On nearly-controllable subspaces of a class of discrete-time bilinear systems

If a linear time-invariant system is uncontrollable, then the state space can be decomposed as a direct sum of a controllable subspace and an uncontrollable subspace. In this paper, for a class of discrete-time bilinear systems which are uncontrollable but can be nearly controllable, by studying the nearly-controllable subspaces and defining the near-controllability index, the controllability properties of the systems are fully characterized. Examples are provided to illustrate the conceptions and results of the paper.     

Controllability of General Linear Discrete Multi-Agent Systems with Directed and Weighted Signed Network

This paper investigates the controllability of general linear discrete-time multi-agent systems with directed and weighted signed networks by using graphic and algebraic methods. The non-delay and delay cases are considered respectively. For the case of no time delay, the upper bound condition of the controllable subspace is given by using the equitable partition method, and the influence of coefficient matrix selection of individual dynamics is illustrated. For the case of single delay and multiple delays, the equitable partition method is extended to deal with time-delay systems, and some conclusions are obtained. In particular, some simplified algebraic criteria for controllability of systems with time delay are obtained by using augmented system method and traditional algebraic controllability criteria.

     

块对角可控规范型多输入线性系统及极点配置

基于向量空间的模结构分解和矩阵的有理标准形给出了定常多输入线性系统一类新的块对角可控规范型,其中的系统矩阵相似与一个块对角矩阵,该块对角矩阵类似于矩阵的有理标准形,与现在有的可控规范型比较,更容易反映系统的结构特征,证明步骤给出了求解方法。作为一个应用,讨论了定常多输入线性系统的极点配置问题,得到了反馈增益矩阵的一般表达式,此表达式中含有任意参数,此方法将多输入线性系统极点配置问题转化为个数为系统矩阵循环指数的单输入系统的极点配置问题,进而推导出确定一个反馈增益矩阵的最少元素个数即为系统的阶数。     

Research on controllability for a class of fractional-orderlinear control systems

1.INTRODUCTION Therealobjectsaregenerallyfractional[1],however,thecontrolsystemsusedsofarareallconsideredas integer ordersystems.Thereasonisthecomplexity andtheabsenceofadequatemathematicaltoolsfor fractional ordersystems.Fractionalcalculusisanatu ralextensionoftheclassicalmathematics.Thefrac tionalcalculustheorywasdevelopedbyalotofmath ematicians[2,3]andtheapplicationdomainsoffrac tionalcalculushaveincreasedsignificantly.Lasttwo decadestheknowledgewasappliedincontroltheory,whichconcerned…     

Conditional Congruence Closure over Uninterpreted and Interpreted Symbols

A framework for generating congruence closure and conditional congruence closure of ground terms over uninterpreted as well as interpreted symbols satisfying various properties is proposed. It is based on some of the key concepts from Kapur’s congruence closure algorithm (RTA97) for ground equations based on introducing new symbols for all nonconstant subterms appearing in the equation set and using ground completion on uninterpreted constants and purified equalities over interpreted symbols belonging to different theories. In the original signature, the resulting rewrite systems may be nonterminating but they still generate canonical forms. A byproduct of this framework is a constant Horn completion algorithm using which ground canonical Horn rewrite systems can be generated for conditional ground theories.

New efficient algorithms for generating congruence closure of conditional and unconditional equations on ground terms over uninterpreted symbols are presented. The complexity of the conditional congruence closure is shown to be O(n*log(n)), which is the same as for unconditional ground equations. The proposed algorithm is motivated by our attempts to generate efficient and succinct interpolants for the quantifier-free theory of equality over uninterpreted function symbols which are often a conjunction of conditional equations and need additional simplification. A completion algorithm to generate a canonical conditional rewrite system from ground conditional equations is also presented. The framework is general and flexible and is used later to develop congruence closure algorithms for cases when function symbols satisfy simple properties such as commutativity, nilpotency, idempotency and identity as well as their combinations. Interesting outcomes include algorithms for canonical rewrite systems for ground equational and conditional theories on uninterpreted and interpreted symbols leading to generation of canonical forms for ground terms, constrained terms and Horn equations.

     

Approximate Controllability for Degenerate Heat Equation with Bilinear Control

This paper investigates the nonnegative approximate controllability for the one-dimensional degenerate heat equation governed by bilinear control. Both non-controllability and approximate controllability are studied for the system. If the control is restricted to act on a fixed domain, it is not controllable. If the control is allowed to mobile, it is approximately controllable.     

A High-Order Fully Actuated System Approach for a Class of Nonlinear Systems

This paper utilizes the high-order fully actuated (HOFA) system approach to synthesize a class of nonlinear systems. First, the original nonlinear system can be rewritten in a quasi-linear form, which is more general than other nonlinear systems, such as strict-feedback systems. Based on a rank condition, the quasi-linear system can be transformed into a canonical form. Second, a simple transformation is adopted to convert the above canonical form into the HOFA model. Once an HOFA model is derived, the authors design a controller to make the closed-loop system a constant linear system with the desired eigenstructure. Finally, a numerical example illustrates the fitness and effectiveness of the proposed approach.

     

EXACT CONTROLLABILITY OF A CLASS OF DISTRIBUTED PARAMETER SYSTEMS

The exact controllability of a class of distributed parameter systems governedby Petrowsky equations is considered.On the basis of the Hilbert Uniqueness Methodproposed by J.L.Lions,it is found that the Petrowsky systems with Dirichlet boundarycontrol are exactly controllable.     

状态空间设计方法的CAD

本文介绍状态空间设计方法的CAD软件工具,通过化Yokoyama或Hessenberg能控、能观标准型,分析系统的能控性和能观性,给出了状态反馈极点配置及观测器设计和输出反馈极点配置设计。     

Safety Control of a Class of Fully Actuated Systems Subject to Uncertain Actuation Dynamics

Safety is an essential requirement for control systems. Typically, controlled mobile robots are subject to safety constraints, to which control laws in typical forms may not be directly applicable. This paper employs barrier function to describe safety constraints, analyzes the interaction between the barrier function and the uncertain actuation dynamics by employing the ideas of interconnected systems, and proposes a quadratic-programming-based integration of the control algorithms subject to the safety constraint for a class of fully actuated systems.

     

Controllability and observability of networked control systems with time-varying delays

The controllability and observability of networked control systems are studied. Aiming at the networked control system with time-varying delay, the sufficient and necessary conditions for complete controllability and complete observability of the system are presented, respectively. Because of Markov characteristic of the network-induced delay, in terms of stochastic theory, a sufficient and necessary condition for completely mean value controllability of networked control systems is obtained. Further, the conditions that the controllability and observability of networked control systems are equivalent to the initial time-invariant system are given. Controllability and observability realization indexes are also discussed, respectively. The numerical example demonstrates the effectiveness of the proposed theory.     

二维广义系统Roesser模型局部能达和局部能控性

研究了二维广义系统Roesser模型的性质,推导出了该系统的状态响应公式.给出了其在矩形区域上局部能达和局部能控的充分必要条件.同时,利用二维Z变换理论,给出了二维广义系统Roesser模型局部能达和局部能控的等价定义,并得出该模型相应的局部能达和局部能控的新的充分必要条件.     

Networked Learning Predictive Control of Nonlinear Cyber-Physical Systems

Cyber-physical systems integrate computing, network and physical environments to make the systems more efficient and cooperative, and have important and extensive application prospects, such as the Internet of things. This paper studies the control problem of nonlinear cyber-physical systems with unknown dynamics and communication delays. A networked learning predictive control scheme is proposed for unknown nonlinear cyber-physical systems. This scheme recursively learns unknown system dynamics, actively compensates for communication delays and accurately tracks a desired reference. Learning multi-step predictors are presented to predict various step ahead outputs of the unknown nonlinear cyber-physical systems. The optimal design of controllers minimises a performance cost function which measures the tracking error predictions and control input increment predictions. The system analysis leads to the stability criteria of closed-loop nonlinear cyber-physical systems employing the networked learning predictive control scheme. An example illustrates the outcomes of the proposed scheme.

     

挠性结构振动控制中压电致动器/敏感器的优化配置

针对挠性结构的主动振动控制问题,给出了粘贴有若干压电片的挠性梁的数学模型。基于结构模态的可控可观性,提出一种压电致动器/敏感器同位位置的优化方法。该方法利用模态在可控可观性子空间上的正交投影来反映可控可观性的测度,并根据各阶模态在系统输出中的相对重要程度加权模态可控可观测性测度,由此得到致动器/敏感器的优化配置指标。通过数学仿证明了该优化方法的有效性。     

Impulse Controllability and Impulse Observability of Stochastic Singular Systems

This paper discusses the impulse controllability and impulse observability of stochastic singular systems. Firstly, the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform. Secondly, the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory. Finally, an example is given to illustrate the effectiveness of the obtained theoretical results.     

On controllability for stochastic control systems when the coefficient is time-variant

<正> This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful algebraic criterion for stochastic control systems.Furthermore,when the stochasticsystems degenerate to deterministic systems,the algebraic criterion becomes the counterpart for thecomplete controllability of deterministic control systems.     

Controllability of Quantum Systems with SU(1, 1) Dynamical Symmetry

This paper presents sufficient and necessary conditions for the propagator controllability of a class of infinite-dimensional quantum systems with SU(1, 1) dynamical symmetry through the isomorphic mapping to the non-unitary representation of SU(1, 1). The authors prove that the elliptic condition of the total Hamiltonian is both necessary and sufficient for the controllability and strong controllability. The obtained results can be also extended to control systems with SO(2, 1) dynamical symmetry.     

Leader selection for strong structural controllability of single-integrator multi-agent systems

This paper addresses the leader selection problem for strong structural controllability (SSC) of multi-agent systems (MASs). For a path-bud graph, it is proved that only one leader is required to guarantee the SSC of MASs. For a special type of topologies, based on the partition of the topology into disjoint pathes and path-buds, it is proved that the MASs is strongly structurally controllable if the root nodes of the pathes are selected as leaders. For general topologies, an algorithm is provided to determine the agents that can behave as leaders. For some special topologies, the minimum number of leaders guaranteeing the robust strong structural controllability (RSSC) of MASs is also obtained. Two examples are given to verify the effectiveness of the results.     

On Almost Controllability of Dynamical Complex Networks with Noises

This paper discusses the controllability problem of complex networks. It is shown that almost any weighted complex network with noise on the strength of communication links is controllable in the sense of Kalman controllability. The concept of almost controllability is elaborated by both theoretical discussions and experimental verifications.