高阶系统方法—Ⅱ.能控性与全驱性

本文首先简述了基于状态空间模型的一阶动态系统的能控性进展, 指出了一阶系统方法中卡尔曼能控性体系的一些问题.然后证明了线性定常系统能控的充要条件是它能化成一个高阶全驱系统, 同时还在一定程度上将这一结果推广到非线性系统的情形.基于这一发现, 本文定义了一般动态系统的完全能控性, 明确其意义在于存在控制律使得闭环系统为一线性定常的高阶系统, 并且可以任意配置闭环特征多项式的系数矩阵, 同时还指出其多方面相关结论.     

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.     

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.     

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。     

广义系统的能控、能观性判别条件

该文讨论广义系统能控、能观性问题,给出了广义系统能控和能观性一种新的判别条件.     

二阶邻居协议下多智能体系统能控能观性保持

为了研究多智能体系统的一致性特点及能控、能观性保持策略,分析了具有时变拓扑结构的多智能体系统在一阶邻居协议和二阶邻居协议下的一致性速度,针对拓扑结构的特殊性,利用结构能控性性质和拉普拉斯矩阵第二小特征值与一致性速度之间存在的关系设计出一种使能控性和能观测性保持的控制策略。此外,得出多智能体系统在二阶邻居协议下,具有更快的一致性速度的结论。文中2个主要定理分别通过算例和仿真进行验证,算例和仿真结果与定理结论一致。     

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.     

复杂网络能控性鲁棒性研究进展

研究复杂网络能控性鲁棒性对包括社会网络、生物和技术网络等在内的复杂系统的控制和应用具有重要价值. 复杂网络的能控性是指: 可通过若干控制节点和适当的输入, 在有限时间内将系统状态驱动至任意目标状态. 能控性鲁棒性则是指在受到攻击的情况下, 复杂网络依然维持能控性的能力. 设计具有优异能控性鲁棒性的复杂网络模型和优化实际网络的能控性鲁棒性一直是复杂网络领域的重要研究内容. 本文首先比较了常用的能控性鲁棒性定义及度量, 接着从攻击策略的角度分析了3类攻击的特点及效果, 包括随机攻击、基于特征的蓄意攻击和启发式攻击. 然后比较了常见模型网络的能控性鲁棒性. 介绍了常用优化策略, 包括模型设计和重新连边等. 目前的研究在攻击策略和拓扑结构优化方面都取得了进展, 也为进一步理论分析提供条件. 最后总结全文并提出潜在研究方向.     

广义系统能控性的几个注记

本文首先给出了广义系统能控性与正常系统能控性的关系,并由此讨论了广义系统最优 经济结构综合问题及能控性程度的度量形式.最后给出了工程算例.     

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.     

On the approximate controllability of semilinear fractional differential systems

Fractional differential equations have wide applications in science and engineering. In this paper, we consider a class of control systems governed by the semilinear fractional differential equations in Hilbert spaces. By using the semigroup theory, the fractional power theory and fixed point strategy, a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems. The results are established under the assumption that the associated linear system is approximately controllable. Further, we extend the result to study the approximate controllability of fractional systems with nonlocal conditions. An example is provided to illustrate the application of the obtained theory.     

Approximate controllability of partial neutral functional differential systems of fractional order with state-dependent delay

We prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state-dependent delay in an abstract space. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the Krasnoselskii–Schaefer type fixed point theorem with the fractional power of operators. An example is provided to illustrate the main results.     

On The Exact Controllability of Impulsive Fractional Semilinear Functional Differential Inclusions

In this paper, we deal with the exact controllability for impulsive fractional semilinear functional differential inclusions in Hilbert spaces. Under suitable assumptions, the exact controllability of the control systems are formulated and proved. The main tools in our study rely on the fixed point theorem for multivalued maps due to Dhage associated with evolution systems.     

Graph-theoretic characterisations of structural controllability for multi-agent system with switching topology

This article considers the controllability problem for multi-agent systems. In particular, the structural controllability of multi-agent systems under switching topologies is investigated. The structural controllability of multi-agent systems is a generalisation of the traditional controllability concept for dynamical systems, and purely based on the communication topologies among agents. The main contributions of this article are graph-theoretic characterisations of the structural controllability for multi-agent systems. It turns out that the multi-agent system with switching topology is structurally controllable if and only if the union graph 𝒢 of the underlying communication topologies is connected (single leader) or leader–follower connected (multi-leader). Finally, this article concludes with several illustrative examples and discussions of the results and future work.     

The Controllability,Observability, and Stability Analysis of a Class of Composite Systems with Fractional Degree Generalized Frequency Variables

This paper is concerned with fundamental properties of a class of composite systems with fractional degree generalized frequency variables, including controllability, observability and stability. Firstly, some necessary and sufficient conditions are given to guarantee controllability and observability of such composite systems. Then we prove that the stability problem of such composite systems can be reduced to judging whether a fractional degree polynomial is stable. Finally, the stability analysis result is applied in the supervisory control of fractional-order multi-agent systems, and an example is provided to illustrate the effectiveness of the proposed methods.      

Controllability analysis for a class of linear quadratic conformable fractional game-based control systems

Controllability analysis for a class of linear quadratic conformable fractional game-based control systems (CFGBCSs) is investigated in this article. Supported by the definition and property of conformable fractional, the payoff function for linear quadratic CFGBCSs is proposed, and Nash equilibrium solution is obtained via variational method for Hamilton function correspondingly. Subsequently, the state transition matrix and controllability matrix are presented to deduce the sufficient and necessary conditions for the controllability of Nash equilibrium solution of time-varying linear quadratic CFGBCSs and time-invariant linear quadratic CFGBCSs, respectively. Finally, two numerical examples are furnished to justify the validity of the matrix full rank condition.     

信标可控性定义及问题

死锁是资源分配系统中极不希望出现的现象,目前死锁控制的一个重要的方法是信标控制法,信标控制法的基础是信标可控性的定义.对于普通Petri网,已有一个完善的信标可控性定义,而对于一般Petri网,这方面的工作还需改进和完善.近年来,学者们针对一般Petri 网及其子类提出了不少信标可控性定义,但这些定义并不完善,仍有大量的问题亟待解决.首先回顾了文献中的各个信标可控性定义,提出了两个新的信标可控性定义,然后从可控性定义的宽松程度、应用范围以及等价性等方面分析比较了现有的信标可控性定义优缺点.最后给出了今后的研究方向.     

Approximate controllability results for non-densely defined fractional neutral differential inclusions with Hille–Yosida operators

In this paper, we mainly focused the approximate controllability results for a class of non-densely defined fractional neutral differential control systems. First, we establish a set of sufficient conditions for the approximate controllability for a class of fractional differential inclusions with infinite delay where the linear part is non-densely defined and satisfies the Hille–Yosida condition. The main techniques rely on Bohnenblust– Karlin's fixed point theorem, operator semigroups and fractional calculus. Further, we extend the result to study the approximate controllability concept with nonlocal conditions. Finally, an example is also given for the illustration of the obtained theoretical results.     

高维拟线性抛物系统能控性的近期进展

本文综述高维拟线性抛物型方程、拟线性复Ginzburg-Landau方程以及只含一个控制变量的高维耦合拟线性抛物型方程组的能控性方面的一些近期的结果.通过使用不动点技术,采用主部具有C1系数的线性抛物型方程或方程组一些新的精细的Carleman估计.这一方法的要点是在古典解的框架下考虑能控性问题,并且当给定的数据具有一定的正则性时,线性抛物型方程或方程组在H¨older空间中来选取控制函数.利用类似的方法,还建立了拟线性抛物型方程不灵敏控制的存在性,其关键是将不灵敏问题转化为由拟线性抛物型方程和线性抛物型方程构成的耦合方程组在单个控制下一个非标准的能控性问题.     

On the Controllability of Anomalous Diffusions Generated by the Fractional Laplacian

This paper introduces a “spectral observability condition” for a negative self-adjoint operator which is the key to proving the null-controllability of the semigroup that it generates, and to estimating the controllability cost over short times. It applies to the interior controllability of diffusions generated by powers greater than 1/2 of the Dirichlet Laplacian on manifolds, generalizing the heat flow. The critical fractional order 1/2 is optimal for a similar boundary controllability problem in dimension one. This is deduced from a subsidiary result of this paper, which draws consequences on the lack of controllability of some one-dimensional output systems from Müntz–Szász theorem on the closed span of sets of power functions.