Aperiodic Systems Research Articles

Stability analysis of aperiodic impulsive delay systems using sum of squares approach

AbstractThe stability problem of aperiodic impulsive delay systems with unstable continuous and discrete dynamics is addressed in this article. New delay‐dependent stability conditions are proposed by employing a clock‐dependent Lyapunov–Krasovskii‐like functional composed of a Lyapunov–Krasovskii functional and a high‐order polynomial matrix function. The stability conditions are then solved using sum of squares programming techniques, yielding less conservative results than the looped‐functionals approach. Finally, the simulation results demonstrate the effectiveness of the results.

Enhanced elastic stability of a topologically disordered crystalline metal–organic framework

By virtue of their open network structures and low densities, metal–organic frameworks (MOFs) are soft materials that exhibit elastic instabilities at low applied stresses. The conventional strategy for improving elastic stability is to increase the connectivity of the underlying MOF network, which necessarily increases the material density and reduces the porosity. Here we demonstrate an alternative paradigm, whereby elastic stability is enhanced in a MOF with an aperiodic network topology. We use a combination of variable-pressure single-crystal X-ray diffraction measurements and coarse-grained lattice-dynamical calculations to interrogate the high-pressure behaviour of the topologically aperiodic system TRUMOF-1, which we compare against that of its ordered congener MOF-5. We show that the topology of the former quenches the elastic instability responsible for pressure-induced framework collapse in the latter, much as irregularity in the shapes and sizes of stones acts to prevent cooperative mechanical failure in drystone walls. Our results establish aperiodicity as a counter-intuitive design motif in engineering the mechanical properties of framework structures that is relevant to MOFs and larger-scale architectures alike.

Improved looped-functional approach for dwell-time-dependent stability analysis of impulsive systems

This paper studies the dwell-time-dependent stability analysis of impulsive systems by using a new time-square-dependent looped-functional. Based on the Lyapunov theory and two-sided looped-functional method, a time-square-dependent looped-functional is proposed, which fully utilizes the information of both the intervals [tk,t] and [t,tk+1]. Then, by applying Jensen’s inequality and free-matrix-based inequalities to deal with integral terms in the functional derivatives, sufficient stability conditions in the form of linear matrix inequality are derived for periodic and aperiodic impulsive systems. Finally, numerical examples and simulation tests are given to illustrate the effectiveness and superiority of the proposed method.

Light switching between localized and delocalized states in chiral moiré-like photonic lattice

Abstract We constructed a chiral moiré-like lattice pattern by the interference between two sets of plane waves and two circular polarized beams. The study shows that the intensity distributions of the lattice pattern are a moiré-like structure in the transverse direction and a spiral structure in the longitudinal direction. By tuning the relative rotation angle between two sets of beams, moiré-like lattice pattern can be switched between periodic to aperiodic systems. Further, we numerically study the impacts of relative rotation angle, the screw pitch of the lattice waveguide, the width and incident direction of the probe beam on the light behavior in chiral moiré-like photonic lattice fabricated with photon-induction method. It turns out that light propagation can be switched between localization and delocalization. Our study enriches the physical content of moiré-like lattice patterns and paves a novel way to the light modulation in photonic lattices.

Research progress on topological states in aperiodic systems

最近，拓扑物态的相关研究已经从晶体扩展到非周期系统，例如准晶和非晶体系. 本文结合我们研究组近期的工作，简要介绍了在非周期系统拓扑物态和拓扑相变方面的若干研究进展. 首先，我们概括了非周期系统中拓扑物态的研究背景. 随后以量子自旋霍尔效应为例，具体介绍了拓扑物态在准晶体系中的推广. 由于非周期体系缺乏平移对称性，因此拓扑不变量的实空间计算方法成为判定非周期体系拓扑态的有效工具. 在此基础上，我们进一步讨论了准晶中独有的拓扑态，提出了与准晶特殊旋转对称性相容的高阶拓扑态，并构建了描述准晶中分数拓扑角模的有效模型. 此外，我们介绍了非晶系统中的拓扑物态，重点探究了由于结构非晶化导致的拓扑相变。最后，我们对非周期拓扑物态的相关研究和未来可能的发展方向进行了总结和展望。

Magnetic dynamics and nonreciprocal excitation in uniform hedgehog order in icosahedral 1/1 approximant crystal

The hedgehog state in the icosahedral quasicrystal (QC) has attracted great interest as the theoretical discovery of topological magnetic texture in aperiodic systems. The revealed magnetic dynamics exhibits nonreciprocal excitation in the vast extent of the reciprocal lattice {varvec{q}}-energy omega space, whose emergence mechanism remains unresolved. Here, we analyze the dynamical as well as static structure of the hedgehog order in the 1/1 approximant crystal (AC) composed of the cubic lattice with spatial inversion symmetry. We find that the dispersion of the magnetic excitation energy exhibits nonreciprocal feature along the N-P-Gamma line in the {varvec{q}} space. The dynamical structure factor exhibits highly structured intensities where high intensities appear in the high-energy branches along the Gamma-H line and the P-Gamma-N line in the {varvec{q}} space. The nonreciprocity in the 1/1 AC and also in the QC is understood to be ascribed to inversion symmetry breaking by the hedgehog ordering. The sharp contrast on the emergence regime of nonreciprocal magnetic excitation between the QC and the 1/1 AC indicates that the emergence in the vast {varvec{q}}-omega regime in the QC is attributed to the QC lattice structure.

Bandwidth-Aware Event-Triggered Load Frequency Control For Power Systems Under Time-Varying Delays

Networked Load frequency control (LFC) inevitably subjects to constrained bandwidth and time delays. However, the network traffic essentially varies from time to time and then the bandwidth status may be only busy during some specific peak periods but idle during others. This paper proposes a bandwidth-aware event-triggered load frequency control (ETLFC) scheme for multi-area power systems under time-varying delays by incorporating bandwidth-aware adaptive regulation scheme into decentralized ETLFC scheme. Different from existing time-delay ETLFC model, a model of aperiodic sampled-data system with time delay is constructed for the ETLFC scheme to obtain less conservative stability and co-design conditions based on looped Lyapunov functional. The regulation scheme is designed to adaptively adjust the threshold parameter of the ETLFC scheme based on variable bandwidth status and system output change in order to lessen communication burden while ensuring desired control performance. For fixed output change, a better bandwidth status generates a smaller threshold parameter to raise the triggering frequency in order to utilize available communication resources to improve control performance rather than unilaterally reduce data transmissions in the existing research. Case studies are undertaken by an IEEE 39-bus test system to show the effectiveness and advantages of the proposed scheme.

Stability and reachability analysis for aperiodic sampled-data systems

In this paper, the sampled-data intervals comparison under stability criteria and reachable set estimation of aperiodic sampled-data systems are studied by means of uniform fragmented loop-based Lyapunov functional method. Firstly, by dividing the corresponding sampled-data intervals into sub-intervals on average, using fragmentation of system state and symbolic fragmentation expression, uniform fragmented loop-based Lyapunov functional is constructed. Furthermore, for the proposed stability criterion, a criterion for obtaining a larger upper bound of sampled-data is given in combination with the free weight matrix. Secondly, the reachable set estimation problem for aperiodic sampled-data systems with unit-peak bounded disturbance is investigated. Finally, the effectiveness of the proposed method is demonstrated by using numerical simulation and the experiment of vehicle active suspension device, it is also fully demonstrated that the proposed method can obtain the larger upper bound on the sampled-data interval and the more accurate reachable set estimation results.

Aperiodic switching event-triggered stabilization of continuous memristive neural networks with interval delays

The stabilization problem is studied for memristive neural networks with interval delays under aperiodic switching event-triggered control. Note that, most of delayed memristive neural networks models studied are discontinuous, which are not the real memristive neural networks. First, a real model of memristive neural networks is proposed by continuous differential equations, furthermore, it is simplified to neural networks with interval matrix uncertainties. Secondly, an aperiodic switching event-trigger is given, and the considered system switches between aperiodic sampled-data system and continuous event-triggered system. Thirdly, by constructing a time-dependent piecewise-defined Lyapunov functional, the stability criterion and the feedback gain design are obtained by linear matrix inequalities. Compared with the existing results, the stability criterion is with lower conservatism. Finally, two neurons are taken as examples to ensure the feasibility of the results.

High Minimum Inter-Execution Time Sigmoid Event-Triggered Control for Spacecraft Attitude Tracking With Actuator Saturation

This paper investigates the attitude tracking problem for spacecraft with limited communication, network congestion, unknown model parameters, actuator saturation, and external disturbances. To alleviate communication load, a novel sigmoid event-triggered mechanism is proposed with the special ability to guarantee a high minimum inter-execution time to avoid network congestion like package loss or time delay effectively. A neural network-based adaptive control algorithm is designed to deal with unknown model parameters. Besides, the problem of actuator saturation is tackled by introducing a dynamic loop gain function-based approach. System stability is proved by Lyapunov stability analysis and the high minimum inter-event time is substantiated by Zeno Behavior analysis with explanatory remarks. Numerical simulation results also show that a high minimum inter-event time and a high average inter-event time can be realized on the premise of high attitude tracking accuracy. Compared with all the previous studies, the ratio of the minimum inter-execution time to the average minimum inter-execution time has been improved by nearly 10 times with the proposed approach. Note to Practitioners—This paper was motivated by the problem of spacecraft attitude takeover control, but it also applies to other aperiodic discrete-time control systems. Existing event-triggered control methods have solved the problem of limited communication for attitude takeover control of spacecraft by reducing the number of times wireless communication is required. This paper proposes a new method for realizing quasi-periodic control with a large time gap between any two consistent control impulses using a hyperbolic tangent function or another sigmoid function in an event-triggered mechanism. The proposed sigmoid event-triggered mechanism (ETM) can magnify the event-triggered threshold dozens of times in a short time to avoid unnecessary frequent triggering without decreasing the precision of control. It’s feasible to employ the proposed sigmoid ETM to deal with limited communication and network congestion in other network control systems that are constructed with similar dynamic structures. Furthermore, it would be marvelous if we could transform this sigmoid ETM into a high-efficiency decision-making mechanism in some control systems without using a wireless network. Now we are studying how to realize orbital-attitude (maneuver) control with a relatively average time interval and fewer times of orbit transfer by using the proposed sigmoid ETM. Besides, to further improve the system performance, we are also seeking to further increase the ratio of the minimum inter-execution time to the average inter-execution time. For the purpose of a more even distribution of the triggering events on the time axis, we may modify the proposed sigmoid event-triggered method or associate it with other methods.

Approach to the synthesis of an aperiodic robust automatic control system based on the gradient-speed method of Lyapunov vector functions

One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements

Covariant Lyapunov Vectors and Finite-Time Normal Modes for Geophysical Fluid Dynamical Systems

Dynamical vectors characterizing instability and applicable as ensemble perturbations for prediction with geophysical fluid dynamical models are analysed. The relationships between covariant Lyapunov vectors (CLVs), orthonormal Lyapunov vectors (OLVs), singular vectors (SVs), Floquet vectors and finite-time normal modes (FTNMs) are examined for periodic and aperiodic systems. In the phase-space of FTNM coefficients, SVs are shown to equate with unit norm FTNMs at critical times. In the long-time limit, when SVs approach OLVs, the Oseledec theorem and the relationships between OLVs and CLVs are used to connect CLVs to FTNMs in this phase-space. The covariant properties of both the CLVs, and the FTNMs, together with their phase-space independence, and the norm independence of global Lyapunov exponents and FTNM growth rates, are used to establish their asymptotic convergence. Conditions on the dynamical systems for the validity of these results, particularly ergodicity, boundedness and non-singular FTNM characteristic matrix and propagator, are documented. The findings are deduced for systems with nondegenerate OLVs, and, as well, with degenerate Lyapunov spectrum as is the rule in the presence of waves such as Rossby waves. Efficient numerical methods for the calculation of leading CLVs are proposed. Norm independent finite-time versions of the Kolmogorov-Sinai entropy production and Kaplan-Yorke dimension are presented.

Further Stability Criteria for Sampled-Data-Based Interval Type-2 Fuzzy Systems via a Refined Two-Side Looped-Functional Method

This article investigates the stability and stabilization problem of aperiodic sampled-data nonlinear systems in the framework of interval type-2 (IT-2) fuzzy models. First, by introducing two adjustable parameters and splitting the sampling intervals into four nonuniform intervals, a refined two-side looped-functional method is constructed to fully utilize inner state information during the whole aperiodic sampling interval. Simultaneously, the positive definiteness constraint for the individual matrix in Lyapunov–Krasovskii functional can be further relaxed. Then, via constructing a novel fuzzy Lyapunov–Krasovskii functional (FLKF) together with a fuzzy-dependent-switching scheme, the available features of fuzzy membership functions (FMFs) can be further taken into consideration to increase the design flexibility. Consequently, the stability condition and corresponding controller design approach for aperiodic sampled-data IT-2 fuzzy systems can be obtained with less design conservatism and larger sampling intervals. Finally, two simulation examples are employed to demonstrate the validity and superiority of the proposed method.

Resilient Control for Multiagent Systems With a Sampled-Data Model Against DoS Attacks

To reduce the computational burden and resist the denial-of-service (DoS) attacks, a resilient distributed sampled-data control scheme is proposed for multiagent systems. The agent states are sampled periodically by the sensors. DoS attacks disrupt the data communication from transmitters to controllers randomly or periodically with a limited duration time. Information on DoS attacks can be obtained by introducing novel logic processors embedded in corresponding controllers. Next, the problem of resilient control can be converted into one concerned with the upper and lower bound of the sampling interval of an aperiodic sampled-data control system. Some sufficient criteria for developing resilient distributed controllers are derived using the novel looped Lyapunov functional approach and the free-matrix-based inequality method. Finally, two illustrative examples, unmanned aerial vehicles and the two-mass-spring systems, are provided to demonstrate the efficiency of the proposed resilient distributed sampled-data control protocols against the DoS attacks.

Stability analysis of sampled-data systems with sector-bounded input nonlinearity

This work proposes a method for the stability analysis of aperiodic sampled-data control systems with sector and slope bounded input nonlinearities. The stability conditions are derived by using a hybrid system representation and a timer-dependent Lur'e type Lyapunov function. Considering a polynomial timer-dependence, the stability conditions are cast in sum-of-squares optimization problems aiming at computing the largest range of sampling intervals or the largest sector bounds on the nonlinearity for which the origin of the closed-loop system is globally asymptotically stable.

Thermoelectricity in a Quasiperiodic Lattice Beyond Nearest‐Neighbor Electron Hopping

AbstractA new route to obtain a large figure of merit (>1) is reported, for the first time, by considering a one‐dimensional quasiperiodic lattice where an electron can hop beyond usual nearest‐neighbor sites. A finite positional correlation is imposed among the constituent lattice sites, following the well‐known Aubry‐André‐Harper (AAH) form. In the presence of second‐neighbor hopping, the AAH lattice exhibits energy dependent mobility edge which plays the central role for efficient energy conversion. Employing a tight‐binding framework, all the thermoelectric quantities are computed based on the standard nonequilibrium Green's function formalism. The analysis can be utilized to investigate thermoelectric phenomena in similar kinds of other aperiodic systems possessing higher order electron hopping.

Wave localization in number-theoretic landscapes

We investigate the localization of waves in aperiodic structures that manifest the characteristic multiscale complexity of certain arithmetic functions with a central role in number theory. In particular, we study the eigenspectra and wave localization properties of tight-binding Schr\"{o}dinger equation models with on-site potentials distributed according to the Liouville function $\lambda(n)$, the M\"{o}bius function $\mu(n)$, and the Legendre sequence of quadratic residues modulo a prime (QRs). We employ Multifractal Detrended Fluctuation Analysis (MDFA) and establish the multifractal scaling properties of the energy spectra in these systems. Moreover, by systematically analyzing the spatial eigenmodes and their level spacing distributions, we show the absence of level repulsion with broadband localization across the entire energy spectra. Our study introduces deterministic aperiodic systems whose eigenmodes are all strongly localized in realistic finite one-dimensional systems and provides opportunities for novel quantum and classical devices of particular importance to cold-atom experiments in engineered speckle potentials and enhanced light-matter interactions.

Efficient Implementation of Density Functional Theory Based Embedding for Molecular and Periodic Systems Using Gaussian Basis Functions.

A practical and effective implementation of density functional theory based embedding is reported, which allows us to treat both periodic and aperiodic systems on an equal footing. Its essence is the expansion of orbitals and electron density of the periodic system using Gaussian basis functions, rather than plane-waves, which provides a unique all-electron direct-space representation, thus avoiding the need for pseudopotentials. This makes the construction of embedding potential for a molecular active subsystem due to a periodic environment quite convenient, as transformation between representations is far from trivial. The three flavors of embedding, molecule-in-molecule, molecule-in-periodic, and periodic-in-periodic embedding, are implemented using embedding potentials based on non-additive kinetic energy density functionals (approximate) and level-shift projection operator (exact). The embedding scheme is coupled with a variety of correlated wave function theory (WFT) methods, thereby providing an efficient way to study the ground and excited state properties of low-dimensional systems using high-level methods for the region of interest. Finally, an implementation of real time-time-dependent density functional embedding theory (RT-TDDFET) is presented that uses a projection operator-based embedding potential and provides accurate results compared to full RT-TDDFT for systems with uncoupled excitations. The embedding potential is calculated efficiently using a combination of density fitting and continuous fast multipole method for the Coulomb term. The applicability of (i) WFT-in-DFT embedding, in predicting the adsorption and excitation energies, and (ii) RT-TDDFET, in predicting the absorption spectra, is explored for various test systems.

Appointed-time guaranteed adaptive fault-tolerant attitude tracking for quadrotors with aperiodic data updating

In this paper, an appointed-time guaranteed adaptive fault-tolerant attitude tracking for quadrotors with aperiodic data updating is concerned, where inertial moment variation, extraneous disturbance and unknown actuator faults are simultaneously involved. An adaptive parameter estimation law is updated to identify the partial effectiveness loss of actuation and alleviate the estimation burden of suggested observer. Then through filtering manipulations upon aperiodic system states, a novel event-triggered unknown system dynamics estimator (ETUSDE) is developed to learn the remaining uncertainties with exponential error decaying and decreased updating cost, where an event-triggering criterion is incorporated to schedule the transmission instants for control behavior and angular rate, and the explicit formulation between estimation error upper boundary and design coefficients is derived. An appointed-time prescribed performance control (APPC) is introduced to allow for pregiven attitude behaviors. By fusion of adaptive law, ETUSDE and APPC, an adaptive event-triggered attitude control policy is synthesized that delivers appointed-time convergence, accurate steady response and decreased sampling burden. Meanwhile, Lyapunov analysis shows that all the error variables contained in the closed-loop system are ultimately uniformly bounded. Eventually, experiments on a quadrotor attitude test rig are conducted to confirm the superiorities of suggested control strategy.

Aperiodic two-layer energy management system for community microgrids based on blockchain strategy

Regulatory changes in different countries regarding self-consumption and growing public concern about the environment are encouraging the establishment of community microgrids. These community microgrids integrate a large number of small-scale distributed energy resources and offers a solution to enhance power system reliability and resilience. This work proposes a geographically-based split of the community microgrids into clusters of members that tend to have similar consumption and generation profiles, mimicking the most typical layout of cities. Assuming a community microgrid divided into clusters, a two-layer architecture is developed to facilitate the greater penetration of distributed energy resources in an efficient way. The first layer, referred as the market layer, is responsible for creating local energy markets with the aim of maximising the economic benefits for community microgrid members. The second layer is responsible for the network reconfiguration, which is based on the energy balance within each cluster. This layer complies with the IEC 61850 communication standard, in order to control commercial sectionalizing and tie switches. This allows the community microgrid network to be reconfigured to minimise energy exchanges with the main grid, without requiring interaction with the distributed system operator. To implement this two-layer energy management strategy, an aperiodic market approach based on Blockchain technology, and the additional functionality offered by Smart Contracts is adopted. This embraces the concept of energy communities since it decentralizes the control and eliminates intermediaries. The use of aperiodic control techniques helps to overcome the challenges of using Blockchain technology in terms of storage, computational requirements and member privacy. The scalability and modularity of the Smart Contract-based system allow each cluster of members to be designed by tailoring the system to their specific needs. The implementation of this strategy is based on low-cost off-the-shelf devices, such as Raspberry Pi 4 Model B boards, which operate as Blockchain nodes of community microgrid members. Finally, the strategy has been validated by emulating two use cases based on the IEEE 123-node system network model highlighting the benefits of the proposal.