Guaranteeing String Stability of Multiple Interconnected Vehicles Using Heterogeneous Controllers

2020 ◽  
Author(s):  
Arash Farnam ◽  
Guillaume Crevecoeur
Keyword(s):  
Sufficient Conditions ◽  
Control Synthesis ◽  
String Stability ◽  
Local Disturbance ◽  
Vector Norm ◽  
Distributed Controllers ◽  
Simulation Results ◽  
A Chain ◽  
Strict Definition

Abstract In this paper the issue of string stability for acceleration-controlled vehicles interconnected in a chain is studied. String stability is concerned with having bounded displacements between vehicles in such a way that displacements should not grow unboundedly with respect to the perturbation. Different definitions can be given to string stability: one that relates to the amplification of a local disturbance acting on one vehicle towards the whole vehicle chain, more strict definition that is related to the boundedness of vector norm of displacements with respect to the bounded vector norm of disturbance inputs acting on all vehicles; and, most practical definition that considers the boundedness of signal norm of each individual displacement with respect to the bounded signal norm of disturbance inputs acting on all vehicles, independently from the number of vehicles. It has been proven that these definitions are all impossible to be achieved using any linear homogeneous unidirectional distributed controllers with constant spacing policy. This paper proposes linear heterogeneous controllers where each vehicle behaves differently from others in a vehicle chain. We prove that three different definitions of string stability can be attained using the proposed heterogenous controller. We propose sufficient conditions to guarantee string stability and boundedness of acceleration of each vehicle. Finally, simulation results are given to illustrate the effectiveness of proposed heterogenous control synthesis.

scholarly journals Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenhua Gao ◽  
Feiqi Deng ◽  
Ruiqiu Zhang ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Time Stability ◽  
Finite Time Stability ◽  
Weighting Matrix ◽  
Simulation Results ◽  
Dependent State

This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

scholarly journals On number of moduli for gradient surface height function flows

2018 ◽  
Vol 20 (4) ◽  
pp. 419-428
Author(s):  
V. E. Kruglov
Keyword(s):  
Finite Number ◽  
Sufficient Conditions ◽  
Height Function ◽  
Orientable Surface ◽  
Topological Conjugacy ◽  
Topological Equivalence ◽  
Gradient Flows ◽  
A Chain ◽  
Gradient Surface ◽  
Equivalence Invariant

In 1978 J. Palis invented continuum topologically non-conjugate systems in a neighbourhood of a system with a heteroclinic contact; in other words, he invented so-called moduli. W. de Melo and С. van Strien in 1987 described a diffeomorphism class with a finite number of moduli. They discovered that a chain of saddles taking part in the heteroclinic contact of such diffeomorphism includes not more than three saddles. Surprisingly, such effect does not happen in flows. Here we consider gradient flows of the height function for an orientable surface of genus g>0. Such flows have a chain of 2g saddles. We found that the number of moduli for such flows is 2g−1 which is the straight consequence of the sufficient topological conjugacy conditions for such systems given in our paper. A complete topological equivalence invariant for such systems is four-colour graph carrying the information about its cells relative position. Equipping the graph's edges with the analytical parameters --- moduli, connected with the saddle connections, gives the sufficient conditions of the flows topological conjugacy.

Preliminary Investigation of Mesh Stability for Linear Systems

1999 ◽  
Author(s):  
Pete Seiler ◽  
Aniruddha Pant ◽  
J. K. Hedrick
Keyword(s):  
Linear Systems ◽  
Mimo Systems ◽  
Preliminary Investigation ◽  
Two Dimensions ◽  
String Stability ◽  
Significant Research ◽  
Simple Class ◽  
The Subject ◽  
A Chain ◽  
The One

Abstract Damping of disturbances as they propagate through a chain of interconnected systems, termed string stability, has been the subject of significant research. In this paper, we investigate mesh stability, which is the two-dimensional extension of string stability. We review the key results used for string stability analysis and then generalize the conditions for MIMO systems. These results are then applied to a simple class of linear systems which form a mesh in two-dimensions. It is shown (as in the one-dimensional case) that communicating the velocity and acceleration of the lead vehicle to all subsystems is sufficient for mesh stability. This result is then verified by simulation.

Adaptive Synchronization in Unknown Stochastic Chaotic Neural Networks with Mixed Time-Varying Delays

2011 ◽  
pp. 289-313
Author(s):  
Jian-an Fang ◽  
Yang Tang
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Adaptive Synchronization ◽  
Output Coupling ◽  
Time Varying ◽  
Connection Weight ◽  
Chaotic Neural Networks ◽  
Simulation Results ◽  
Feedback Techniques

Neural networks (NNs) have been useful in many fields, such as pattern recognition, image processing etc. Recently, synchronization of chaotic neural networks (CNNs) has drawn increasing attention due to the high security of neural networks. In this chapter, the problem of synchronization and parameter identification for a class of chaotic neural networks with stochastic perturbation via state and output coupling, which involve both the discrete and distributed time-varying delays has been investigated. Using adaptive feedback techniques, several sufficient conditions have been derived to ensure the synchronization of stochastic chaotic neural networks. Moreover, all the connection weight matrices can be estimated while the lag synchronization and complete synchronization is achieved in mean square at the same time. The corresponding simulation results are given to show the effectiveness of the proposed method.

Multi look‐ahead consensus of vehicular networks in the presence of random data missing

2020 ◽  
pp. 107754632093346
Author(s):  
Hossein Chehardoli
Keyword(s):  
Vehicular Networks ◽  
Sufficient Conditions ◽  
Practical Implementation ◽  
Huge Amount ◽  
Third Order ◽  
Random Data ◽  
String Stability ◽  
Look Ahead ◽  
Loop Dynamics ◽  
Data Missing

This study deals with internal and string stability analyses of vehicular platoons with centralized multi-look ahead network topology in the presence of communication and parasitic delays and random data missing. In vehicular networks, because of huge amount of information exchanged between vehicles and highway infrastructures, some adverse effects such as data missing and communication delay are unavoidable in practical implementation. In this study, a third-order dynamical model is used to describe the longitudinal dynamics of each following vehicle, and the constant spacing strategy is used to adjust the inter-vehicle spacing. By considering communication and parasitic delays and random data missing, the closed-loop dynamics of platoon is derived. Afterward, by using the Lyapunov–Krasovskii theorem, sufficient conditions assuring the internal stability are introduced. In continuance, the string stability of platoon under the aforementioned effects is studied. It will be shown that the proposed controller always guarantees the string stability of platoon without any limitations. Several simulation results are provided to show the effectiveness of the proposed approaches.

ASYMPTOTIC BEHAVIOR OF A STOCHASTIC DELAYED CHEMOSTAT MODEL WITH NUTRIENT STORAGE

2018 ◽  
Vol 26 (02) ◽  
pp. 225-246 ◽  
Author(s):  
SHULIN SUN ◽  
XIAOFENG ZHANG
Keyword(s):  
Asymptotic Behavior ◽  
Time Delay ◽  
Function Analysis ◽  
Sufficient Conditions ◽  
Classical Approach ◽  
Nutrient Storage ◽  
Chemostat Model ◽  
Global Positive Solution ◽  
The Mean ◽  
Simulation Results

In this paper, a stochastic delayed chemostat model with nutrient storage is proposed and investigated. First, we state that there is a unique global positive solution for this stochastic system. Second, using the classical approach of Lyapunov function analysis, this stochastic delayed chemostat model is discussed in detail. We establish some sufficient conditions for the extinction of the microorganism, furthermore, we prove that the microorganism will become persistent in the mean in the chemostat under some conditions. Finally, the obtained results are illustrated by computer simulations, and simulation results reveal the effects of time delay on the persistence and extinction of the microorganism.

Distributed and Centralized H∞ Control of Large Segmented Telescopes

2010 ◽  
Author(s):  
Baris Ulutas ◽  
Afzal Suleman ◽  
Edward J. Park
Keyword(s):  
Next Generation ◽  
Vast Number ◽  
Primary Mirror ◽  
Performance Requirements ◽  
Distributed Controller ◽  
Nodal Model ◽  
Distributed Controllers ◽  
Simulation Results ◽  
Imaging Performance ◽  
Large Primary

Next generation telescopes are to employ segmented mirrors to realize extremely large primary mirror surfaces. Most of the current ground-based telescopes has monolithic mirrors with radius upto 8 metres. Due to limitations segmentation is preferred for larger size mirrors. Segmentation of mirrors brings a challenging task of controlling the vast number of individual units. In this paper, the H∞ control of the primary mirror of the next generation telescopes are investigated. Both spatially-invariant distributed and centralized controllers are designed for simplified dynamic model of a 37 segment test unit. Firstly, the 37 segment system is modelled by adopting a nodal model. Secondly, an analytic calculation of a H∞ controller is presented. A centralized H∞ controller is, then, designed and simulated in MatLab-Simulink environment. Next, the simulation results are presented and the performance of the controller is evaluated. Thirdly, spatially-invariant distributed controller synthesis is described and a spatially-invariant distributed controller is designed for 37 segment system by controller truncation. The spatially-invariant distributed controller is simulated for the 37 segment system. The simulation results of the controller is presented and compared with the results from centralized scheme. It is shown that both centralized and spatially-invariant distributed controllers satisfy the imaging performance requirements.

Phantom Track Generation Through Cooperative Control of Multiple ECAVs Based on Feasibility Analysis

2007 ◽  
Vol 129 (5) ◽  
pp. 708-715 ◽  
Author(s):  
D. H. A. Maithripala ◽  
Suhada Jayasuriya ◽  
Mark J. Mears
Keyword(s):  
Multiagent Systems ◽  
Mobile Agents ◽  
Cooperative Control ◽  
General Framework ◽  
Sufficient Conditions ◽  
Feasibility Analysis ◽  
Rigorous Treatment ◽  
Simulation Results ◽  
Feasible Solutions ◽  
Generation Problem

Radar deception through phantom track generation using multiple electronic combat air vehicles is addressed, which serves as a motivating example for cooperative control of autonomous multiagent systems. A general framework to derive sufficient conditions for the existence of feasible solutions for an affine nonlinear control system comprising of a team of nonholonomic mobile agents having to satisfy actuator and interagent constraints is presented. Based on this feasibility analysis, an algorithm capable of generating trajectories online and in real time, for the phantom track generation problem, is developed. A rigorous treatment of the phantom track generation problem, which includes results on its accessibility, feasibility, local asymptotic straightening of trajectories, and a limited result on system controllability, is given. The basic approach to the algorithm based on the results developed here is presented along with simulation results, validating the proposed approach.

scholarly journals Discretized Lyapunov Function Approach for Switched Linear Systems under Dwell Time Constraint

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yongchi Zhao ◽  
Shengxian Zhuang ◽  
Weiming Xiang ◽  
Lin Du
Keyword(s):  
Lyapunov Function ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Time Constraint ◽  
Switched System ◽  
Function Approach ◽  
Disturbance Attenuation ◽  
Function Technique ◽  
Synthesis Process ◽  
Control Synthesis

This paper is concerned with the stability and disturbance attenuation properties of switched linear system with dwell time constraint. A novel time-scheduled Lyapunov function is introduced to deal with the problems studied in this paper. To numerically check the existence of such time-scheduled Lyapunov function, the discretized Lyapunov function technique usually used in time-delay system is developed in the context of switched system in continuous-time cases. Based on discretized Lyapunov function, sufficient conditions ensuring dwell-time constrained switched system global uniformly asymptotically stable are established, then the disturbance attenuation properties in the sense ofL2gain are studied. The main advantage of discretized Lyapunov function approach is that the derived sufficient conditions are convex in subsystem matrices, which makes the analysis results easily used and generalized. Thus, theH∞control synthesis problem is considered. On the basis of analysis results in hand, the control synthesis procedures including both controller and switching law design are unified into one-step method which explicitly facilitates the control synthesis process. Several numerical examples are provided to illustrate the results within our paper.

Robust H∞ control of stochastic linear systems with input delay by predictor feedback

2017 ◽  
Vol 40 (7) ◽  
pp. 2396-2407
Author(s):  
Ali Javadi ◽  
Mohammad Reza Jahed-Motlagh ◽  
Ali Akbar Jalali
Keyword(s):  
Linear Systems ◽  
Multiplicative Noise ◽  
Sufficient Conditions ◽  
Input Delay ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
External Disturbances ◽  
Delayed Systems ◽  
Simulation Results ◽  
Stochastic Linear Systems

This study investigates the prediction-based (dynamic) stabilization of linear systems with input delay in the presence of external disturbances and multiplicative noise modelled as Itô type stochastic differential equations. Conventional memory-less (static) controllers are widely used for the stabilization of both deterministic and stochastic delayed systems. However, using these methods the upper bound for delay is strongly restricted. Motivated by acceptable performances of dynamic controllers for deterministic delayed systems, the extension of these methods for stochastic delayed systems is considered in this paper. The structure of the dynamic controller for stabilization of stochastic delayed systems is firstly derived utilizing the prediction vector. Then two sufficient conditions are given in the form of linear matrix inequalities that in the case of feasibility provide the stabilizing gain of the controller. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

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