对称非线性控制系统的能控分解

本文利用群作用来定义非线性系统的对称性,在此基础上讨论对称系统的能控分解,并证明:若对称非线性控制系统在某点可能控分解,那么该系统在此点所属的轨道上的所有点均可能控分解;特别是若状态流形是齐次流形的话,则由系统在某一点可能控分解就能推出系统可全局能控分解。这表明,对称结构能使系统可能控分解的区域扩大。     

非线性控制系统的特性（I）

本文采用与线性系统理论相比较的方法，阐述非线性控制系统理论。文中通过一些例子来分析非线性控制系统在能控性，能观性，抗干扰性，解耦和稳定性等方面的特性，从而进一步说明非线性控制系统理论在提法，论述和结论上的特点。第一部分介绍非线性系统的能控性和能观性。     

非线性控制系统的特性（Ⅰ）

本文采用与线性系统理论相比较的方法，阐述非线性控制系统理论。文中通过一些例子来分析非线性控制系统在能控性、能观性、抗干扰性、解耦和稳定性等方面的特性，从而进一步说明非线性控制系统理论在提法、论述和结论上的特点。第一部分介绍非线性系统的能控性和能观性。     

非线性控制系统的特性（Ⅱ）

本文采用与线性系统理论比较的方法来阐述非线性控制系统理论。文章通过例子分析了非线性控制系统在能控性、能观性、抗干扰性、解耦和稳定性等方面的特性，从而进一步说明非线性控制系统理论在提法、论述和结论上的特点。文章的第一部分介绍了非线性控制系统的能控性和能观性，这一部分揭示非线性控制系统在干扰解耦和无交互作用控制方面的特性。     

非线性控制系统的特性（Ⅲ）

本文采用线性系统理论比较的方法来阐述非线性控制系统理论。文章通过一些例子来分析非线性控制系统的能控性、能观性、抗干扰性、解耦和稳定性等方面的特性，从而进一步说明非线性控制系统理论在提法、论述和结论上的特点。     

非线性奇异系统的能控性子分布

研究非线性奇异控制系统的能控性子分布问题.提出了非线性奇异系统的能控性子分 布的概念;研究了非线性奇异系统能控性子分布的反馈不变性质;给出了非线性奇异系统能控 性子分布的算法,并讨论这个算法的一些性质;证明了在一定条件下,该算法给出的分布确为包 含在某给定分布中的非线性奇异系统的最大能控性子分布.     

离散对称非线性控制系统的全局结构

本文给出离散非线性控制系统的对称性概念，并证明了在一定条件下，对称离散非线性控制系统通过反馈及坐标变换化成具有简单的结构形式。     

非线性系统的对称性与线性化

本文考察具有对称结构的仿射非线性控制系统的零动态与精确线性化之间的关系。结果表明，对一类关于群对称的仿射非线性控制系统，能够得到它的低维零动态，从而在系统研究和设计中便于问题的简化。特别，文中指明了一个有意义的事实：具有关于线性群或自由适当群对称结构的仿射非线性控制系统不能通过状态反馈实现精确线性化。     

非线性控制系统与状态空间的几何结构

首行从整体化的观点定义了一种建立在黎曼流形上的非线性控制系统,给出了系统的状态方程在黎曼流形的局部坐标系下的表达式,讨论了黎曼流形的几何结构对非线性系统的影响,研究了非线性系统的能控性和能观测性,其次,利用对合分布与全测地子流形的性质,给出了建立在黎曼流形上的非线性系统的局部能控结构分解,局部能观结构分解和Kalman分解,第三,分别利用彼此正交的对合分布族和递增对合分布族与全测地子流形族的性质。研究了建立在黎曼流形上的非线性控制系统平等解耦问题和级联解耦问题,以及仿射非线性控制系统的局部干扰解耦问题。     

对称非线性系统的结构简化

文献[1]对于对称非线性控制系统作了结构上的简化分解,本文在此基础上,利用李代数的半直和分解及其Cartan子代数的概念,对一般李群作用下的对称非线性控制系统作了进一步的降低变量个数的简化分解。这一分解是较为深入和彻底的,更进一步简化了系统的结构。     

Modeling and Control of Head Raising Snake Robots by Using Kinematic Redundancy

In this paper, we consider trajectory tracking control of a head raising snake robot on a flat plane by using kinematic redundancy. We discuss the motion control requirements to accomplish trajectory tracking and other tasks, such as singular configuration avoidance and obstacle avoidance, for the snake robot. The features of the internal motion caused by kinematic redundancy are considered, and a kinematic model and a dynamic model of the snake robot are derived by introducing two types of shape controllable point. The first is the head shape controllable point, and the other is the base shape controllable point. We analyzed the features of the two kinds of shape controllable point and proposed a controller to accomplish the trajectory tracking of the robot’s head as its main task along with several sub-tasks by using redundancy. The proposed method to accomplish several sub-tasks is useful for both the kinematic model and the dynamic model. Experimental results using a head raising snake robot which can control the angular velocity of its joints show the effectiveness of the proposed controller.     

关于非线性系统的对程性、可达性与可控性*

本文讨论对称及广义对称非线性系统的可达性与可控性。文中证明了如果广义对称系统在一点的邻域可控,那么系统在包含该点群作用轨道的一个开集上是可控的。利用广义对称性还给出了控制律的原则算法。对于对称系统,给出了可控性的充要条件。     

Kalman controllability decompositions for differential-algebraic systems

We study linear differential-algebraic control systems and investigate decompositions with respect to controllability properties. We show that the augmented Wong sequences can be exploited for a transformation of the system into a Kalman controllability decomposition (KCD). The KCD decouples the system into a completely controllable part, an uncontrollable part given by an ordinary differential equation and an inconsistent part, which is behaviorally controllable but contains no completely controllable part. This decomposition improves a known KCD from a behavioral point of view. We conclude the paper with some features of the KCD in the case of regular systems.     

Control of the wave equation at a rational point

The wave equation is controlled by a force at one point, which is a rational point of the interval [−1, 1]: geometric interpretations are given of the controllable subclasses.     

Null controllability of planar bimodal piecewise linear systems

This article investigates the null controllability of planar bimodal piecewise linear systems, which consist of two second order LTI systems separated by a line crossing through the origin. It is interesting to note that even when both subsystems are controllable in the classical sense, the whole piecewise linear system may be not null controllable. On the other hand, a piecewise linear system could be null controllable even when it has uncontrollable subsystems. First, the evolution directions from any non-origin state are studied from the geometric point of view, and it turns out that the directions usually span an open half space. Then, we derive an explicit and easily verifiable necessary and sufficient condition for a planar bimodal piecewise linear system to be null controllable. Finally, the article concludes with several numerical examples and discussions on the results and future work.     

Controllability and local accessibility - a normal form approach

Given a system with an uncontrollable linearization at the origin, we study the controllability of the system at equilibria around the origin. If the uncontrollable mode is nonzero, we prove that the system always has other equilibria around the origin. We also prove that these equilibria are linearly controllable provided a coefficient in the normal form is nonzero. Thus, the system is qualitatively changed from being linearly uncontrollable to linearly controllable when the equilibrium point is moved from the origin to a different one. This is called a bifurcation of controllability. As an application of the bifurcation, systems with a positive uncontrollable mode can be stabilized at a nearby equilibrium point. In the last part of this paper, simple sufficient conditions are proved for local accessibility of systems with an uncontrollable mode. Necessary conditions of controllability and local accessibility are also proved for systems with a convergent normal form.     

On strong controllability for planar affine nonlinear systems

Different to linear systems, a controllable nonlinear system does not generally imply that it is strongly controllable. This paper will investigate the strong controllability of planar affine nonlinear systems and obtain its necessary and sufficient condition by introducing the variation function of the control curve. These conditions are imposed on the system structure only. In addition, we also point out that, for a class of polynomial systems, their strong controllability is equivalent to their controllability. Finally, some examples are given to show the application of our results.     

On interconnections, control, and feedback

The purpose of this paper is to study interconnections and control of dynamical systems in a behavioral context. We start with an extensive physical example which serves to illustrate that the familiar input-output feedback loop structure is not as universal as we have been taught to believe. This leads to a formulation of control problems in terms of interconnections. Subsequently, we study interconnections of linear time-invariant systems from this vantage point. Let us mention two of the results obtained. The first one states that any polynomial can be achieved as the characteristic polynomial of the interconnection with a given plant, provided the plant is not autonomous. The second result states that any subsystem of a controllable system can be implemented by means of a singular feedback control law. These results yield pole placement and stabilization of controllable plants as a special case. These ideas are finally applied to the stabilization of a nonlinear system around an operating point     

Stability improvement of nonlinear systems by feedback

This paper is concerned with the property of stabilizing a nonlinear system to a specified equilibrium point arbitrarily fast by appropriate smooth feedback. Two closely related forms of this property are explored. One refers to the asymptotic transfer to the critical point with exponential decay, and it is shown that the systems possessing the above property are precisely those whose corresponding linearization is controllable. The second stabilizability form defined here amounts to driving the system back to an arbitrarily small neighborhood of the given point arbitrarily fast by smooth feedback. A global stabilization result is also included, finding application in Hamiltonian systems. Special emphasis is given to the bilinear case.