DOCSLIB.ORG

Stochastic Consentability of Linear Systems with Time Delays And

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Stochastic Consentability of Linear Systems with Time Delays And IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 63, NO. 4, APRIL 2018 1059 Stochastic Consentability of Linear Systems With Time Delays and Multiplicative Noises Xiaofeng Zong, Tao Li , Senior Member, IEEE, George Yin , Fellow, IEEE, Le Yi Wang , Fellow, IEEE, and Ji-Feng Zhang , Fellow, IEEE Abstract—This paper develops stochastic consentability Index Terms—Consentability, consensus, multiagent of linear multiagent systems with time delays and multi- system, multiplicative noise, time delay. plicative noises. First, the stochastic stability for stochastic differential delay equations driven by multiplicative noises is examined, and the existence of the positive definite so- I. INTRODUCTION lution for a class of generalized algebraic Riccati equations (GAREs) is established. Then, sufficient conditions are de- ULTIAGENT systems have attracted much attention in duced for the mean square and almost sure consentability recent years. The research progress in such systems has and stabilization based on the developed stochastic stabil- M ity and GAREs. Consensus protocols are designed for linear provided valuable insights and benefits in understanding, de- multiagent systems with undirected and leader-following signing, and implementing distributed controllers for such sys- topologies. It is revealed that multiagent consentability de- tems; see [1]–[3]. To date, the consensus problem of perfect pends on certain characterizing system parameters, in- models, which assume that each agent can obtain its neighbor in- cluding linear system dynamics, communication graph, formation timely and precisely, has reached a reasonable degree channel uncertainties, and time delay of the deterministic term. It is shown that a second-order integrator multiagent of maturity; see [4] for example. However, networked systems in system is unconditionally mean square and almost surely practical applications often operate in uncertain communication consentable for any given noise intensities and time delay, environments and are inevitably subjected to communication and that the mean square and almost sure consensus can latency and measurement noises [5]–[7]. Hence, time delays be achieved by carefully choosing the control gain accord- and measurement noises should be taken into consideration for ing to certain explicit conditions. examining multiagent consensus problems. Manuscript received February 20, 2017; accepted July 14, 2017. Date In the literature, Olfati-Saber and Murray [7] gave optimal of publication July 27, 2017; date of current version March 27, 2018. delay bounds for consensus under undirected graphs. Bliman This work was supported in part by the National Natural Science Foun- and Ferrari-Trecate [8] studied average consensus problems for dation of China under Grant 61522310, in part by Shanghai Rising-Star Program under Grant 15QA1402000, in part by the National Key Basic undirected networks with constant, time varying and nonuni- Research Program of China (973 Program) under Grant 2014CB845301, form time delays, and presented some sufficient conditions for in part by the Fundamental Research Funds for the Central Universities, average consensus. Different types of time delays (communi- China University of Geosciences (Wuhan) under Grant CUG170610, and in part by the U.S. Air Force Office of Scientific Research under FA9550- cation delay, identical self-delay and different self-delay) were 15-1-0131. This paper was presented in part at 12th IEEE Conference investigated in [9] for output consensus. These works have fo- on Control and Automation, Kathmandu, Nepal, June 1–3, 2016. Rec- cused on first-order multiagent systems. For second-order mul- ommended by Associate Editor E. Zhou. (Corresponding author: George Yin.) tiagent systems, Yu et al. [10] gave necessary and sufficient X. Zong is with the School of Automation, China University of Geo- consensus conditions related to time delays. Zhou and Lin [11] sciences, Wuhan 430074 China, and with Hubei Key Laboratory of Ad- showed that consensus problems of linear multiagent systems vanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China (e-mail: [email protected]). with input and communication delays could also be solved by T. Li was with the School of Mechatronic Engineering and Automation, truncated predictor feedback protocols. Shanghai University, Shanghai 200072 China. He is now with the Shang- For multiplicative noises (or state-dependent noise), Ni and hai Key Laboratory of Pure Mathematics and Mathematical Practice, Department of Mathematics, East China Normal University, Shanghai Li [12] studied consensus problems of continuous-time systems 200241, China (e-mail: [email protected]). in which the noise intensity functions are the absolute values of G. Yin is with the Department of Mathematics, Wayne State University, relative states. Li et al. [13] revealed that multiplicative noises Detroit, MI 48202 USA (e-mail: [email protected]). L. Y. Wang is with the Department of Electrical and Computer En- may enhance the almost sure consensus, but may have damaging gineering, Wayne State University, Detroit, MI 48202 USA (e-mail: effect on the mean square consensus, indicating a distinct fea- [email protected]). ture from additive noises which are always destabilizing factors. J.-F.Zhang is with the Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, These results have been established for first-order multiagent Chinese Academy of Sciences, Beijing 100190 China, and also with systems. For linear discrete-time systems, Li and Chen [14] gave School of Mathematical Sciences, University of Chinese Academy of the mean square consensus analysis by solving a modified alge- Sciences, Beijing 100149, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available braic Riccati equation. When the time delay and multiplicative online at http://ieeexplore.ieee.org. noise coexist, stochastic consensus conditions were examined Digital Object Identifier 10.1109/TAC.2017.2732823 in [15] for second-order discrete-time models. However, little is 0018-9286 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information. 1060 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 63, NO. 4, APRIL 2018 known about the consensus for general continuous-time linear designing control protocols under time delays and measurement multiagent systems with time delays and multiplicative noises. noises. The contribution of this paper is detailed as follows. All the aforementioned works have focused on the issue 1) Two new techniques (Theorems II.1 and II.2) are devel- of convergence to consensus, which is concerned with con- oped to study the multiagent consentability and consensus ditions on the given control protocols under which the agents under measurement noises and time delays. We first ex- can achieve certain agreements asymptotically. However, they ploit the degenerate Lyapunov functional [25] to establish do not address the issue of consentability. Consentability is the mean square and almost sure exponential stability cri- concerned with conditions on system parameters under which a teria of stochastic differential delay equations (SDDEs). consensus protocol exists, and is of great importance, both theo- We show that the stability is independent of the time delay retically and practically, for cooperative control protocol devel- with stochastic influence. Then, the existence of positive opment such as flocking behavior, agent rendezvous, and robot definite solutions to GARE is obtained. The GARE plays coordination. Note that Ma and Zhang [16] considered general an important role in stochastic linear-quadratic control linear continuous-time multiagent systems and obtained nec- problems [26]–[28]. Here, both sufficient and necessary essary and sufficient conditions on system parameters for con- conditions are presented for guaranteeing the existence of sentability. This problem was then generalized in [17] to the case a positive definite solution to the GARE. As a byproduct, with input constraints and uncertain initial conditions in terms necessary and sufficient conditions are given for the ex- of linear matrix inequalities (LMIs). For discrete-time models, istence of stochastic feedback stabilization control laws. Zhang and Tian [18] investigated second-order multiagent sys- That is, it is sufficient that the open-loop dynamics (A, B) tems with Markov-switching topologies, and proved that such is controllable and the product of the sum of real parts of networked systems are mean square consentable under linear unstable open-loop poles and the square of noise inten- consensus protocols if and only if the union of the graphs in sity is less than 1/2, while it is necessary that (A, B) is the switching topology has globally reachable nodes. For linear stabilizable and the product of the maximal real part of multiagent systems, You and Xie [19] obtained necessary and the open-loop poles and the square of noise intensity is sufficient conditions for single-input multiagent consentability less than 1/2. and revealed how the agent dynamic, network topology, and 2) The necessary and sufficient conditions for multiagent communication data rate affect consentability. Gu et al. [20] consentability and consensus are revealed. We first de- employed a properly designed dynamic filter into local
Load more

Recommended publications
  • Delay Tolerance for Stable Stochastic Systems and Extensions Xiaofeng Zong , Tao Li , Senior Member, IEEE, George Yin , Fellow, IEEE, and Ji-Feng Zhang , Fellow, IEEE
    2604 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 66, NO. 6, JUNE 2021 Delay Tolerance for Stable Stochastic Systems and Extensions Xiaofeng Zong , Tao Li , Senior Member, IEEE, George Yin , Fellow, IEEE, and Ji-Feng Zhang , Fellow, IEEE Abstract—This article establishes a “robustness” type I. INTRODUCTION result, namely, delay tolerance for stable stochastic sys- tems under suitable conditions. We study the delay toler- HIS article presents an effort to address the important ance for stable stochastic systems and delayed feedback T question: How much delay can a stochastic system endures controls of such systems, where the delay can be state- so that the stability is still achieved. This, in fact, can be thought dependent or induced by the sampling-data. First, we con- of as a robustness consideration. The range of allowable delays sider systems with global Lipschitz continuous coefficients can be thought of as a “stability margin” in certain sense. Our and show that when the original stochastic system without consideration stems from the fact that stochastic systems are delay is pth moment exponentially stable, the system with used frequently in the real-world applications ranging from small delays is still pth moment exponentially stable. In p numerous dynamic systems in engineering, computer science, particular, when the th moment exponential stability is and network science to population biology, epidemiology, and based on Lyapunov conditions, we can obtain explicit delay bounds for moment exponential stability. Then, we consider economics [1]. While the study of stochastic systems has a long a class of stochastic systems with nonglobal Lipschitz con- history, one of the central issues drawing much attention in the ditions and find a delay bound for almost sure and mean literature is stability [2]–[5], which offers challenges and oppor- square exponential stability.
    [Show full text]
  • What Democracy Means in China After 30 Years of Reform
    WHAT DEMOCRACY MEANS IN CHINA AFTER 30 YEARS OF REFORM ROUNDTABLE BEFORE THE CONGRESSIONAL-EXECUTIVE COMMISSION ON CHINA ONE HUNDRED ELEVENTH CONGRESS FIRST SESSION MAY 22, 2009 Printed for the use of the Congressional-Executive Commission on China ( Available via the World Wide Web: http://www.cecc.gov U.S. GOVERNMENT PRINTING OFFICE 51–188 PDF WASHINGTON : 2009 For sale by the Superintendent of Documents, U.S. Government Printing Office Internet: bookstore.gpo.gov Phone: toll free (866) 512–1800; DC area (202) 512–1800 Fax: (202) 512–2104 Mail: Stop IDCC, Washington, DC 20402–0001 VerDate Nov 24 2008 17:42 Oct 28, 2009 Jkt 000000 PO 00000 Frm 00001 Fmt 5011 Sfmt 5011 U:\DOCS\51188.TXT DEIDRE CO N T E N T S Page Opening statement of Charlotte Oldham-Moore, Staff Director, Congressional- Executive Commission on China ........................................................................ 1 Grob, Douglas, Cochairman’s Senior Staff Member, Congressional-Executive Commission on China .......................................................................................... 2 Cheng, Li, Director of Research and Senior Fellow, Foreign Policy, John L. Thornton China Center, Brookings Institution ............................................. 4 Manion, Melanie, Professor of Public Affairs and Political Science, University of Wisconsin-Madison .......................................................................................... 6 Liu, Yawei, Director, China Program, The Carter Center ................................... 9 Dickson, Bruce J.,
    [Show full text]
  • Rendering the Regional
    Rendering the Regional Rendering the Regional LOCAL LANGUAGE IN CONTEMPORARY CHINESE MEDIA Edward M.Gunn University of Hawai`i Press Honolulu Publication of this book was aided by the Hull Memorial Publication Fund of Cornell University. ( 2006 University of Hawai`i Press All rights reserved Printed in the United States of America 111009080706654321 Library of Congress Cataloging-in-Publication Data Gunn, Edward M. Rendering the regional : local language in contemporary Chinese media / Edward M. Gunn. p. cm. Includes bibliographical references and index. ISBN 0-8248-2883-6 (alk. paper) 1. Language and cultureÐChina. 2. Language and cultureÐTaiwan. 3. Popular cultureÐChina. 4. Popular cultureÐTaiwan. I. Title. P35.5.C6G86 2005 306.4400951Ðdc22 2005004866 University of Hawai`i Press books are printed on acid-free paper and meet the guidelines for permanence and durability of the Council on Library Resources. Designed by University of Hawai`i Press Production Staff Printed by The Maple-Vail Book Manufacturing Group Contents List of Maps and Illustrations /vi Acknowledgments / vii A Note on Romanizations /ix Introduction / 1 1 (Im)pure Culture in Hong Kong / 17 2 Polyglot Pluralism and Taiwan / 60 3 Guilty Pleasures on the Mainland Stage and in Broadcast Media / 108 4 Inadequacies Explored: Fiction and Film in Mainland China / 157 Conclusion: The Rhetoric of Local Languages / 204 Notes / 211 Sources Cited / 231 Index / 251 ±v± List of Maps and Illustrations Figure 1. Map showing distribution of Sinitic (Han) Languages / 2 Figure 2. Map of locations cited in the text / 6 Figure 3. The Hong Kong ®lm Cageman /42 Figure 4. Illustrated romance and pornography in Hong Kong / 46 Figure 5.
    [Show full text]
  • Program 11-13 October 2019·Nanjing·China
    The 12th International Workshop on Complex-sys- tems for Future Technologies and Applications (IWCFTA 2019) Program 11-13 October 2019·Nanjing·China Sponsors Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, Southeast University Technical Committee on Network Science and Engineering of Chinese Institute of Command and Control City University of Hong Kong Technical support: IEEE CASS (Nonlinear CAS Technical Committee) Northeastern University Conference site: Nanjing Zhongshan Hotel Website: https://nci.seu.edu.cn/wome_23639/list.htm Index General Information .......................................................................................................................................... 5 Organizing Committee ..................................................................................................................................... 6 Honorary Chairs ......................................................................................................................................... 6 General Chairs ............................................................................................................................................ 6 General Co-Chairs .................................................................................................................................... 6 Program Chairs .......................................................................................................................................... 6 Program Co-Chairs .................................................................................................................................
    [Show full text]
  • China and the World Since 1945 an International History
    MAKING OF THE CONTEMPORARY WORLD MAKING OF THE CONTEMPORARY CHINA AND THE WORLD SINCE 1945 AN INTERNATIONAL HISTORY CHI-KWAN MARK China and the World since 1945 The emergence of China as a dominant regional power with global influence is a significant phenomenon in the twenty-first century. Its origin can be traced back to 1949 when the Chinese Communist Party under Mao Zedong came to power and vowed to transform China and the world. After the ‘century of humiliation’, China was in constant search of a new identity on the world stage. From alliance with the Soviet Union in the 1950s, China normalized relations with America in the 1970s and embraced the global economy and the international community from the 1980s. In China and the World since 1945: An International History, Chi-kwan Mark examines China’s changing relations with the two superpowers, Asian neighbours, developing countries, and European powers. The book offers an overview of China’s involvement in the Korean War, the Sino-Soviet split, Sino-American rapprochement, the end of the Cold War, and globalization. It also assesses the roles of security, ideology, and domestic politics in Chinese foreign policy and provides a synthesis of the latest archival-based research on China’s diplomatic history and Cold War international history. Examining the rise of China from a long-term historical perspective, it will be a valuable resource to students of Chinese history and contemporary international relations. Chi-kwan Mark is Lecturer in International History at Royal Holloway College, University of London. His research interests focus on British– American–Chinese relations during the Cold War and Hong Kong’s colonial and international history.
    [Show full text]
  • Re-Evaluating the History Behind China's Economic Boom
    Working Papers No. 175/13 From Divergence to Convergence: Re-evaluating the History Behind China’s Economic Boom Loren Brandt, Debin Ma, and Thomas G. Rawski © Loren Brandt, Debin Ma, and Thomas G. Rawski March 2013 Department of Economic History London School of Economics Houghton Street London, WC2A 2AE Tel: +44 (0) 20 7955 7860 Fax: +44 (0) 20 7955 7730 2 From Divergence to Convergence: Re-evaluating the History Behind China’s Economic Boom1 By Loren Brandt, Debin Ma, and Thomas G. Rawski2 This version: Jan. 23, 2013 ABSTRACT China’s long-term economic dynamics pose a formidable challenge to economic historians. The Qing Empire (1644-1911), the world’s largest national economy before 1800, experienced a tripling of population during the 17th and 18th centuries with no signs of diminishing per capita income. While the timing remains in dispute, a vast gap emerged between newly rich industrial nations and China’s lagging economy in the wake of the Industrial Revolution. Only with an unprecedented growth spurt beginning in the late 1970s did this great divergence separating China from the global leaders substantially diminish, allowing China to regain its former standing among the world’s largest economies. This essay develops an integrated framework for understanding that entire history, including both the divergence and the recent convergent trend. We explain how deeply embedded political and economic institutions that contributed to a long process of extensive growth before 1800 subsequently prevented China from capturing the benefits associated with the Industrial Revolution. During the 20th century, the gradual erosion of these historic constraints and of new obstacles erected by socialist planning eventually opened the door to China’s current boom.
    [Show full text]
  • FINAL PROGRAM and BOOK of ABSTRACTS
    FINAL PROGRAM and BOOK OF ABSTRACTS 2017 IEEE 6th Data Driven Control and Learning Systems Conference (DDCLS’17) Chongqing, China May 26 –27, 2017 Organized by Technical Committee on Data Driven Control, Learning and Optimization, Chinese Association of Automation Locally Organized by Chongqing Jiaotong University Sponsored by IEEE Beijing Section IEEE Industrial Electronics Society Beijing Jiaotong University Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the Publisher. IEEE Catalog Number: CFP17HAG-CDR ISBN: 978-1-5090-5460-2 CONTENTS Organizing Committee ··························································································· 1 Welcome Message from General Chairs ··································································· 3 Message from Technical Program Chairs ··································································· 5 Plenary Lectures ·································································································· 7 Distinguished Lectures ························································································· 11 Program at a Glance ··························································································· 15 Technical Programmes and Book of Abstracts ··························································
    [Show full text]
  • Parallel Control for Continuous-Time Linear Systems: a Case Study Qinglai Wei, Member, IEEE, Hongyang Li, and Fei-Yue Wang, Fellow, IEEE
    IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 7, NO. 4, JULY 2020 919 Parallel Control for Continuous-Time Linear Systems: A Case Study Qinglai Wei, Member, IEEE, Hongyang Li, and Fei-Yue Wang, Fellow, IEEE Abstract—In this paper, a new parallel controller is developed of industrial control systems, the intelligent control theory, for continuous-time linear systems. The main contribution of the such as fuzzy control [6], neural network control [7], adaptive method is to establish a new parallel control law, where both dynamic programming [8], [9], is attracted by researchers. state and control are considered as the input. The structure of the parallel control is provided, and the relationship between the Among these previous stages, most system control problems parallel control and traditional feedback controls is presented. are analyzed by state feedback control methods in present Considering the situations that the systems are controllable and study: we generally design state feedback controllers to form incompletely controllable, the properties of the parallel control closed-loop systems, that is, the control laws are functions of law are analyzed. The parallel controller design algorithms are the system states. However, the state feedback controllers have given under the conditions that the systems are controllable and incompletely controllable. Finally, numerical simulations are some disadvantages: carried out to demonstrate the effectiveness and applicability of 1) The traditional state feedback controllers are only related the present method. to the system states rather than the properties of the controllers Index Terms—Continuous-time linear systems, digital twin, and it causes that the control signals may change greatly with parallel controller, parallel intelligence, parallel systems.
    [Show full text]
  • (USCR) Is the Official Publication of the US-China Peoples Friendship Association
    INTRODUCTION The US-China Review (USCR) is the official publication of the US-China Peoples Friendship Association. Its predecessor, New China, was created by USCPFA-New York in 1973 and sold by subscription. When New China discontinued publication in 1979, the USCR was already in existence as a broadside newsletter. After New China’s demise, it was upgraded to magazine form. This index covers the years from 1981 through 2012, Volumes V-XXXVI. It does not include letters to the editor, Newsbriefs or the section’s successor China Currents, Travel Notes or resource listings. Exceptions have been made for longer Travel Notes pieces. Over the years under different editors, formatting for titles of articles (use of capital letters and punctuation, for example) has changed. The index reflects these changes except in cases where additional punctuation was added for clarification. The index will be available on line for use by USCR editors and researchers. It should be noted that Yale University houses a complete run of the USCR, and updated indices will be added to that collection annually. Beginning with the winter 2013 issue, USCR editors are responsible for updating to the index. Several people contributed much needed assistance during the preparation of the index. Barbara Cobb, USCR Coordinator; Marci Duryea, USCR Production Coordinator; Richard Pendleton, USCPFA-New England; Douglas Reynolds, Co-president, USCPFA- Atlanta; Bart Trescott, USCPFA-Carbondale; and Kitty Trescott, USCPFA-Carbondale and Director of the Center for Teaching about China provided information and advice, and loaned back issues of the USCR. Any mistakes and/or erroneous judgment calls are the compiler’s alone.
    [Show full text]
  • What Democracy Means in China After 30 Years of Reform Roundtable Congressional-Executive Commission on China
    WHAT DEMOCRACY MEANS IN CHINA AFTER 30 YEARS OF REFORM ROUNDTABLE BEFORE THE CONGRESSIONAL-EXECUTIVE COMMISSION ON CHINA ONE HUNDRED ELEVENTH CONGRESS FIRST SESSION MAY 22, 2009 Printed for the use of the Congressional-Executive Commission on China ( Available via the World Wide Web: http://www.cecc.gov U.S. GOVERNMENT PRINTING OFFICE 51–188 PDF WASHINGTON : 2009 For sale by the Superintendent of Documents, U.S. Government Printing Office Internet: bookstore.gpo.gov Phone: toll free (866) 512–1800; DC area (202) 512–1800 Fax: (202) 512–2104 Mail: Stop IDCC, Washington, DC 20402–0001 VerDate Nov 24 2008 17:42 Oct 28, 2009 Jkt 000000 PO 00000 Frm 00001 Fmt 5011 Sfmt 5011 U:\DOCS\51188.TXT DEIDRE CO N T E N T S Page Opening statement of Charlotte Oldham-Moore, Staff Director, Congressional- Executive Commission on China ........................................................................ 1 Grob, Douglas, Cochairman’s Senior Staff Member, Congressional-Executive Commission on China .......................................................................................... 2 Cheng, Li, Director of Research and Senior Fellow, Foreign Policy, John L. Thornton China Center, Brookings Institution ............................................. 4 Manion, Melanie, Professor of Public Affairs and Political Science, University of Wisconsin-Madison .......................................................................................... 6 Liu, Yawei, Director, China Program, The Carter Center ................................... 9 Dickson, Bruce J.,
    [Show full text]