对称非线性控制系统的能控性

本文采用微分几何方法,研究了具有对称结构的非线性控制系统的能控性。本文证明:若对称非线性控制系统在某点能控,那么该系统在此点所属的轨道上的所有点均能控。     

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.     

仿 射 非 线 性 系 统 的 能 控 性

研究仿射非线性系统的能控性问题. 利用向量场族对应的积分曲线定义系统的能控性,建立一个新的基于漂移向量场弱泊松稳定的能控性判据,并给出了完整的证明 .利用该结论对定义在紧致黎曼流形上的解析系统,给出了漂移向量场为保守场条件下的能控性的充要条件,并用状态流形的紧致性证明了弱泊松稳定性的几个等价条件.进一步利用保守系统的判据给出了一般仿射非线性系统能控的充分条件,并应用所得结论分析了欠驱动航天器姿态系统的能控性.

     

周期性系统的能控性理论

主要探讨周期性系统(包括连续和离散两种情形)的能控性问题，对文献中有关周期为To的连续周期性系统的能控性结论进行了完善，推导出系统能控等价于单周期(0，To)内能控的结论，并将这些结论直接推广到离散周期性系统；然后讨论了离散前后周期性系统能控性保持不变的可能性，证明在采用不等间距采样方式时，离散前后周期性系统的能控性保持不变。     

基于神经网络的非仿射块控非线性系统动态反演控制

即使已知非仿射非线性系统的逆存在,利用隐函数定理求解该显式逆仍然非常困难.为此,针对一类不确定块控非仿射系统,将动态反馈、反演、神经网络和反馈线性化技术相结合,提出一种自适应鲁棒控制器的设计方法.利用神经网络来逼近和消除未知函数,并证明了整个闭环系统在李雅普诺夫意义下是稳定的.仿真结果表明了所提出方法的有效性.     

有界区域上Petrowsky系统的能控性和能稳性

利用D.L.Russel关于“能稳性导致能控性”的论断,研究Petrow sky系统的能控性,首先取线性反馈控制,得到线性反馈Petrow sky系统的能量的指数衰减,从而由D.L.Russel的“能稳性导致能控性”的论断得到能控性.其次取非线性反馈控制,得到Petrow sky系统的一些能量估计,但是不能得到指数能稳.     

DC-DC变换器在恒功率负载下的能控性

带有恒功率负载的DC-DC变换器是切换非线性系统.以Boost变换器为例,本文建立了其切换系统模型;它包括三个模态.模态I,II,III分别对应于开关器件导通、关断、电感电流断续时的电路拓扑.因为电容电压是非负的,所以本文对平面拓扑学的最新结果加以修正,导出了半平面仿射非线性系统全局能控的充分必要条件——判别函数在任意非零控制曲线上变号.据此证明了模态II的全局能控性.由于模态II为运转中的必经阶段,故切换系统能控.研究方法也适用于Buck等变换器的能控性分析.     

感应电动机系统的能控性与能观测性分析

分析了感应电动机系统的能控性与能观测性。结果表明系统是弱能控与弱能观的。而且,采用非线性状态反馈解耦控制和非线性坐标变换后的局部闭环解耦线性系统是能控与能观的。     

基于非线性系统受控因子的能控性分析方法

提出一种基于受控因子的非线性能控性分析方法，引入受控因子与阶次差的概念，分析了相同阶次差的受控因子间的关系，给出了一种判别多项式矩阵满秩的方法，最后以文献（１）给出的结论为基础，推导了判别非线性系统弱能控性的新判据。     

线性切换系统的能控性与能达性*

本文针对一般线性切换系统,严格定义了系统的能控性、能达性和能控集、能达集,导出了能控性的一个必要条件,给出了三维单输入双切换系统能控性的充分必要条件,并指出现有文献中有关结论的一个错误.     

Controllability of nonlinear stochastic control systems

In the paper sufficient conditions for ‘deterministic weak controllability’ of nonlinear Itô equations of the form are given.     

Controllability of nonlinear systems consisting of a bilinear mode with time-varying delays in control

Sufficient conditions are established for the global relative controllability of nonlinear system consisting of a bilinear mode with time-varying delays in control. The results are a generalization of previous results and are obtained by using Schauder's fixed point theorem.     

Invertibility of affine nonlinear control systems: a geometric approach

The paper deals with the invertibility of multivariable non-linear control systems. By using the recently developed theory on controlled invariant and controllability distributions necessary and sufficient conditions for invertibility are derived.     

Decompositions for control systems on manifolds with an affine connection

In this letter we present a decomposition for control systems whose drift vector field is the geodesic spray associated with an affine connection. With the geometric insight attained with this decomposition, we are able to easily prove some special results for this class of control systems. Examples illustrate the theory.     

Non-zenoness of piecewise affine dynamical systems and affine complementarity systems with inputs

In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs.     

Controllability for single-input mechanical control systems with dissipation

Within the affine connection framework of Lagrangian control systems , based on the results of Sussmann on small- time locally controllability of single- input affine nonlinear control systems , the controllability results for mechanical control systems with single- input are extended to the case of the systems with isotropic damping ,where the Lagrangian is the kinetic energy associated with a Riemannian metric. A sufficient condition of negative small- time locally controllability for the system is obtained. Then ,it is demonstrated that such systems are small- time locally configuration controllable if and only if the dimension of the configuration manifold is one. Finally , two examples are given to illustrate the results. Lie bracketting of vector fields and the symmetric product show the advantages in the discussion.     

Controllability for single-input mechanical control systems with dissipation

Within the affane connection framework of Lagrangian control systems, based on the results of Sussmann on small-time locally controllability of single-input affine nonlinear control systems, the controllability results for mechanical control systems with single-input are extended to the case of the systems with isotropic damping, where the Lagrangian is the kinetic energy associated with a Riemannian metric, A sufficient condition of negative small-time locally controllability for the system is obtained.Then,it is demonstrated that such systems are small-time locally configuration controllable if and only if the dimemion of the configuration manifold is one. Finally, two examples are given to illustrate the results. Lie bracketting of vector fields and the symmetric product show the advantages in the discussion.     

Controller design for nonlinear affine systems by control Lyapunov functions

This paper addresses the stabilization problems for nonlinear affine systems. First of all, the explicit feedback controller is developed for a nonlinear multiple-input affine system by assuming that there exists a control Lyapunov function. Next, based upon the homogeneous property, sufficient conditions for the continuity of the derived controller are developed. And then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems. It is shown that under some homogeneous assumptions on control Lyapunov functions and the interconnection term, the cascaded system can be globally stabilized. Finally, some interesting results of finite-time stabilization for nonlinear affine systems are also obtained.