Constrained approximate boundary controllability

In this paper, constrained approximate boundary controllability for linear disturbed parameter dynamical systems described by partial differential equations of parabolic-type with mixed boundary conditions is considered. Using methods of spectral analysis for linear self-adjoint operators and general constrained controllability results, given by Son (1990), necessary and sufficient conditions for constrained approximate boundary controllability are formulated and proved. Moreover, in illustrative examples the constrained approximate boundary controllability of 1D distributed parameter dynamical systems is investigated. The constrained controllability conditions obtained represent an extension of the unconstrained controllability results given by Glothin (1974)     

On the controllability of linear systems with delays in the control

Relative controllability and absolute controllability of linear time-varying systems with lumped and distributed delays in the control are considered. Necessary and sufficient conditions for relative and absolute controllability of these systems are derived. The problem of minimum energy control is also examined, and a control law is given.     

Constrained approximate controllability

In the paper, constrained approximate controllability for linear dynamical systems described by abstract differential equations with unbounded control operator is considered. Using methods of spectral analysis for linear self-adjoint operators and general constrained controllability results given by Son (1990), necessary and sufficient conditions of the constrained approximate controllability for the piecewise polynomial controls with values in a given cone are formulated and proved. Moreover, as illustrative examples, constrained approximate boundary controllability of one-dimensional distributed parameter dynamical systems described by partial differential equations of parabolic type with Dirichlet and Neumann boundary conditions are investigated. The constrained controllability conditions obtained in the paper represent an extension of the unconstrained controllability results given by Glothin (1974) and Klamka (1991)     

Control aspects of linear discrete time-varying systems

Results for time-invariant linear systems concerning controllability, reachability, output controllability, stabilizability, and target path controllability are extended to time-varying systems. For the extensions which are already known in the literature elementary proofs are given. Moreover, necessary and sufficient conditions are given for the (strong) admissibility of a target path.     

On controllability of a class of discrete‐time homogeneous bilinear systems with solvable controls

This paper studies the controllability of a class of discrete‐time homogeneous bilinear systems. Necessary and sufficient conditions for the controllability are obtained. In particular, an algorithm for computing the controls, which achieve given states transition, for the controllable systems is given with examples. Furthermore, the necessary and sufficient conditions are applied to present four cases of the change of the controllability for Euler discretization, which show that Euler discretization may and may not change the controllability of nonlinear systems. Copyright © 2011 John Wiley & Sons, Ltd.     

二阶分布参数系统的稳定性和能控性

讨论Hilbert空间上两个二阶线性系统的稳定性和能控性,在较一般的假设下,得到了 这两个系统的指数稳定性和精确能控性,渐近稳定性和近似能控性之间的关系.最后,给出 线性系统渐近稳定的一个充分必要条件.     

On controllability of homogeneous and inhomogeneous discrete-time multi-input bilinear systems in dimension two

In this paper, the controllability problem of two-dimensional discrete-time multi-input bilinear systems is completely solved. The homogeneous and the inhomogeneous cases are studied separately and necessary and sufficient conditions for controllability are established by using a linear algebraic method, which are easy to apply. Moreover, for the uncontrollable systems, near-controllability is considered and similar necessary and sufficient conditions are also obtained. Finally, examples are provided to demonstrate the results of this paper.     

Discrete-time linear periodic systems: gramian and modal criteria for reachability and controllability†

This paper deals with the reachability and controllability of periodic discrete-time systems. First, we supply two necessary and sufficient complete reachability conditions, which apply to reversible and non-reversible systems, respectively. Then, a necessary and sufficient complete controllability condition is provided. This condition, as well as the complete reachability criteria, is given in terms of the reachability gramian matrix. Equivalent modal criteria for reachability and controllability are established in the second part of the paper.     

On Near‐controllability of Discrete‐time Upper‐triangular Bilinear Systems with Applications to Controllability

Near‐controllability is defined for those systems that are uncontrollable but have a large controllable region. It is a property of nonlinear control systems introduced recently, and it has been demonstrated on two classes of discrete‐time bilinear systems. This paper studies near‐controllability of discrete‐time upper‐triangular bilinear systems, which are uncontrollable and are more general than the two classes mentioned. A necessary and sufficient condition for the systems in dimension two to be nearly controllable is presented, which covers the existing results. For the systems with high dimensions, necessary conditions and sufficient conditions of near‐controllability are provided, which generalize the existing results. In particular, the obtained near‐controllability results are applied to controllability of discrete‐time bilinear systems. An example also is given to demonstrate the effectiveness, which shows that the controllability problems of discrete‐time bilinear systems can be solved by near‐controllability.     

定常2-D系统控制能量受限下的完全能控性

本文研究了定常2-D系统Roesser模型在控制能量受限下的完全能控性,得到了一个 充分必要条件,并对一种特殊的2-D可分离分母系统给出了控制能量受限下完全能控的一种 非常简洁的代数条件.     

Reachability and controllability of discrete-time linear periodic systems

In this paper, we consider discrete-time linear systems with periodic coefficients. Two necessary and sufficient conditions for complete controllability and reachability are given. The conditions are stated in terms of the reachability Gramian and hold for both reversible and nonreversible systems.     

Structured time-delay systems: A graph approach

In this paper, linear structured systems with delays are defined and a simple graph representation for these systems is given. Then, the generic controllability of time-delay systems is introduced and a graph criterion for controllability is provided. The generic row-by-row decoupling problem without prediction of such systems is then studied and graphical necessary and sufficient solvability conditions for this problem is derived.     

Necessary and sufficient conditions for the controllability andobservability of a class of linear, time-invariant systems with intervalplants

We establish necessary and sufficient conditions for the controllability of single-input/multi-output linear time-invariant systems with interval plants and for the observability of multi-input/single-output linear time-invariant systems with interval plants. In arriving at our results, we determine allowable plant uncertainty bounds for controllability and observability. Two specific examples are considered to demonstrate the applicability of our results     

Block Decoupling by Precompensation Revisited

The block decoupling problem by admissible dynamic precompensation for LTI systems is considered. Admissibility refers to the preservation of the class of controlled output trajectories, i.e. functional output controllability is concerned, which is more demanding than just pointwise output controllability. This problem has been solved by Hautus and Heyman, within a transfer function matrix approach. Different new equivalent solvability conditions in terms of controllability subspaces, transfer function matrices or matrix pencils are given. One of these conditions (expressed in the input space) is at the origin of new necessary and sufficient conditions for block decoupling by general precompensation (possibly non admissible and nonsquare), in the wider sense of Basile and Marro     

Relative controllability of nonlinear systems with delays in control

Relative controllability of nonlinear time-varying systems with time-variable delays in control is considered. Using Schauder's fixed point theorem, sufficient conditions for global relative controllability are given. The results obtained are a generalization of Davison [3], and Klamka [7].     

Fractional variable order discrete-time systems,their solutions and properties

In this paper, fractional variable order discrete state-space systems based on different definitions of fractional variable order difference are investigated.The general solution of these systems is derived. Moreover, necessary and sufficient conditions for reachability and observability are given and proven. The sufficient conditions for controllability are proposed too.     

网络控制系统的能控性和能观性

给出了网络控制系统的定义，并基于线性时不变系统的被控对象，建立了传感器为时钟驱动，控制器和作动器为事件驱动时长时滞网络控制系统的数学模型，对网络控制系统的均值能控、均方能控、均值能观及均方能观作了定义，得到了网络控制系统能控的充分或必要条件及能观的充要条件．     

Controllability of multi-agent systems with time-delay in state and switching topology

In this article, the controllability issue is addressed for an interconnected system of multiple agents. The network associated with the system is of the leader–follower structure with some agents taking leader role and others being followers interconnected via the neighbour-based rule. Sufficient conditions are derived for the controllability of multi-agent systems with time-delay in state, as well as a graph-based uncontrollability topology structure is revealed. Both single and double integrator dynamics are considered. For switching topology, two algebraic necessary and sufficient conditions are derived for the controllability of multi-agent systems. Several examples are also presented to illustrate how to control the system to shape into the desired configurations.     

Local controllability of nonlinear systems

The local controllability of control systems with an arbitrary number of controls is considered, first on an open set and then at a given point; necessary conditions are derived concerning the Lie algebra T′ generated by the input vector fields, and applied to gradient systems.The main results are a geometric sufficient condition for local controllability at a point, and an equivalent condition based on the computation of Lie brackets, assuming T′ to be (n − 1)-dimensional.     

Controllability and observability for time‐varying switched impulsive controlled systems

This paper is concerned with the controllability and observability for linear time‐varying switched impulsive systems. First, some new results about the variation of parameters for time‐varying switched impulsive systems are derived. Then less conservative sufficient conditions and necessary conditions for state controllability and observability of such systems are established. And for such system without impulsive control input, sufficient and necessary conditions for controllability and observability are derived. Furthermore, corresponding criteria applied to time‐varying impulsive systems are also discussed and examples are presented to show the effectiveness of the proposed results. Copyright © 2009 John Wiley & Sons, Ltd.