Controllability of discrete-time inhomogeneous bilinear systems with real spectrum: Algebraically verifiable criteria

One of the drawbacks of the controllability theory for nonlinear systems is that most existing controllability criteria are not algebraically verifiable, which makes them difficult to apply especially if the system dimension is high. Thus, it is a significant task to seek algebraically verifiable controllability criteria for nonlinear systems. In this paper, we study controllability of discrete-time inhomogeneous bilinear systems. In the classical results on controllability of such systems, a necessary condition is that the linear part has to be controllable. However, we will show that this condition is in fact not necessary for controllability. Specifically, we first define the spectrum for discrete-time inhomogeneous bilinear systems and reveal that the spectrum is a fundamental property which is very useful in investigating the controllability problems. We then present controllability criteria for the systems with real spectrum, which are algebraically verifiable. Furthermore, we also provide algorithms for the controllable systems to compute the exact or approximated control inputs to achieve the transition between any given pair of states. The presented controllability criteria and algorithms work for the systems in any finite dimension and are easy to implement. More importantly, through our controllability criteria, we reveal that controllability of the linear part is not necessary for discrete-time inhomogeneous bilinear systems to be controllable. Examples are given to illustrate the presented algebraic controllability criteria.     

A variational method for the numerical simulation of a boundary controllability problem for the linear and semilinear 1D wave equations

We pursue the numerical implementation of a boundary controllability problem for the 1D wave equation based on a recent variational approach to deal with such situations that consists in analyzing an error functional defined for feasible functions complying with appropriate initial, boundary, and final constraints. The nature of such scheme, as a minimization process for a certain error functional, leads to a natural numerical implementation by using typical descent algorithms. Our aim here is to explore the basic ingredients to set up such practical numerical approximations which allow us to address linear and semilinear equations with the same numerical scheme.     

Algebraic criterion for robust controllability of continuous linear time-delay systems with parametric uncertainties

The robust controllability problem for the continuous linear time-delay systems with structured parametric uncertainties is studied in this paper. A new sufficient algebraic criterion for the robust controllability of uncertain linear time-delay systems is established. The proposed sufficient condition can provide the explicit relationship of the bounds on system uncertainties for guaranteeing the controllability property. Three numerical examples are given to illustrate the application of the proposed sufficient algebraic criterion and to compare the results with those obtained from the approaches in the literature.     

Group controllability of two-time-scale multi-agent networks

As a basic concept in modern control theory, controllability reveals the fundamental structural characteristics of a dynamic system, and it also plays an important part in the analysis and control of a dynamic system. With the increasing complexity of multi-agent systems, the multi-agent networks can be divided into some subnetworks in terms of time scales. This paper concentrates on the group controllability of two-time-scale multi-agent networks, establishes the necessary and sufficient criterion of group controllability based on singular perturbation methods, and deduces easy-to-use group controllability criteria by using matrix theory and graph theory. Lastly, a simulation example is presented to illustrate the effectiveness of the proposed methods.     

Balanced truncation for discrete time-delay systems via the interpretation of system energy

In this paper, the balanced truncation method is investigated for discrete time-delay systems. We show that the energy associated with the system controllability and observability can be characterized via the delay Lyapunov matrices, similar to the case of continuous time-delay systems. Then, we balance the system via a coordinate transformation in order to retain the delay structure of systems naturally. In this way, the balanced truncation method is conducted to obtain structure-preserving reduced models. Further, we provide an efficient process to compute a low-rank approximation to delay Lyapunov matrices based on the equivalent expression of discrete time-delay systems, which enables an approximate but fast execution of the proposed method. The stability of reduced models is also discussed in the paper. Finally, numerical examples are simulated to verify the feasibility and efficiency of the proposed method.     

The impact of graph symmetry on the number of driver nodes in complex networks

This study investigates on a strong correlation between complex network (CN) controllability (characterized by the number of required driver nodes) and graph symmetry (described by automorphism groups) in undirected and unweighted networks. Based on the properties of permutation products of elementary automorphisms, novel necessary conditions for CN controllability are presented which are computationally more effective than previous method. In addition, a novel index of symmetry is proposed upon which a more meaningful understanding of symmetry impact on CN controllability can be comprehended. Based on this new index, a modification strategy is suggested aiming to satisfy CN controllability with a lower number of driver nodes. The study shows that the proposed modification approach can result in a minimal set of driver nodes with a reasonable computational complexity. Further, the critical components of complex networks, in terms of their impact on the number of required driver nodes, are identified. The results of the proposed methodologies have been verified for several synthetic and real test systems including small, medium, and large power networks.     

Sampling and control of switched linear systems

In this paper, we address the sampling and control issues for switched linear systems. Under synchronous switching and piecewise constant control, a continuous-time switched system is naturally related to a discrete-time sampled-data system. We prove that, with almost any sampling rate, the controllable subspace will be preserved for a switched linear system. We also investigate the possibility of achieving controllability using regular switching mechanisms. We show that, to achieve controllability for a switched linear system, it is sufficient to use cyclic and synchronous switching paths and constant control laws.     

Trajectory controllability of nonlinear integro-differential system

A stronger concept of complete (exact) controllability which we call Trajectory Controllability is introduced in this paper. We study the Trajectory Controllability of an abstract nonlinear integro-differential system in the finite and infinite dimensional space setting.     

On direct controllability of discrete time jump linear system

In this paper we consider a problem of controllability of discrete time linear system with randomly jumping parameters which can be described by finite state Markov chain. Necessary and sufficient conditions for existence of control which governs the system from any initial conditions to zero, from zero initial condition to any final value and from any initial condition to any final value in given time and with probability one are given. The relations between such kinds of controllability and stochastic stabilizability are discussed.     

Stability and controllability of fuzzy singular dynamical systems

This paper is assigned to study the stability and controllability of fuzzy singular dynamical systems. Some new notions such as granular fuzzy matrix norm, the algebraic operations on the space of fuzzy matrices, fuzzy equilibrium point, and the granular fuzzy transfer function of fuzzy singular dynamical systems are introduced. Furthermore, by presenting some theorems proved in this paper, the fuzzy solutions of fully fuzzy singular dynamical systems are obtained. Moreover, some new notions regarding the analysis of the stability of fuzzy singular dynamical systems are given. The stability analysis underlies the concepts of fuzzy stable, fuzzy critical stable, and fuzzy unstable singular dynamical systems. Besides using the notions of controllability of the fuzzy slow and fast subsystems, the concept of granular controllability of the fuzzy singular dynamical system is investigated.     

On controllability of discrete-time bilinear systems

In this paper, necessary and sufficient conditions for the controllability of a class of discrete-time bilinear systems are proposed, which extend the existing results and show that the controllability counterexample in [1] that is derived by Euler discretization of an uncontrollable bilinear system, is a special case of the necessary and sufficient conditions.     

数值分析教学中的一般科学方法

数值分析研究的对象是根据数学模型提出求解的数值计算方法,是信息与计算科学专业重要的专业课,同时也是工科研究生专业必修学位课,在科学与工程计算中应用广泛。在教学中,数值分析与哲学中的方法论有相通相融之处,由此归纳出其中的一般科学方法即化归法、归纳与演绎结合法、类比推广法等,用于指导教学和学生的数学建模工作,取得了较好的效果。     

Boron doping-induced interconnected assembly approach for mesoporous silicon oxycarbide architecture

Despite desirable progress in various assembly tactics, the main drawback associated with current assemblies is the weak interparticle connections limited by their assembling protocols. Herein, we report a novel boron doping-induced interconnection-assembly approach for fabricating an unprecedented assembly of mesoporous silicon oxycarbide nanospheres, which are derived from periodic mesoporous organosilicas. The as-prepared architecture is composed of interconnected, strongly coupled nanospheres with coarse surfaces. Significantly, through delicate analysis of the as-formed boron doped species, a novel melt-etching and nucleation-growth mechanism is proposed, which offers a new horizon for the developing interconnected assembling technique. Furthermore, such unique strategy shows precise controllability and versatility, endowing the architecture with tunable interconnection size, surface roughness and switchable primary nanoparticles. Impressively, this interconnected assembly along with tunable surface roughness enables intrinsically dual (both structural and interfacial) stable characteristics, achieving extraordinary long-term cycle life when used as a lithium-ion battery anode.     

Finite-time controllability and stabilization of probabilistic logical systems with state-dependent constraint via subset transition method

Constraints are very common for practical control systems. For logical systems, the existing technique of pre-feedback is an effective way of treating state-dependent constraints in control when the state is measurable. However, it is inapplicable for the case when measurement information is not available. In this situation, in order for the control input to not violate the state-dependent constraint, the control at each step must be selected from the common admissible controls of all possible states. Motivated by this observation, in this study, we propose a novel technique, termed the subset transition method, for finite-time controllability and stabilization of probabilistic logical dynamic control system (PLDCS) with a state-dependent control constraint. The main idea of this method is to construct an unconstrained deterministic logical control system over the power set of the state space, called the subset transition system (SubSTS), characterizing the transitional dynamics between subsets under common admissible controls. We prove that a control sequence is admissible with respect to all states in an initial subset if and only if it does not steer the SubSTS from the initial subset to the empty set. Based on this, necessary and sufficient conditions for set controllability and set stabilizability are obtained. Examples are presented to demonstrate the application of the obtained results.     

Null controllability of some nonlinear degenerate 1D parabolic equations

The main goal of the present paper is twofold: (i) to establish the well-posedness of a class of nonlinear degenerate parabolic equations and (ii) to investigate the related null controllability and decay rate properties. In a previous step, we consider an appropriate regularized system, where a small parameter α is involved. More precisely, the usual nonlinear term b(x)uu_x is replaced by b(x)zu_x, where $z={(\text{Id}.?{\alpha }^{2}A)}^{?1}u$ and A is a Poisson–Dirichlet operator. We investigate the behavior of the null controls and their associated states as α → 0.     

Experimental verification of Faradaic charging in ac electrokinetics

This paper investigates the phenomenon of Faradaic charging in ac electrokinetics. Faradaic reactions were suggested as a key effect responsible for the reversal of pumping direction in ac micropumps. However, this hypothesis has yet to be proven convincingly and directly. Here we present an ion detection strategy to determine the production of ions through Faradaic hydrolytic reactions originating from direct application of voltage to electrolytic solutions during ac electrokinetics. Experiments were performed with symmetrical planar electrodes aligned along a microfluidic channel. Fluorescein, a pH-dependent dye, was employed as the pH indicator for the detection of ion production. Images were captured for analysis at various voltage levels. From analyzing the fluorescence intensity and its distribution, it can be concluded that the production of ions from hydrolytic reactions takes place and increases with the ac voltage. The coefficient of deviation indicates a significant enhancement at ac voltage above 11 V_pp. Lastly, we demonstrate a strategy using dc-biased ac electrokinetics to achieve controllability in direction and magnitude of the net fluid flow in pumping application.     

Overcoming backstepping limitations via a novel MIMO non-affine-in-control convex optimization technique

Limitations of the standard backstepping control technique are overcome in this paper by yielding global conditions for regional ones; specifically, flexible cascade arrangements that do not require the system to be put in a pure- or strict-feedback form to ensure controllability beforehand, handling of nonlinear MIMO blocks without invertible input distribution matrices, calculation of virtual and real control laws regardless of the non-affine-in-control nature of subsystems, and systematic numerical synthesis of Lyapunov-based control laws at each step of the cascade connection via linear matrix inequalities. All these benefits derive from exploiting exact convex rewriting of nonlinear terms, splitting available and non-available signals for control implementation, and applying the direct Lyapunov method to cast conditions as a convex optimization problem. Examples of academic and practical interest illustrate the advantages of the novel methodology over former approaches.     

高校网络舆情的控制与引导

高校网络舆情具有突发性、情绪化、影响广、易控制等特点,目前的控制和引导方式存在响应慢、指令多、投入少等问题;要预防和干预高校网络舆情突发性事件,需要构建包括三级工作体系、两级报送体系和一支高素质团队的快速响应机制及快速收集、紧急应对、迅速联动与及时反馈4个部分的快速响应流程;通过快速响应机制和流程采用事前干预、网上干预和网后干预等方法实施干预.     

Structural aspects of controllability and observability—I. tensorial aggregation

The classical criteria for controllability and observability are given a tensorial formulation which is then extended into Boolean form directly related to a digraph interpretation of system structure. This is examined in detail with particular reference to group theoretic aspects, invariant properties under transformation, the term rank test and the existence of zero eigenvalues.Within this framework the structural design concepts of potential controllability and observability are presented in generalised terms.