First-order Integrator Research Articles

Radial-Angular Singularity Cancellation Transformations Derived by Variable Separation

The variable separation method is utilized to construct new radial-angular- ${R^n}$ coordinate transformation schemes for the singularity cancellation technique. Derived from the concept of achieving an ideal Jacobian of the transformations and with different parameter settings in the variable separation method, a new augmented radial-angular- ${R^1}$ transformation, new radial-angular- ${R^2}$ , and radial-angular- ${R^2}$ -cosh transformations, as well as a new radial-angular- ${R^3}$ , an augmented radial-angular- ${R^3}$ and an arcsinh- ${R^3}$ transformation are introduced. The proposed ${R^2}$ and ${R^3}$ transformations are efficient and applicable to all types of near-singular kernels occurring in the method of moments (MoM) solution of electromagnetic surface integral equations, whereas the ${R^1}$ transformation is only suitable for the first-order singular integrals. The newly proposed transformation schemes are verified and they are also applied to deformed triangles, where good performances are still achieved.

Time-Causal and Time-Recursive Spatio-Temporal Receptive Fields

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, based on a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about (i) parameterizing the intermediate temporal scale levels, (ii) analysing the resulting temporal dynamics, (iii) transferring the theory to a discrete implementation, (iv) computing scale-normalized spatio-temporal derivative expressions for spatio-temporal feature detection and (v) computational modelling of receptive fields in the lateral geniculate nucleus (LGN) and the primary visual cortex (V1) in biological vision. We show that by distributing the intermediate temporal scale levels according to a logarithmic distribution, we obtain much faster temporal response properties (shorter temporal delays) compared to a uniform distribution. Specifically, these kernels converge very rapidly to a limit kernel possessing true self-similar scale-invariant properties over temporal scales, thereby allowing for true scale invariance over variations in the temporal scale, although the underlying temporal scale-space representation is based on a discretized temporal scale parameter. We show how scale-normalized temporal derivatives can be defined for these time-causal scale-space kernels and how the composed theory can be used for computing basic types of scale-normalized spatio-temporal derivative expressions in a computationally efficient manner.

Vibration suppression of distributed parameter flexible structures by Integral Consensus Control

Integral Consensus Control (ICC) is proposed and implemented in this paper for the first time, as a novel approach for vibration control in distributed parameter flexible structures. The ICC consists of multiple parallel first-order lossy integrators, with the goal of targeting all major participating resonant modes in the oscillation of the structure. The vibration control design is taken to a different level, by integrating the concept of consensus control design into the new dynamics. Each control patch on the flexible structure is considered as a node of a network, and a communication topology with consensus control terms are augmented in the controller design dynamics. The result is an effective vibration controller, which is also robust to failures and inconsistencies in the control system. A cantilever is used as a sample flexible structure to investigate the control method. Multi-agent representation of the system, state estimator dynamics and the ICC model are designed for the structure. Extensive numerical simulations have been conducted to show the suppression performance of the ICC under different input disturbances. A comparative study is presented to show the advantage of the decentralized design over the conventional centralized approach. The new consensus control design provides new possibilities to vibration control problems, where an effective, robust and synchronized suppression is needed.

Study of interdigitated electrode arrays using experiments and finite element models for the evaluation of sterilization processes.

In this work, a sensor to evaluate sterilization processes with hydrogen peroxide vapor has been characterized. Experimental, analytical and numerical methods were applied to evaluate and study the sensor behavior. The sensor set-up is based on planar interdigitated electrodes. The interdigitated electrode structure consists of 614 electrode fingers spanning over a total sensing area of 20 mm2. Sensor measurements were conducted with and without microbiological spores as well as after an industrial sterilization protocol. The measurements were verified using an analytical expression based on a first-order elliptical integral. A model based on the finite element method with periodic boundary conditions in two dimensions was developed and utilized to validate the experimental findings.

Consensus Analysis of Heterogeneous Multi-Agent Systems with Time-Varying Delay

This paper studies consensus and \(H_\infty\) consensus problems for heterogeneous multi-agent systems composed of first-order and second-order integrator agents. We first rewrite the multi-agent systems into the corresponding reduced-order systems based on the graph theory and the reduced-order transformation. Then, the linear matrix inequality approach is used to consider the consensus of heterogeneous multi-agent systems with time-varying delays in directed networks. As a result, sufficient conditions for consensus and \(H_\infty\) consensus of heterogeneous multi-agent systems in terms of linear matrix inequalities are established in the cases of fixed and switching topologies. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results.

Finite-Time Consensus With Disturbance Rejection by Discontinuous Local Interactions in Directed Graphs

In this technical note we propose a decentralized discontinuous interaction rule which allows to achieve consensus in a network of agents modeled by continuous-time first-order integrator dynamics affected by bounded disturbances. The topology of the network is described by a directed graph. The proposed discontinuous interaction rule is capable of rejecting the effects of the disturbances and achieving consensus after a finite transient time. An upper bound to the convergence time is explicitly derived in the technical note. Simulation results, referring to a network of coupled Kuramoto-like oscillators, are illustrated to corroborate the theoretical analysis.

Adaptive coordinated tracking of multi-agent systems with quantized information

In this paper, we study the adaptive coordinated tracking problem for continuous-time first-order integrator systems with quantized information under switching undirected and fixed directed communication graphs, respectively. The combined effect of quantized relative information error and quantized absolute information error on the tracking result is investigated. Both the logarithmic quantizers and uniform quantizers are considered. It is shown that when logarithmic quantizers are used, exact coordinated tracking can still be achieved by properly choosing the design parameters in the controller while when uniform quantizers are used, practical coordinated tracking can be achieved with tracking error bounds proportional to the quantizer parameter. Simulation examples are provided to illustrate the results.

Darboux integrable discrete equations possessing an autonomous first-order integral

Darboux integrable difference equations on the quad-graph are completely described in the case of the equations that possess autonomous first-order integrals in one of the characteristics. A generalization of the discrete Liouville equation is obtained from a subclass of this equation via a non-point transformation. The detailed proof of the general proposition on the symmetry structure for the quad-graph equations is given as an auxiliary result.

Distributed consensus of a class of networked heterogeneous multi-agent systems

In this paper, we consider the consensus problem of a class of heterogeneous multi-agent systems composed of the linear first-order and second-order integrator agents together with the nonlinear Euler–Lagrange (EL) agents. First, we propose a distributed consensus protocol under the assumption that the parameters of heterogeneous system are exactly known. Sufficient conditions for consensus are presented and the consensus protocol accounting for actuator saturation is developed. Then, by combining adaptive controller and PD controller together, we design a protocol for the heterogeneous system with unknown parameters (in the nonlinear EL dynamics). Based on graph theory, Lyapunov theory and Barbalat's Lemma, the stability of the controllers is proved. Simulation results are also provided to illustrate the effectiveness of the obtained results.

Distributed Cooperative Current-Sharing Control of Parallel Chargers Using Feedback Linearization

We propose a distributed current-sharing scheme to address the output current imbalance problem for the parallel chargers in the energy storage type light rail vehicle system. By treating the parallel chargers as a group of agents with output information sharing through communication network, the current-sharing control problem is recast as the consensus tracking problem of multiagents. To facilitate the design, input-output feedback linearization is first applied to transform the nonidentical nonlinear charging system model into the first-order integrator. Then, a general saturation function is introduced to design the cooperative current-sharing control law which can guarantee the boundedness of the proposed control. The cooperative stability of the closed-loop system under fixed and dynamic communication topologies is rigorously proved with the aid of Lyapunov function and LaSalle invariant principle. Simulation using a multicharging test system further illustrates that the output currents of parallel chargers are balanced using the proposed control.

An Improved Frequency Modeling Corresponding to the Location of the Anjok of the Gayageum

본 논문은 기존의 가야금 안족 모델을 분석하고 안족의 위치에 따른 주파수 모델링을 개선하기 위한 방법에 대해서 기술한다. 기존의 모델은 안족의 위치별 기본 주파수의 변화를 지수 함수로 가정, 리키 적분기를 이용하여 이들 주파수를 적분한 후 선형 회귀 모델을 이용하여 주파수와 안족의 위치에 관한 수식의 파라미터를 구하였다. 이 모델은 평균적으로 2.5 Hz의 오차를 보였으나 낮은 주파수에 대해서는 최대 7.75 Hz의 오차를 보였다. 이에 제안하는 모델은 안족의 위치를 세부 구간으로 나누고 각 구간 내 누적 주파수에 대한 선형 회귀 모델을 적용하였고, 리키 적분기의 계수를 바꿔가며 안족 위치의 세부 구간 내 각 현의 기본 주파수와 계산된 주파수간 RMSE(Root Mean Square Error)가 최소가 되는 계수를 찾음으로써 최적의 파라미터를 구하였다. 이러한 과정을 통해 얻어진 모델은 기존의 오차를 최대 3배가량 줄일 수 있었다. This paper analyzes the previous Anjok model of the Gayageum and describes a method to improve the frequency modeling based on previous model. In the previous work, relation between the fundamental frequency and Anjok's location on the body is assumed as an exponential function and these frequencies are integrated by a first-order leaky integrator. Finally, a parameter of the formula to calculate the fundamental frequency is obtained by applying integrated frequencies to the linear regression. This model shows 2.5 Hz absolute deviation on average and has maximum error 7.75 Hz for the low fundamental frequencies. In order to overcome this problem, this paper proposes that the Anjok's locations are grouped according to the rate of error increase and linear regression is applied to each group. To find the optimal parameter, the RMSE(Root Mean Square Error) between measured and calculated fundamental frequencies is used. The proposed model shows substantial reduction in errors, especially maximum three times.

A New Cooperative Current-Sharing Control of Parallel Chargers for Energy Storage Type Light Rail Vehicles

In order to address the output current imbalanced problem of the parallel chargers for energy storage type light rail vehicles, a current-sharing scheme is proposed based on the distributed cooperative control of multi-agent systems. If each charger is considered to be an agent, the current-sharing control design would resemble a consensus-tracking problem of multi-agent systems with bounded input constraints. The communication network among the chargers can be taken as an undirected graph. Each charger exchanges current information with its neighbors through the communication network. Due to the fact that the charging system has non-identical feature and the control input is bounded, input-output feedback linearization is adopted to transform the current-sharing control of the charging system to a first-order integrator consensus-tracking problem. A saturation function is introduced to design a bounded cooperative current-sharing control law based on the nearest neighborhood rule. The cooperative stability of closed-loop system under the fixed topology is rigorously proved by Lyapunov function integrating LaSalle invariant principle. The output current of parallel chargers can be balanced by adopting the proposed control methodology, which is verified by simulating a multi-charging test system.

Strong disagreement in Mandarin and ELFP

This paper calls for the integration of first order and second order approaches in (im)politeness studies. Most previous research on the (im)politeness of Chinese speech behavior has been based on researchers’ interpretations and second order investigations. However, this study included a first order approach by examining Chinese participants’ lay conceptualizations of the appropriateness of the strong disagreement behavior that appeared in spontaneous mundane conversations. A close analysis of both the participants’ responses to strong disagreement in ongoing conversations and follow-up interviews revealed that the participants’ strong disagreement was perceived as politic and acceptable within their communities of practice. This challenges the general belief of strong disagreement as impolite and that of Chinese native speakers being indirect in communication. The finding indicates the importance of embracing first order investigation of the conventional views/norms that might cause communication misunderstanding in cross-cultural contact.

Decentralised event-triggered cooperative control with limited communication

This note studies event-triggered control of Multi-Agent Systems (MAS) with first-order integrator dynamics. It extends previous work on event-triggered consensus by considering limited communication capabilities through strict peer-to-peer non-continuous information exchange. The approach provides both a decentralised control law and a decentralised communication policy. Communication events require no global information and are based only on local state errors; agents do not require a global sampling period or synchronous broadcasting as in sampled-data approaches. The proposed decentralised event-triggered control technique guarantees that the inter-event times for each agent are strictly positive. Finally, the ideas in this note are used to consider the practical scenario where agents are able to exchange only quantised measurements of their states.

A linear mixed finite element scheme for a nematic Ericksen–Leslie liquid crystal model

In this work we study a fully discrete mixed scheme, based on continuous finite elements in space and a linear semi-implicit first-order integration in time, approximating an Ericksen–Leslie nematic liquid crystal model by means of a Ginzburg–Landau penalized problem. Conditional stability of this scheme is proved via a discrete version of the energy law satisfied by the continuous problem, and conditional convergence towards generalized Young measure-valued solutions to the Ericksen–Leslie problem is showed when the discrete parameters (in time and space) and the penalty parameter go to zero at the same time. Finally, we will show some numerical experiences for a phenomenon of annihilation of singularities.

Containment control of heterogeneous multi-agent systems

In this paper, we consider the containment control problem for a group of autonomous agents modelled by heterogeneous dynamics. The communication networks among the leaders and the followers are directed graphs. When the leaders are first-order integrator agents, we present a linear protocol for heterogeneous multi-agent systems such that the second-order integrator agents converge to the convex hull spanned by the first-order integrator agents if and only if the directed graph contains a directed spanning forest. If the leaders are second-order integrator agents, we propose a nonlinear protocol and obtain a necessary and sufficient condition that the heterogeneous multi-agent system solves the containment control problem in finite time. Simulation examples are also provided to illustrate the effectiveness of the theoretical results.

Numerically stable method for kinetic electrons in gyrokinetic particle-in-cell simulation of toroidal plasmas

The direct implicit method with a second-order implicit integration scheme is formulated for and applied to the electron parallel nonlinearity in global electrostatic gyrokinetic particle-in-cell simulations of toroidal fusion plasmas. The method shows improved numerical accuracy and stability properties compared to the direct implicit method with a first-order integration scheme. The conservation of total energy and toroidal angular momentum are analyzed by both techniques and the results are presented.

Quantized consensus on first-order integrator networks

This paper studies the quantized average consensus problem of first-order integrator agents with connected undirected communication graphs. Because quantized data is inherently associated with discrete-time measurements, a sampled-data based average consensus protocol is proposed, in which each agent uses the quantized states of its neighbors measured synchronously at sampling times to update its own state. It is proved that for a connected network, the distance between the individual state and the average of initial states becomes smaller than the quantization step size in finite time, provided the sampling size is smaller than a constant depending on the degree of the communication topology. When the sampling size tends to zero, an asynchronous protocol is investigated, in which the limitation of the switching frequency of quantizers is considered. It is shown that for a connected network, the given protocol drives the state of each agent into a neighborhood of the average of initial states, provided the dwell-time of quantizers is small enough.

Using Efficient Predictor-Corrector Reaction Path Integrators for Studies Involving Projected Frequencies.

Projected frequencies along a reaction pathway are necessary for computing reaction rates using variational transition state theory or reaction path Hamiltonian methods. The projected frequency analysis is quite sensitive to the accuracy of the reaction path integration. This work demonstrates that second- and first-order predictor-corrector reaction path integrators can be used for computing projected frequencies with high confidence. It is shown that these methods perform equally well with a variety of numerical integration step sizes and that, without a substantive loss in accuracy, Hessian updating can be used with both methods for stepping along the reaction path at points between those where projected frequencies are required.

Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements

This paper studies the finite-time consensus problem of heterogeneous multi-agent systems composed of first-order and second-order integrator agents. By combining the homogeneous domination method with the adding a power integrator method, we propose two classes of consensus protocols with and without velocity measurements. First, we consider the protocol with velocity measurements and prove that it can solve the finite-time consensus under a strongly connected graph and leader-following network, respectively. Second, we consider the finite-time consensus problem of heterogeneous multi-agent systems, for which the second-order integrator agents cannot obtain the velocity measurements for feedback. Finally, some examples are provided to illustrate the effectiveness of the theoretical results.