scholarly journals Computation of Time Delay Stability Margin for the Automated Vehicular Platoon

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xunxun Zhang ◽  
Li Li ◽  
Xu Zhu
Keyword(s):  
Time Delay ◽  
Stability Margin ◽  
Laplacian Matrix ◽  
V2v Communication ◽  
Exact Time ◽  
Vehicle To Vehicle ◽  
Communication Time ◽  
Stability Issue ◽  
The Stability ◽  
Necessary And Sufficient

Due to the limited band width and congestion of communication channels in the wireless vehicle-to-vehicle (V2V) communication, time delay inevitably arises and dramatically leads to the disturbances for the automated vehicular platoon. This paper focuses on computing the exact time delay stability margin. In this study, we treat this problem as a stability issue of a consensus system with time delay, where each vehicle in the platoon is recognized as a node, and the interconnected information flow is represented as a graph. Then, the distributed controller is designed by combining the states of the vehicle itself and its neighbouring vehicles. Furthermore, the stability of the entire platoon is analysed according to the characteristic equation of the closed-loop system, and a necessary and sufficient condition for the exact time delay stability margin is obtained. Especially, for the automated vehicular platoon with undirected topology, it is revealed that exact time delay stability margin is determined by the largest eigenvalue of the augmented Laplacian matrix. Furthermore, a rapid method for finding exact time delay stability margin is proposed. Finally, numerical simulations demonstrate that this work generates exact and satisfactory time delay stability margin for the automated vehicular platoon.

Stabilization of a Translating Tensioned Beam Through a Pointwise Control Force

1998 ◽  
Vol 122 (2) ◽  
pp. 322-331 ◽  
Author(s):  
W. D. Zhu ◽  
B. Z. Guo ◽  
C. D. Mote,
Keyword(s):  
Stability Margin ◽  
Numerical Approach ◽  
Distributed Model ◽  
Control Force ◽  
Stability Margins ◽  
Distribution Of Eigenvalues ◽  
Modes Of Vibration ◽  
The Subject ◽  
The Stability ◽  
Necessary And Sufficient

A spectral analysis determining asymptotically the distribution of eigenvalues of a constrained, translating, tensioned beam in closed form is the subject of this paper. The constraint is modeled by a spring-mass-dashpot subsystem that is located at any position within the span of the beam. It can represent a feedback controller with a collocated sensor and actuator. The necessary and sufficient condition that ensures a uniform stability margin for all the modes of vibration is determined. Influences of system parameters on the distribution of eigenvalues are identified. The analytical predictions are validated by numerical analyses. The constraint location maximizing the stability margin of the distributed model is predicted through a combined analytical and numerical approach. The implications and utility of the results are illustrated. The methodology developed can be extended to predict stability margins and optimize control parameters for controlled translating beams with other types of boundary conditions and controller structures. [S0022-0434(00)00702-4]

scholarly journals Delayed Consensus Problem for Single and Double Integrator Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Martín Velasco-Villa ◽  
Josué Heras-Godínez ◽  
José Alejandro Vázquez-Santacruz ◽  
Varinia Fragoso-Rubio
Keyword(s):  
Time Delay ◽  
Laplacian Matrix ◽  
Constant Time Delay ◽  
Consensus Problem ◽  
Delay Compensation ◽  
Prediction Scheme ◽  
Control Scheme ◽  
Communication Time ◽  
Double Integrator ◽  
Maximum Allowable Time

This work deals with the analysis of the consensus problem for networks of agents constituted by single and double integrator systems. It is assumed that the communication among agents is affected by a constant time-delay. Previous and numerous analysis of the problem shows that the maximum communication time-delay that can be introduced to the network without affecting the consensus of the group of the agents depends on the considered topology. In this work, a control scheme that is based on the estimation of future states of the agents and that allows increasing the magnitude of a possible time-delay affecting the communication channels is proposed. How the proposed delay compensation strategy is independent of the network topology in the sense that the maximum allowable time-delay that could be supported by the network depends on a design parameter and not on the maximum eigenvalue of the corresponding Laplacian matrix is shown. It is formally proven that, under the proposed prediction scheme, the consensus of the group can be achieved by improving the maximum time-delay bounds previously reported in the literature. Numerical simulations show the effectiveness of the proposed solution.

scholarly journals The Stability and Stabilization of Stochastic Delay-Time Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Gang Li ◽  
Ming Chen
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Lyapunov Equation ◽  
Delay System ◽  
Stochastic Delay ◽  
Stability And Stabilization ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Stochastic Time

The aim of this paper is to investigate the stability and the stabilizability of stochastic time-delay deference system. To do this, we use mainly two methods to give a list of the necessary and sufficient conditions for the stability and stabilizability of the stochastic time-delay deference system. One way is in term of the operator spectrum andH-representation; the other is by Lyapunov equation approach. In addition, we introduce the notion of unremovable spectrum of stochastic time-delay deference system, describe the PBH criterion of the unremovable spectrum of time-delay system, and investigate the relation between the unremovable spectrum and the stabilizability of stochastic time-delay deference system.

scholarly journals Distributed Impulsive Consensus of the Multiagent System without Velocity Measurement

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-Wei Liu ◽  
Hong Zhou ◽  
Zhi-Hong Guan ◽  
Wen-Shan Hu ◽  
Li Ding ◽  
...  
Keyword(s):  
Velocity Measurement ◽  
Multiagent System ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Impulsive System ◽  
Consensus Algorithm ◽  
Communication Graph ◽  
The Stability ◽  
Necessary And Sufficient

This paper deals with the distributed consensus of the multiagent system. In particular, we consider the case where the velocity (second state) is unmeasurable and the communication among agents occurs at sampling instants. Based on the impulsive control theory, we propose an impulsive consensus algorithm that extends some of our previous work to account for the lack of velocity measurement. By using the stability theory of the impulsive system, some necessary and sufficient conditions are obtained to ensure the consensus of the controlled multiagent system. It is shown that the control gains, the sampled period and the eigenvalues of Laplacian matrix of communication graph play key roles in achieving consensus. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed algorithm.

scholarly journals Design of the Congestion Control for TCP/AQM Network with Time-Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Dazhong Wang ◽  
Shujing Wu
Keyword(s):  
Time Delay ◽  
Transmission Control Protocol ◽  
Design Method ◽  
Nonlinear Behavior ◽  
Transmission Control ◽  
Model Following Control ◽  
Model Following ◽  
Communication Time ◽  
Internal States ◽  
The Stability

The purpose of this paper is to design congestion controller for TCP/AQM (transmission control protocol/active queue management) networks using model following control; the equilibrium of a class of TCP/AQM networks with time-delay is investigated, and the effect of communication time-delay on the stability is addressed. The features of this design method are bounded property of the internal states of the control system being given and the utility of this control. Such design exhibits important attributes including fast convergence with high accuracy to a desired queue length. Simulation results show that the time-delay nonlinear behavior of the system can be controlled by this method.

scholarly journals Swarming Behaviors in Multiagent Systems with Nonlinear Dynamics and Aperiodically Intermittent Communication

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Anding Dai ◽  
Yicheng Liu ◽  
Dongyun Yi ◽  
Peiying Xiong
Keyword(s):  
Nonlinear Dynamics ◽  
Time Delay ◽  
Multiagent Systems ◽  
Finite Time ◽  
Upper Bounds ◽  
Time Intervals ◽  
Communication Time ◽  
The Stability ◽  
Intermittent Communication ◽  
Theoretical Results

This paper investigates the stability of a class of swarm model with nonlinear dynamics and aperiodically intermittent communication. Different from previous works, it assumes that the agents obtain information from the neighbors at a series of aperiodically time intervals. Moreover, nonlinear dynamics and time delay are considered. It finds that all agents in a swarm can reach cohesion within a finite time under discontinuous communication, where the upper bounds of cohesion depend on the parameters of the swarm model and communication time. A numerical example is given to demonstrate the validity of the theoretical results.

scholarly journals Diagonal Riccati stability of a class of time-delay systems

2018 ◽  
pp. 167-173
Author(s):  
Alexander Aleksandrov ◽  
Nadezhda Kovaleva
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Time Delay ◽  
Mechanical System ◽  
Formation Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
The Stability ◽  
Necessary And Sufficient

A complex system describing interaction of subsystems of the second order with delay in connections between them is studied. Necessary and sufficient conditions of the existence of a diagonal Lyapunov–Krasovskii functional for the considered system are derived. The obtained results are applied for the stability a nalysis of a mechanical system and a model of population dynamics. In addition, it is shown that they can be used in a problem of formation control.

On the stability of a class of nonlinear time delay systems

1999 ◽  
Author(s):  
Dan Ivancscu ◽  
Silviu-Iulian Niculcscu ◽  
Jcan-Michcl Dion ◽  
Luc Dugard
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Time Delay Systems ◽  
The Stability
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