CONTROLLABILITY OF A CLASS OF SINGULAR SYSTEMS

In this paper, several different concepts of controllability are investigated for a class of linear singular systems which system parameters are piecewise constant. Necessary and sufficient geometric criteria for C‐controllability and R‐controllability of such systems are established, respectively. These conditions can be easily transformed into algebraic form. By applying the principle of duality, C‐observability is discussed as well. Furthermore, the intrinsic relationship between these results and existing results are also discussed. Then, a novel necessary, and sufficient criterion for C‐controllability of linear time‐invariant singular systems is derived as a byproduct.     

Atomic Spin Polarization Controllability Analysis: A Novel Controllability Determination Method for Spin-Exchange Relaxation-Free Co-Magnetometers

This paper investigates the atomic spin polarization controllability of spin-exchange relaxation-free co-magnetometers(SERFCMs).This is the first work in the field of controllability analysis for the atomic spin ensembles systems,whose dynamic behaviors of spin polarization are described by the Bloch equations.Based on the Bloch equations,a state-space model of the atomic spin polarization for SERFCM is first established,which belongs to a particular class of nonlinear systems.For this class of nonlinear systems,a novel determination method for the global state controllability is proposed and proved.Then,this method is implemented in the process of controllability analysis on the atomic spin polarization of an actual SERFCM.Moreover,a theoretically feasible and reasonable solution of the control input is proposed under some physical constraints,with whose limitation of realistic conditions,the controller design can be accomplished more practically and more exactly.Finally,the simulation results demonstrate the feasibility and validation of the proposed controllability determination method.     

欠驱动柔性机器人的振动可控性分析

欠驱动柔性机器人的可控性分析是对其进行有效控制的关键问题. 本文以具有柔性杆的3DOF平面欠驱动机器人为例, 分两步分析系统的可控性. 首先,忽略杆件的弹性变形, 研究欠驱动刚性系统在不同驱动电机位置的状态可控性；然后, 考虑柔性因素, 研究欠驱动柔性系统的结构振动可控性. 结果表明振动可控性是随机器人关节位形和驱动电机位置而变化的, 并且欠驱动刚性机器人的状态可控性对相应的柔性系统的振动可控性有很重要的影响. 最后, 将上述研究方法扩展到具有一个被动关节的N自由度平面欠驱动柔性机器人.     

基于模型参考和内模原理的线性系统鲁棒控制设计

不确定性因素会使系统性能恶化,它包括系统不确定性参数和各种外部干扰等.本文针对这种不确定性线性系统,利用模型参考和内模原理,建立鲁棒控制系统结构,分析了其能控性条件,通过选择参考模型和内模实现系统能控,在此条件下,将鲁棒控制设计转换为控制系统的LQR问题进行研究,并运用最优控制理论,计算其反馈控制律.仿真结果表明该设计方法将"模型参考"与"内模原理"有机结合起来,提高了系统的鲁棒稳定性,有效抑制干扰,并实现系统性能的改善.     

DISCRETE OUTPUT FUZZY CONTROLLER DESIGN FOR ACHIEVING COMMON CONTROLLABILITY GRAMIAN

In control theory, the robust properties of linear systems can be related directly to properties of the controllability or observability Gramian. In this paper, a discrete fuzzy controller for a class of nonlinear systems is developed to achieve a common controllability Gramian. We assume that the nonlinear system is represented by the Takagi‐Sugeno fuzzy model. The purpose of this paper is to find the output feedback gains for the T‐S fuzzy controller after assigning a certain common controllability Gramian. Finally, we provide a numerical example to verify the effects of the proposed method.     

Controllability of product systems

For nonlinear continuous-time control systems we introduce the notion of controllability with selectable time, which is a little bit stronger than the usual controllability notion. For a large class of nonlinear systems on compact manifolds, controllability with selectable time is equivalent to controllability together with strong accessibility. It turns out that the controllability of products of independent control systems is related to this new controllability notion. The main result states that a smooth control affine product system is controllable if and only if all factors are controllable and at most one factor is not controllable with selectable time, provided the accessibility algebra of the product system has full rank.     

On controllability of discrete-time bilinear systems by near-controllability

In this paper, controllability of discrete-time bilinear systems is studied. By applying a recent result on near-controllability, a new sufficient condition for controllability of the systems is presented, where controllability is proved by approximation with near-controllability. The new condition is algebraically verifiable and is hence easy to apply compared with a classical result on controllability of discrete-time bilinear systems, which can be effective even when the classical result does not work. Furthermore, the control inputs to achieve the transition of the systems between any given pair of states are approximately computable according to near-controllability. Therefore, near-controllability can be used to not only better characterize the system properties, but also prove controllability with computable control inputs. The new condition is then generalized to derive similar results on controllability and near-controllability of the systems. Finally, examples are given to illustrate the results of this paper.     

Controllability of second-order infinite-dimensional systems

In the paper, the approximate controllability of linear abstract second-order infinite-dimensional dynamical systems is considered. It is proved using the frequency-domain method, that approximate controllability of second-order system can be verified by the approximate controllability conditions for the corresponding simplified first-order system. General results are then applied for approximate controllability investigation of a vibratory dynamical system modeling flexible mechanical structure. Some special cases are also considered. Moreover, remarks and comments on the relationships between different concepts of controllability are given. The paper extends earlier results on approximate controllability of second-order abstract dynamical systems.     

Observability and controllability analysis for sandwich systems with dead-zone

In this paper, an approach to analyze the observability and controllability of sandwich systems with dead-zone is proposed. In this method, a non-smooth state-space function is proposed to describe the sandwich systems with dead-zone which are also non-smooth nonlinear systems. Then, a linearization method based on non-smooth optimization is proposed to derive a linearized state-space function to approximate the non-smooth sandwich systems within a bounded region around the equilibrium points that we are interested in. Afterwards, both observability and controllability matrices are constructed and the methods to analyze the observability as well as controllability of sandwich system with dead-zone are derived. Finally, a numerical example is presented.     

On some controllability aspects of discrete-time systems by matrix generalized inverse

The simplest matrix generalized inverse is used to obtain some necessary and sufficient conditions for state and output controllability or servomechanism controllability of linear time-invariant discrete systems. The nulling-output problem as a very special case of output controllability in the servomechanism sense gives rise to different controllability spaces (Molinari 1976 a, b) that can be explicitly described with the aid of a {l}-inverse of a matrix. In relation to the nulling-output problem, a method of finding zeros and zero directions for discrete systems is also presented.     

一类齐次离散双线性系统可控性分析

在系统分析中,可控性是系统的一个重要特性.在工程实际操作中,往往需要对一个连续系统进行离散化处理,人们希望系统在离散化后能保留原系统的重要系统特征,比如可控性.对于线性系统,我们有成熟的判断方法.然而,对于非线性系统则无统一的判别方法.Elliott在2005年给出了一个二阶双线性系统经过离散化后,可控性发生变化的例子.它表明一个系统在离散化前后,它的可控性可能会发生改变.本文旨在给出一类二阶离散化双线性系统可控性充分条件,并和已有结果作比较,表明本文结果更具有一般性.另外,本文对于3阶及以上的这类系统可控性做出了不可控的判断.     

Necessary and sufficient conditions for quadratic controllability of a class of uncertain systems

We introduce a controllability notion for uncertain systems, namely, quadratic controllability. For a specific class of norm bounded uncertain systems, we show that this notion is equivalent to controllability of a nominal system and the satisfaction of a certain structural condition by the uncertainty. For systems in which the uncertain parameters affect all control inputs, this structural condition is simply the familiar matching condition commonly encountered in the literature on robust and adaptive control of uncertain systems.     

Controllability of switched bilinear systems

The controllability of switched bilinear systems (SBLSs) is considered. Three kinds of controllabilities, including weak controllability, approximate controllability, and global controllability, are investigated one by one. Sets of easily verifiable sufficient conditions are obtained for each case, which are applicable to a large class of switched bilinear systems.     

An Iterative Method of the Structural-Parametric Design of Robust Systems with State Controllers

An iterative method for designing a robust control system with state controllers is proposed that includes a transformation of the plant structure to improve its controllability by correcting the singular values of the controllability Gramian and the subsequent synthesis of the basic controller for the corrected plant using modal control. This approach allows us to design systems satisfying the robust stability condition for the given intervals of variation of the plant parameters.     

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.     

Links between asymptotic controllability and persistence of excitation for a class of time-varying systems

For a class of nonlinear time-varying parameterized systems we prove that persistence of excitation implies global asymptotic controllability to the equilibrium with respect to a set of parameters. The result is used to derive sufficient conditions for global asymptotic controllability for composite systems.     

Partial controllability of stochastic linear systems

The controllability concepts for linear stochastic differential equations, driven by different kinds of noise processes, can be reduced to the partial controllability concepts for the same systems, driven by correlated white noises. Based on this fact, in this article, we study the conditions of exact and approximate controllability for linear stochastic control systems under various kinds of noise processes, including correlated white noises as well as coloured, wide band and shifted white noises. It is proved that such systems are never exactly controllable while their approximate controllability is equivalent to the approximate controllability of the associated linear deterministic systems at all past time moments.     

自旋量子系统的可控李代数计算

动态系统可控性同是经典和量子控制中研究的一个基本问题,本文研究了单自旋和双自旋量子系统的可控李代数的计算.首先基于量子系统可控的等价性条件,通过单量子系统Hamiltonian算符的李括号运算,给出了与基系数相关的系统可控的充要条件.然后利用Cartan分解方法构造了李代数su(4)的矩阵基,同时根据可控性基本定理提出了Hamiltonian算符多重李括号的计算方法及系统的可控性判据.     

Controllability of buildings: A multi-input multi-output stability assessment method for buildings with slow acting heating systems

The paper describes a methodology to assess the controllability of a building and its servicing systems, such as heating, lighting and ventilation. The knowledge for these methods has been transferred from design processes and methods used in the design of aircraft flight control systems to establish a modelling and design process for assessing the controllability of buildings. The paper describes a holistic approach to the modelling of the nonlinear and linear dynamics of the integrated building and its systems. This model is used to analyse the controllability of the building using Nonlinear Inverse Dynamics controller design methods used in the aerospace and robotics industry. The results show that this design approach can help the architects in their decisions on which building design and services to use. Furthermore, the results demonstrate how the same method can assist the control systems designer in developing complex control systems especially for buildings designed with a climate adaptive building (CAB) philosophy.     

Structure of the boundary of the attainable set in certain nonlinear systems

A class of fully nonlinear systems is introduced in which systems are comprised of a weakly homogeneous subsystem and a drift subsystem. We prove that the boundary of any attainable set of a system in this class is foliated by attainable submanifolds of its weakly homogeneous subsystem. We also discuss sufficient conditions for the global controllability of systems in this class and show that the global controllability problem can be reduced to a family of local controllability problems.