非线性系统的状态反馈大范围输出调节

本文首先定义了状态反馈大范围输出调节，然后用常微分方程的不变流形该问题进行了深入的探讨，指出非线性系统状态反馈大范围输出调节问题可解的充要条件是满足某个非线性时变偏微分方程。     

交叉耦合非线性系统的输出调节

利用中心流形定理,给出交叉耦合非线性系统的输出调节问题可解的充要条件,定义了交叉耦合非线性系统的零误差流形.利用幂级数展开的方法,给出该零误差流形存在的充要条件,并讨论了该零误差流形的局部收敛性.     

非线性系统的输出调节与受控中心流形

本文用中心流形理论＾［７］及动力系统方法＾［８］，考虑了一般非线性系统的输出调节问题，在弱于Ｉｓｉｄｏｒｉ和Ｂｙｒｎｅｓ＾［６］的条件下，得到了这问题可解的充分必要条件。     

投影滤波器原理在贝叶斯滤波中的应用

对于非线性滤波问题,给出一种有限维近似滤波算法。它利用统计流形上的微分几何方法,将关于概率密度的随机偏微分方程投影到有限维统计流形上,得到相关参数的有限维随机常微分方程。通过引入指数型概率密度模型,简化投影滤波算法的计算。再结合Bayes定理求解非线性系统状态的后验概率密度,最后应用于立体传感器系统的滤波问题。     

基于奇异摄动理论的非仿射系统的输出调节问题

基于奇异摄动的时标分解理论和动态逆设计的方法,研究了一类非仿射非线性系统的输出调节问题.通过将控制律定义为一个快动态系统的解,得到了指数稳定的误差系统状态方程,从而实现了原系统的输出相对于外系统的参考信号具有零误差的跟踪效果.结果表明在满足标准假设和一组偏微分方程有解的前提下,该输出调节问题是可解的.仿真实例表明了该理论方法的有效性.     

非线性最小相位系统输出反馈镇定的一个注记

讨论了单输入单输出非线性最小相位系统的动态输出反馈镇定.通过加积分器和非线性变换将系统化为一种标准形式,并基于标准形式的线性部分提出了动态补偿器的设计方法.然后根据得到的中心流形的表达式和稳定性定理,在零动态流形为一维时,证明了闭环系统的渐近稳定性,最后给出了一个零动态不具有齐次渐近稳定性但仍能动态输出反馈镇定的非线性最小相位系统的例子.     

基于奇异摄动理论的非仿射系统的输出调节问题

基于奇异摄动的时标分解理论和动态逆设计的方法,研究了一类非仿射非线性系统的输出调节问题.通过将控制律定义为一个快动态系统的解,得到了指数稳定的误差系统状态方程,从而实现了原系统的输出相对于外系统的参考信号具有零误差的跟踪效果.结果表明在满足标准假设和一组偏微分方程有解的前提下,该输出调节问题是可解的.仿真实例表明了该理论方法的有效性.

     

受控磁悬浮系统非线性随机响应分析

讨论了非线性磁悬浮控制系统随机振动响应预测问题．基于等效非线性微分方程方法,从理论上对非线性磁悬浮控制系统的随机响应进行了深入分析,建立了此高维系统非线性模型;根据中心流形理论对系统进行约化、降维,给出了此系统响应的近似解析解．这对此系统实现进一步稳定控制提供了有效的理论依据．     

一类具有复杂执行器动态的双曲线型偏微分方程输出调节

本文研究了一类具有边界执行器动态特性的双曲线型偏微分方程(Partial differential equation, PDE)系统的输出调节问题. 特别地, 执行器由一组非线性常微分方程(Ordinary differential equation, ODE)描述, 控制输入出现在执行器的一端而非直接作用在PDE系统上, 这使得控制任务变得相当困难. 基于几何设计方法和有限维与无限维反步法, 本文提出了显式表达的输出调节器, 实现了该类系统的扰动补偿及跟踪控制. 并且我们采用Lyapunov稳定性理论严格证明了闭环系统及跟踪误差在范数意义上的指数稳定性. 仿真实例对比验证了所提出控制方法的有效性.     

微分几何方法与非线性控制系统（2）

4 向量场与动态系统 众所周知,现代控制理论的研究是在状态空间上,使用状态方程,但有些动态系统,特别是非线性系统,其动态演变是在微分流形上进行的,演化结果是流形上的一条曲线,描述无穷小演化的微分方程是定义在流形上的向量场,因此,研究流形上的动态系统,就要分析流形上的向量场。流形上向量场的局部坐标表示是R~n中的微分方程组。在状态空间中,向量场就是状态方程的几何解释。应用向量场来研究动态系统的方法,就是几何方法。     

On the solvability of the regulator equations for a class of nonlinear systems

Regulator equations arise in studying the output regulation problem for nonlinear systems. The solvability of the regulator equations is the necessary condition for that of the output regulation problem. It has been shown under various assumptions that the solvability of the regulator equations can be reduced to that of a center manifold equation defined by the zero dynamics of a composite system consisting of the plant and exosystem. In this paper we further show that, for a quite general class of nonlinear systems, the solvability of the regulator equations can be reduced to that of a center manifold equation if the relative degree of the composite system at the origin exists.     

Output regulation with nonlinear internal models

This paper addresses the problem of semi-global nonlinear output regulation for a class of nonlinear systems possessing a nonlinear internal model. It is shown that, under appropriate (and verifiable) hypotheses, the standard assumption that the feed-forward inputs needed to keep the zero error manifold invariant satisfy a linear differential equation can be weakened.     

Asymptotic tracking of a nonminimum phase nonlinear system withnonhyperbolic zero dynamics

A two-cart with an inverted-pendulum system is a nonlinear, nonminimum phase system with nonhyperbolic zero dynamics. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems with nonhyperbolic zero dynamics and pointed out that the nonhyperbolicity may be challenging to the application of the standard inversion-based tracking technique. We first show that nonhyperbolicity is not necessary for the applicability of the output regulation theory. In particular, the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a class of sinusoidal reference inputs is actually solvable by the standard output regulation theory. Moreover, an approximation method for calculating the center manifold equation associated with the output regulation problem for general nonlinear systems is given. This approach does not rely on the hyperbolicity condition and, hence, applies to a large class of nonlinear systems     

An algorithm for system immersion into nonlinear observer form: SISO case

The class of nonlinear systems that can be put into nonlinear observer form (linear system with output injection) can be broadened if we employ the system immersion. We provide an immersion algorithm for SISO nonlinear systems with relative degree r. The proposed algorithm is an extension of the previous results and does not require the relative degree 1 assumption. In addition, it is seen that the immersion can always be computed via algebraic computations and simple integrations except in a very special case in which the relative degree equals the system dimension (in this case, only one first order differential equation appears in the algorithm).     

Output regulation of nonlinear systems

The problem of controlling a fixed nonlinear plant in order to have its output track (or reject) a family of reference (or disturbance) signal produced by some external generator is discussed. It is shown that, under standard assumptions, this problem is solvable if and only if a certain nonlinear partial differential equation is solvable. Once a solution of this equation is available, a feedback law which solves the problem can easily be constructed. The theory developed incorporates previously published results established for linear systems     

Nonlinear inversion-based output tracking

An inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory. In the case of minimum phase systems, the trajectory produced agrees with that generated by Hirschorn's inverse dynamic system; however, the preimage trajectory is noncausal (rather than unstable) in the nonminimum phase case. In addition, the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case. With the addition of stabilizing feedback to the preimage trajectory, asymptotically exact output tracking is achieved. Tracking is demonstrated with a numerical example and compared to the well-known Byrnes-Isidori regulator. Rather than solving a partial differential equation to construct a regulator, the inverse is calculated using a Picard-like interaction. When preactuation is not possible, noncausal inverse trajectories can be truncated resulting in the tracking-error transients found in other control schemes     

Dual observer‐based compensators for nonlinear systems

In this article, the concept of dual observer‐based compensators is extended from linear to nonlinear systems. It is shown that a dual observer‐based compensator achieves stabilization by rendering an invariant manifold attractive in which desired dynamics can be assigned. The design of these compensators for nonlinear systems is considerably simple if a flat output of the system to be controlled is known which is illustrated by means of a simple example. Copyright © 2012 John Wiley & Sons, Ltd.     

Centre-manifold-based sliding mode output tracking for non-minimum nonlinear systems

This paper focuses on a problem of sliding mode output tracking for non-minimum-phase nonlinear systems whose zero dynamics is not stable. Sliding mode consists of continuous power functions instead of switch functions, and the power of the function has the term of fraction whose denominator and numerator are all positive odd numbers, so the chattering phenomenon can be avoided. The method of the design is based on the centre manifold theory, and a sliding manifold can be constructed by the combination of the polynomial of tracing error and internal dynamics variable.