函数增长速度不超过线性.要消除或减弱这些约束条件,一般来讲是相当困难的.这就促使我们探究反馈机制的最大能力和根本局限.尽管近年来在这个方向有许多重要进展,但仍有许多非平凡的重要问题有待研究.例如,在反馈通道中有时滞情形,或者系统状态是高维的情形.在本文中,我们将探索两类比较特殊的离散时间不确定非线性动力系统的控制问题,给出关于全局自适应反馈镇定的某些初步结果.     

离散时滞系统的鲁棒无源控制

1 引言在控制系统理论中正实理论起到了很大的作用, 引起了众多学者的关注[1～5]. 对这个问题的研究主要是出于鲁棒控制和非线性控制的需要. 在实际的工业生产过程中, 时滞与不确定现象是普遍存在的且时滞的引入大大增强了控制难度. 因此研究时滞系统的鲁棒正实控制具有一定的复杂性和难度. 文献[6]引入无源性概念, 研究了线性连续时滞系统的无源控制问题,但没有考虑模型的不确定性. 尽管离散时滞系统的无源控制与连续系统具有同等重要的地位, 但据作者所知, 目前尚未见相关报道. 本文考虑了一类时变不确定离散时滞系统的鲁棒无源控制问题, 提出了可将时滞系统的无源控制问题转化为分析一类非时滞离散确定系统的正实性. 基于LMI(Linear Matrix Inequality)研究了采用静态状态反馈和动态输出反馈情形下的鲁棒无源控制问题.     

线性离散时滞系统的鲁棒耗散控制

考虑线性离散时滞系统的二次型耗散控制问题.对于确定系统,给出渐近稳定且严格二次型耗散的条件和动态输出反馈控制器使闭环系统渐近稳定且严格二次型耗散.对于不确定系统,考虑不确定性具有耗散特性的情形,讨论鲁棒耗散性分析和动态输出反馈鲁棒耗散控制问题.通过构造增广系统,将不确定系统的鲁棒严格二次型耗散分析和设计转化为确定系统的情况.所得结果为离散时滞系统的无源控制和H∞控制提供了统一框架,且为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

一类非线性时变系统基于观测器的反馈稳定化

1　引言目前,有关非线性系统的状态反馈控制已取得了许多引人注目的研究结果,其中状态可测是此控制方法中的一个必不可少的假设.在实际中,许多系统的状态是部分可测或不完全可测,故构造观测器,并用估计状态实现反馈控制是一个非常有意义的研究工作.本文研究了一类仿射非线性时变系统基于状态观测器的输出反馈稳定控制问题.首先设计了系统的状态观测器,然后综合控制器和观测器得到了非线性输出反馈控制器,并证明了反馈后闭环系统的指数稳定性.研究结果表明,系统的控制器与观测器可以分离独立进行设计.2　系统的描述及预备知识考虑下列非线性…     

不确定广义系统的圆形区域极点配置

考虑不确定连续或离散广义系统的圆形区域极点配置问题, 目的是设计状态反 馈控制律, 使得闭环系统正则, 无脉冲(连续广义系统情形)或因果(离散广义系统情形), 且 闭环极点位于一给定的圆形区域内. 给出了所期望的状态反馈控制律存在的充分条件及其解 析表达式.     

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.     

基于广义扩张状态观测器的干扰不匹配离散系统状态反馈控制

针对一类干扰不匹配的线性离散时间系统, 研究基于广义扩张状态观测器的稳定化状态反馈控制器设计问题. 在经典的自抗扰控制器中, 扩张状态观测器主要针对干扰匹配的积分串联型系统. 然而, 在许多实际系统中往往存在干扰不匹配的情况, 例如存在采样抖动的离散时间控制系统. 针对这一问题, 基于一类存在不匹配干扰的离散时间系统, 提出广义扩张状态观测器和相应的稳定化状态反馈控制器设计方法. 最后通过永磁同步电机调速控制仿真实例验证了所设计的观测器和控制器的有效性.

     

一类非线性系统模糊自适应固定时间量化反馈控制

研究了一类严格反馈不确定非线性系统的模糊自适应实际固定时间量化反馈控制问题. 基于李雅普诺夫有限时间稳定理论、自适应模糊控制理论及反演控制算法, 提出了一种非线性系统模糊自适应实际固定时间量化反馈跟踪控制方案. 所设计的控制方案能够保证闭环系统的输出跟踪误差在固定时间内收敛于原点的一个充分小邻域内, 且闭环系统内所有信号均有界. 最后, 数值示例验证了设计方案的有效性.     

基于未知控制增益的非线性系统自适应迭代反馈控制

针对一类单输入单输出不确定非线性重复跟踪系统, 提出一种基于完全未知控制增益的自适应迭代反馈控制. 与普通迭代学习控制需要学习增益稳定性前提条件不同, 所提自适应迭代反馈控制律通过不断修改Nuss baum形式的反馈增益达到收敛. 证明当迭代次数i→δ时, 重复跟踪误差可一致收敛到任意小界δ. 仿真显示了所提控制方法的有效性.     

一种离散型非线性自适应反馈控制器的设计与实现

针对运动控制低速跟踪系统中存在的非线性摩擦力影响的实际问题, 采用结构和参数完全未知的离散时间不确定非线性系统的反馈控制策略, 具体地进行了控制器的设计, 并利用MATLAB环境下的SIMULINK仿真来检验其控制效果, 进而运用到实际的电机控制系统中, 分析其控制性能, 并将其控制效果与PID控制相比较, 最后得出结论.     

Robust control of set-valued discrete-time dynamical systems

This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced. The problem is formulated as a dynamic game, wherein the controller plays against the set-valued system. Both necessary and sufficient conditions in terms of (stationary) dynamic programming equalities are presented. The output feedback problem is solved using the concept of an information state, where a decoupling between estimation and control is obtained. The methods yield a conceptual approach for constructing controlled-invariant sets and stabilizing controllers for uncertain nonlinear systems     

A parametric Lyapunov equation approach to low gain feedback design for discrete-time systems

Low gain feedback, a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero, has found several applications in constrained control systems, robust control and nonlinear control. In the continuous-time setting, there are currently three ways of constructing low gain feedback laws: the eigenstructure assignment approach, the parametric ARE based approach and the parametric Lyapunov equation based approach. The eigenstructure assignment approach leads to feedback gains explicitly parameterized in the low gain parameter. The parametric ARE based approach results in a Lyapunov function along with the feedback gain, but requires the solution of an ARE for each value of the parameter. The parametric Lyapunov equation based approach possesses the advantages of the first two approaches and results in both an explicitly parameterized feedback gains and a Lyapunov function. The first two approaches have been extended to discrete-time setting. This paper develops the parametric Lyapunov equation based approach to low gain feedback design for discrete-time systems.     

区域极点约束下线性离散系统的Riccati鲁棒控制

讨论区域极点约束下,含结构参数扰动的不确定线性离散系统的鲁棒控制问题,即设计一 鲁棒状态反馈控制器,使线性离散系统在可允许的参数扰动下,闭环矩阵极点始终位于一预先 给定的圆形区域中,从而闭环系统具有期望的动态性能.上述控制目的可通过求解一含参数 的代数离散Riccati方程达到.     

A dynamical inequality for the output of uncertain nonlinear systems

An important task in control theory is to study the limitations of feedback principle in dealing with uncertainties.Although some progresses have been achieved in this area,they are all focused on some special classes of linearly parameterized nonlinear uncertain systems.In this paper,we will present a dynamic inequality for the output process of a quite general class of nonlinear dynamical control systems with nonlinearly parameterized uncertain parameters.This inequality will be established using a stochastic imbedding approach based on a Cramér-Rao inequality for dynamical systems,and will be shown to play a crucial role in investigating the fundamental limitations of the feedback mechanism.     

Optimal infinite-horizon control and the stabilization of linear discrete-time systems: State-control constraints and nonquadratic cost functions

Stability results are given for a class of feedback systems arising from the regulation of time-invariant, discrete-time linear systems using optimal infinite-horizon control laws. The class is characterized by joint constraints on the state and the control and a general nonlinear cost function. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee asymptotic stability of the optimal feedback systems. Prior results, which concern the linear quadratic regulator problem, are included as a special case. The proofs make no use of discrete-time Riccati equations and linearity of the feedback law, hence, they are intrinsically different from past proofs.     

不确定非线性切换系统的鲁棒H∞控制

讨论了一类不确定非线性切换系统的鲁棒H∞控制问题．首先,基于多Lyapunov函数方法,设计状态反馈控制器以及切换律,使得对于所有允许的不确定性．相应的闭环系统渐近稳定又具有指定的L2-增益．该问题可解的充分条件以一组含有纯量函数的偏微分不等式形式给出,此偏微分不等式较一般Hamilton-Jacobi不等式更具可解性．所提出的方法不要求任何一个子系统渐近稳定．接着作为应用,借助混杂状态反馈策略讨论了非切换不确定非线性系统的鲁棒H∞控制问题．最后通过一个简单例子说明了控制设计方法的可行性．     

确定学习与基于数据的建模及控制

确定学习运用自适应控制和动力学系统的概念与方法, 研究未知动态环境下的知识获取、表达、存储和利用等问题. 针对产生周期或回归轨迹的连续 非线性动态系统, 确定学习可以对其未知系统动态进行局部准确建模, 其基本要 素包括: 1)使用径向基函数(Radial basis function, RBF)神经网络; 2)对于周期(或回归)状态轨迹 满足部分持续激励条件; 3)在周期(或回归)轨迹的邻域内实现对非线性系统动态的局部准确神经网络逼近(局部准确建模); 4)所学的知识以时不变且空间分布的方式表达、以常值神经网络权值的方式存储, 并可在动态环境下用于动态模式的快速识别或者闭环神经网络控制. 本文针对离散动态系统, 扩展了确定学习理论, 提出一个根据时态数据序列对离散动态系统进行建模与控制的框架. 首先, 运用确定学习原理和离散系统的自适应辨识方法, 实现对产生时态数据的离散非线性系统的未知动态进行局部准确的神经网络建模, 并利用此建模结果对时态数据序列进行时不变表达. 其次, 提出时态数据序列的基于动力学的相似性定义, 以及对离散动态系统产生的时态数据序列(亦可称为动态模式)进行快速识别方法. 最后, 针对离散非线性控制系统, 实现了基于时态数据序列对控制系统动态的闭环辨识(局部准确建模). 所学关于闭环动态的知识可用于基于模式的智能控制. 本文表明确定学习可以为时态数据挖掘的研究提供新的途径, 并为基于数据的建模与控制等问题提供新的研究思路.     

Adaptive Dynamic Inversion via Time-Scale Separation

This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.     

Identification and control of a nonlinear discrete-time system based on its linearization: a unified framework

This paper presents a unified theoretical framework for the identification and control of a nonlinear discrete-time dynamical system, in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a "higher order function." This representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system, and reveals the role played by the linearized system in a more transparent form. Under the assumption that the linearized system is controllable and observable, it is shown that: 1) the nonlinear system is also controllable and observable in a local domain; 2) a feedback law exists to stabilize the nonlinear system locally; and 3) the nonlinear system can exactly track a constant or a periodic sequence locally, if its linearized system can do so. With some additional assumptions, the nonlinear system is shown to have a well-defined relative degree (delay) and zero-dynamics. If the zero-dynamics of the linearized system is asymptotically stable, so is that of the nonlinear one, and in such a case, a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly, in a neighborhood of the equilibrium state. The tracking can be achieved by using the state vector for feedback, or by using only the input and the output, in which case the nonlinear autoregressive moving-average (NARMA) model is established and utilized. These results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete-time dynamical systems.     

Small-gain theory for stability and control of dynamical networks: A Survey

This paper provides a personal account of the small-gain theory as a tool for stability analysis, control synthesis, and robustness analysis for interconnected uncertain systems. A milestone in modern control theory is the development of a transformative stability criterion known as the classical small-gain theorem proposed by George Zames in 1966, that surpasses Lyapunov theory in that there is no need to construct Lyapunov functions for the finite-gain stability of feedback systems. Under the small-gain framework, a feedback system composed of two finite-gain stable subsystems remains finite-gain stable if the loop gain is less than one. Despite its apparent simplicity at first sight, Zames’s small-gain theorem plays a crucial role in the development of linear robust control theory. Borrowing techniques in modern nonlinear control, especially Sontag’s notion of input-to-state stability (ISS), the first generalized, nonlinear ISS small-gain theorem proposed by one of the authors in 1994 overcomes the two shortcomings of Zames’s small-gain theorem. First, the use of nonlinear gains allows to consider strongly nonlinear, interconnected systems. Second, the role of initial conditions is made explicit so that both internal Lyapunov stability and external input-output stability can be studied in a unified framework. In this survey paper, we first review early developments in the nonlinear small-gain theory for interconnected systems of various types such as continuous-time systems, discrete-time systems, hybrid systems and time-delay systems, along with applications in robust nonlinear control. Then, we describe how to obtain a network small-gain theory for large-scale dynamical networks that are comprised of more than two interacting nonlinear systems. Constructive methods for the generation of Lyapunov functions for the total network are presented as well. Finally, this paper discusses how the network/nonlinear small-gain theory can be applied to obtain innovative solutions to quantized and event-based nonlinear control problems, that are important for the development of a complete theory of controlling cyber-physical systems subject to communications and computation constraints.