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.     

Compensating periodic descriptor systems

The compensating problem for forward–backward periodic systems in discrete-time has been studied. A normal compensator for this kind of systems is proposed using a suitable observer. In addition, some properties to construct the periodic observer and compensator can be obtained from the associated invariant systems.     

Controllability of linear stochastic systems

We discuss several concepts of controllability for stochastic systems and derive sufficient (and in most cases also necessary) algebraic conditions for the controllability of the state and the output of white and colored noise linear systems. These criteria reduce to the well known deterministic ones in the absence of noise.     

Controllability of 2-D systems

The concept of controllability of 2-D systems is introduced in a behavioral framework. This property is defined as a systems concept and is characterized in terms of system representations. State-space realizations for controllable 2-D systems are presented. The structure of state-space systems is analyzed, and the notions of trimness, reachability, and observability are introduced and characterized. These realizations do not depend on any assumptions concerning causality     

Controllability of piecewise linear systems

The paper deals with a discontinuous control system that consists of two finite-dimensional linear systems; the first describes the motion in a given half-space, the second in the complementary half-space. Necessary and sufficient conditions for local controllability are obtained.     

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.     

Controllability of non-linear stochastic systems

Complete controllability of a semi-linear stochastic system assuming controllability of the associated linear sytem is studied. It is also shown that a non-linear stochastic system is locally null controllable provided that the corrsponding linearized system is controllable.     

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,井应用所得结论分析了欠驱动航天器姿态系统的能控性.     

Controllability of general nonlinear systems

Consider the nonlinear system $$\dot x(t) = f(x(t)) + \sum\limits_{i = 1}^m {u_i (t)g_i (x(t)), x(0) = x_0 \in M}$$ whereM is aC ^∞ realn-dimensional manifold,f, g ₁,?.,g _m areC ^∞ vector fields onM, andu ₁ ,..,u _m are real-valued controls. Ifm=n?1 andf, g ₁ ,?,g _m are linearly independent, then the system is called a hypersurface system, and necessary and sufficient conditions for controllability are known. For a generalm, 1 ≤m ≤n?1, and arbitraryC ^∞ vector fields,f, g ₁ ,?,g _m , assume that the Lie algebra generated byf, g ₁ ,?,g _m and by taking successive Lie brackets of these vector fields is a vector bundle with constant fiber (vector space) dimensionp onM. By Chow's Theorem there exists a maximalC ^∞ realp-dimensional submanifoldS ofM containingx ₀ with the generated bundle as its tangent bundle. It is known that the reachable set fromx ₀ must contain an open set inS. The largest open subsetU ofS which is reachable fromx ₀ is called the region of reachability fromx ₀. IfO is an open subset ofS which is reachable fromx ₀,S we find necessary conditions and sufficient conditions on the boundary ofO inS so thatO = U. Best results are obtained when it is assumed that the Lie algebra generated byg ₁,?,g _m and their Lie brackets is a vector bundle onM.     

Controllability of semilinear stochastic systems

The Picard type approximation is used to derive sufficient conditions for approximate and complete controllability of semilinear stochastic systems with non-Lipschitz coefficients under the assumption that the corresponding linear system is appropriately controllable.