Distributed Exponential Formation Control of Multiple Wheeled Mobile Robots
|
|
- Barbara Paul
- 6 years ago
- Views:
Transcription
1 Proceedngs of the Internatonal Conference of Control, Dynamc Systems, and Robotcs Ottawa, Ontaro, Canada, May Paper No. 46 Dstrbuted Exponental Formaton Control of Multple Wheeled Moble Robots Wene Dong, Felpe De La Torre Department of Electrcal Engneerng, the Unversty of Texas-Pan Amercan 121 Unversty Dr., Ednburg, TX, USA Abstract - Ths paper consders the dstrbuted formaton control of multple nonholonomc wheeled moble robots wth a leader. Dstrbuted trackng control laws are proposed wth the ad of results of cascade systems such that the centrod of the states of a group of moble robot exponentally tracks the leader. Smulaton results show the effectveness of the proposed algorthms. Keywords: Wheeled moble robots, cooperatve control, formaton control, dstrbuted control. 1. Introducton There are lots of applcatons of wheeled moble robots n practce and control strateges have been developed for decades. Wheeled moble robots wth nonslp constrants are typcally nonhonomc systems. Stablzaton of a sngle nonholonomc system s challengng due to the fact that no smooth pure state feedback control law exsts for stablzaton. Moreover, no dynamc contnuous tme-nvarant feedback controller s avalable to render the closed loop system locally asymptotcally stable Pomet 1992). Wth the efforts of researchers, several approaches have been proposed for stablzng nonholonomc systems, whch can be classfed nto the followng three aspects: dscontnuous tmenvarant feedback, the tme-varyng feedback, and the hybrd feedback. For detals, see Kolmanovsky and McClamroch 1995) and the references theren. It s challengng to desgn trackng controllers for wheeled moble robots because of ther nonlnear features. Samson and At-Abderrahm proposed the frst trackng controller for a moble robot n Samson and At-Abderrahm 1991). Then a trackng controller was desgned through lnear approxmaton for nonholonomc systems n Walsh et al 1994). In D'Andrea-Novel et al 1995), the trackng task of wheeled moble robots was fulflled by lnearzng both statc and dynamc feedback. Fless et al solved the trackng problem utlzng results of dfferentally flat nonlnear systems Fless et al 1995). Wth the ad of backsteppng technques, sem-global trackng controllers were proposed for a chaned-form system n Jang and Nmeer 1999). In Jang 2), global state and output trackng controllers were proposed for chaned-form systems wth the ad of Lyapunov technques. Based on the results of cascade systems, lnear trackng controllers were proposed for chaned-form systems n Lefeber et al 2) and Tan and Cao 27). Due to the practcal requrement of specfc tasks, the consensus problem wthout a leader has been extensvely studed n the past decades. In Jadbabae et al 23), matrx theory was appled to propose local control laws for fst-order lnear dscrete-tme systems such that the states of multple systems converge to a constant value. In N and Cheng 21), Laplacan matrx of a communcaton graph was exploted to propose local control laws for the consensus problem of multple frst-order lnear contnuous-tme systems. In Ren and Beard 25), consensus algorthms were proposed wth relaxed assumpton on the communcaton graphs n N and Cheng 21). Consensus problem wth a leader has also been studed systematcally and several control laws have been proposed. In Cao and Ren 21), consensus problems of frst-order and second-order lnear systems were consdered. Dstrbuted controllers were proposed such that the state of each system converge to a desred traectory wthn fnte tme under the condton that the desred traectory s avalable to a porton of the group of systems. In N and Cheng 21), leader-followng consensus of hgh-order lnear systems was consdered over a 46-1
2 swtchng communcaton topology. Dstrbuted controllers were proposed wth the ad of Rccatnequalty-based approach. In Lu and Ja 21), consensus control of mult-agent systems was consdered. Output feedback controllers were proposed wth the ad of theory. In Scardov and Sepulchre 29), consensus of hgh-order lnear systems was consdered for tme-varyng and drected communcaton topologes. Dstrbuted controllers were proposed wth the ad of the observer desgn approach. In L et al 211) and L et al 21), consensus of multple lnear systems was consdered n an unfed vewpont and a notaton of concensus regon was ntroduced. In Meng et al 212), the leaderfollowng consensus problem for a group of agents wth dentcal lnear systems subect to control nput saturaton was consdered. Lnear feedback laws were proposed for fxed and swtchng communcaton topology. In Cao and Ren 212a,212b), consensus of frst-order and second-order nonlnear systems was consdered. Fnte-tme control laws were proposed wth the ad of a comparson lemma. In Dong 212), cooperatve control of multple moble robots was consdered. Dstrbuted control laws were proposed wth the ad of a consensus approach. In ths paper, we study dstrbuted formaton control of multple nonholonomc wheeled moble robots wth a leader whose state s not avalable to each system such that the group of robots converges to a desred geometrc pattern whose centrod follows the leader. New dstrbuted control laws are proposed based on the results of cascade systems and the propertes of persstently exctng sgnals. Compared to the results n lterature, n ths paper cooperatve trackng control s solved for multple nonlnear systems. Compared to the results n Dong 212), a new approach s proposed for cooperatve trackng control problem of multple wheeled moble robots and the proposed control laws can make the trackng errors unformly exponentally converge to zero, whch s much more applcable n practce. The remanng parts of ths paper are organzed as follows. In Secton 2, the consdered problem s formulated and some prelmnary results are presented. In Secton 3, dstrbuted trackng controllers are proposed. In Secton 4, controllers are proposed for swtchng communcaton graphs. In Secton 5, smulaton results are presented. The last secton concludes ths paper. 2. Problem Statement It s consdered a group of m wheeled moble robots whch move on a horzontal plane. The moton of robot s descrbed by x v cos, y v sn, 1) where x, y ) s the poston of robot n a coordnate system, s the orentaton of robot, v s the speed of robot, and s the angular speed of robot. The control nputs are v and. For m systems, each system knows ts own state and ts neghbors' states by communcaton and/or sensors. For smplcty, t s assumed that the communcatons between the systems are bdrectonal. If we consder each system as a node, the communcaton between the systems can be descrbed by an undrected) graph G { V, E}, where V {1,2,, m} s a node set, and E s an edge set wth unordered par, ) whch descrbes the communcaton between node and node. If the state of node s avalable to node, node s called a neghbor of node. The set of all neghbors of node s denoted by N. A graph s called connected f for any two dfferent nodes there exsts a set of edges whch connect the two nodes. A formaton of m robots s defned by a geometrc pattern P. The pattern P can be descrbed by orthogonal coordnates p, p ) 1 m). Wthout loss of generalty, we assume that x y m m p and p,.e., the center of the geometrc pattern P s at the orgn of a local 1 x 1 y 46-2
3 orthogonal coordnate system. It s gven a reference traectory q t) x t), y t), t)) whch satsfes x v cos, y v sn, 2) where v and are known tme-varyng functons. The state q s assumed to be avalable to a porton of the m wheeled moble robots. Let q [ x, y, ], the control problem consdered n ths artcle s defned as follows. Control Problem: Desgn control laws v and for system usng ts own state q, ts neghbor's state q l, the relatve poston wth ts neghbor p lx, ply) for l N, and the desred traectory q f t s avalable to the system such that x x px p x lm t y y py p y 3) lm ) 4) t m m xl yl lm x,lm y t l1 m t l1 m for 1 m. In order to solve the defned problem, the followng assumpton s made on the desred traectory. d t T Assumpton 1 The 2 ) are bounded and 2 ) d > dt for some > and T >. t 3. Cooperatve Controller Desgn Defne the varables z, z x p )cos y p )sn, z x p )sn y p ) cos 6) 1 2 x y 3 x y 5) for m, where k > and p p. The transformed state space model s 3 x y z 1 z2 v z3 z3 z2. 8) 9) 7) We have the followng results. Lemma 1 If lm t z1 z1), lm t z2 z2), and lm t z3 z3) for 1 m, then 3)-5) hold. System 7)-9) can be consdered as a cascade system of 7) and 8)-9). We frst desgn control law for system 7) such that lm t z1 z1). For a group of m robots 1 m ), the communcaton between the robots s descrbed by a graph G { A, E}. Gven an m m constant matrx 46-3
4 A [ a ] wth a a >, the Laplacan matrx L [ L ] of the graph G wth weght matrx A s defned by L l a,, ln, a l, f N f N f and and. For the Laplacan matrx, the followng result s useful n ths paper. Lemma 2 Dong 212)) If the communcaton graph G s connected, then L dag )) s a postve [ 1, 2,, m], defnte symmetrc matrx, where constant vector 1 m) and at least one of the elements of s nonzero. Wth the ad of Lemma 2, we have the followng lemma. Lemma 3 For the m 1) systems n eqn. 7) m ), f the communcaton graph G s connected and the system s avalable to at least one of the m systems, the control laws 1 a z1 z1 ) b z1 z1) 1) N 1 a 1 1 ) b 1 1) 1 sgn a 1 1 ) b 1 1) N N 11) exp for 1 m guarantee that lmt z1 z1) and lmt ), where 1, b >, s suffcently large, the parameter 1 f system s avalable to system and f 1 system s not avalable to system. The proof of Lemma 3 s the same as the proof of Lemma 4 n Dong 212) and s omtted here for space lmtaton. Wth the ad of Lemma 3 and the results of cascade system, we have the followng results. Theorem 1 For the m 1) systems n eqn. 8) m ), under Assumpton 1, f the communcaton graph G s connected, then the dstrbuted control laws 1)-11) and v k1z2 k2 z3 z3 2 12) 2 a 2 2 ) b 2 2) sgn a 2 2 ) b 2 2) N N 13) for 1 m ensure that z, z, z ) unformly exponentally converges to z, z, ) and exp 1 2 z3 1, 2 ) exponentally converges to ), where s a suffcently large postve constant, k >, k >, and v z k z k , z3 In Dong 212), dstrbuted control laws for multple wheeled moble robots were proposed such that the state of each system asymptotcally converges to a desred state. In ths paper, new dstrbuted 46-4
5 trackng control laws are proposed wth the ad of the results of cascade systems. Moreover, the proposed control laws ensure that the state of each system globally unformly exponentally converges to a desred state. 4. Smulatons To show the effectveness of the proposed results, smulaton has been done for three robots. The desred geometrc pattern P s shown n Fgure 1. The pattern P can be descrbed by orthogonal coordnates p, p ) 1,1.7), p, p ) 1, 1.7), and p, p ) 2,). Assume the 1x 1y, y, 2x 2 y 3x 3y reference traectory s x ) 1sn.5t ), 1cos.5 t),.5t ), by 2) v 5 and.5. So, Assumpton 1 s satsfed. Assume the communcaton graph s shown n Fgure 2. The cooperatve controllers can be obtaned by Theorem 1. We chose the control parameters a 2, k 2, b 2, 2, and 2. Fgure 3 3 shows the centrod of x 1 3 ).e., x /3 1 ) and x. Fgure 4 shows the centrod of y ).e., y /3 1 ) and y. Fgure 5 shows ) 1 3 ). Fgure 6 shows the path of the centrod of the three robots and ts desred path. From the smulaton 4)-5) are satsfed. Eqn. 3) s also verfed and the response of them s omtted here Fg. 1. Desred formaton. Fg. 2. Informaton exchange graph G. 46-5
6 Fg. 3. Response of the centrod of x sold) for 1 3 and x dashed). Fg. 4. Response of the centrod of y sold) for 1 3 and y dashed). Fg. 6. Response of ) for
7 Fg. 6. The path of the centrod of the three robots dashed lne), the desred path sold lne) of the centrod of robots, and formaton of the three robots at several moments red trangles). 4. Concluson Ths paper has dscussed the formaton control of multple wheeled moble robots under the condton that a desred traectory s avalable to only a porton of the systems. Dstrbuted control laws were proposed wth the ad of Lyapunov technques and results from graph theory. Smulaton results show the effectveness of the proposed control laws. In ths paper, the nformaton exchange graph s assumed to be bdrectonal. The future work s to extend our results to more general nformaton exchange graphs. Acknowledgements Ths work was supported by DoD ARO under Grant No. W911NF References Cao Y., Ren W. 21). Dstrbuted coordnated trackng va a varable structure approach - part I: Consensus trackng. Proc. Of Amercan Control Conference, pp Cao Y., Ren W. 212a). Fnte-tme consensus for second-order systems wth unknown nherent nonlnear dynamcs under an undrected swtchng graph. Proc. of Amercan Control Conference. pp Cao Y., Ren W. 212b). Fnte-tme consensus for sngle-ntegrator knematcs wth unknown nherent nonlnear dynamcs under a drected nteracton graph. Proc. of Amercan Control Conference. pp D'Andrea-Novel B, Bastn G., Campon G. 1995). Control of nonholonomc wheeled moble robots by state feedback lnearzaton. Int. J. of Robotc Research, 14, pp Dong W. 212). Trackng control of multple wheeled moble robots wth lmted nformaton of a desred traectory. IEEE Trans. on Robotcs, 28, pp Fless M., Levne J., Martn P., Rouchon P. 1995). Flatness and defect of nonlnear systems: ntroductory theory and examples. Int. J. Control, 61, pp Jadbabae A., Ln J., Morse A.S., 23). Coordnaton of groups of moble autonomous agents usng nearest neghbor rules. IEEE Trans. On Automatc Control, 48, pp Jang Z.-P. 2). Lyapunov desgn of global state and output feedback trackers for nonholonomc control systems. Int. J. of Control, 73, pp Jang Z.-P., Nmeer N., 1999). A recursve technque for trackng control of nonholonomc systems n chaned form. IEEE Trans. on Auto. Contr., 44, pp Kolmanovsky I., McClamroch N.H., 1995). Development n nonholonomc control problems. IEEE Control System Magazne, pp
8 Lefeber E., Robertson A., Nmeer H., 2) Lnear controllers for exponental trackng of systems n chaned form. Int. J. of Robust and Nonlnear control, 1, pp L Z., Duan Z., Chen G., 211). Dynamc consensus of lnear multagent systems. IET Control Theory and Applcatons, 5, pp L Z., Duan Z., Chen G., Huang L., 21). Consensus of multagent systems and synchronzaton of complex networks: a unfed vewpont. IEEE Trans. on Crcuts and Systems - I: Regular Papers, 57, pp Lu Y., Ja Y., 21). H_nfty consensus control of mult-agent systems wth swtchng topology: a dynamc output feedback protocol. Int. J. of Control, 83, pp Meng Z., Zhao Z., Ln Z., 212). On global consensus of lnear mult-agent systems subect to nput saturaton. Proc. of Amercan Control Conference, pp N W., Cheng D., 21). Leader-followng consensus of mult-agent systems under fxed and swtchng topologes. Systems and Control Letters, 59, pp Olfat-Saber R., Murray R.M., 24). Consensus problems n networks of agents wth swtchng topology and tme-delays. IEEE Trans. on Auto. Contr., 49, pp Pomet J.-B., 1992). Explct desgn of tme-varyng stablzng control laws for a class of controllable systems wthout drft. Systems and Control Letters, 18, pp Ren W., Beard R. W. 25). Consensus seekng n mult-agent systems under dynamcally changng nteracton topologes. IEEE Trans. on Automatc Control, 5, pp Samson C., At-Abderrahm K., 1991). Feedback control of a nonholonomc wheeled moble cart n cartesan space. Proc. of IEEE Conf. on Robotcs and Automaton, pp Scardov L., Sepulchre R., 29). Synhronzaton n networks of dentcal lnear systems. Automatca, 45, pp Tan Y.P., Cao K.C., 27). Tme-varyng lner controllers for exponental trackng of non-holonomc systems n chaned form. Int. J. of Robust and Nonlnear control, 17, pp Walsh G., Tlbury D., Sastry S.S, Murray R.M., Laumond J.P., 1994). Stablzaton of traectores for systems wth nonholonomc constrants. IEEE Trans. on Auto. Contr., 39, pp
Controller Design of High Order Nonholonomic System with Nonlinear Drifts
Internatonal Journal of Automaton and Computng 6(3, August 9, 4-44 DOI:.7/s633-9-4- Controller Desgn of Hgh Order Nonholonomc System wth Nonlnear Drfts Xu-Yun Zheng Yu-Qang Wu Research Insttute of Automaton,
More informationChanging Topology and Communication Delays
Prepared by F.L. Lews Updated: Saturday, February 3, 00 Changng Topology and Communcaton Delays Changng Topology The graph connectvty or topology may change over tme. Let G { G, G,, G M } wth M fnte be
More informationAdaptive Consensus Control of Multi-Agent Systems with Large Uncertainty and Time Delays *
Journal of Robotcs, etworkng and Artfcal Lfe, Vol., o. (September 04), 5-9 Adaptve Consensus Control of Mult-Agent Systems wth Large Uncertanty and me Delays * L Lu School of Mechancal Engneerng Unversty
More informationDynamic Systems on Graphs
Prepared by F.L. Lews Updated: Saturday, February 06, 200 Dynamc Systems on Graphs Control Graphs and Consensus A network s a set of nodes that collaborates to acheve what each cannot acheve alone. A network,
More informationCooperative Output Regulation of Linear Multi-agent Systems with Communication Constraints
2016 IEEE 55th Conference on Decson and Control (CDC) ARIA Resort & Casno December 12-14, 2016, Las Vegas, USA Cooperatve Output Regulaton of Lnear Mult-agent Systems wth Communcaton Constrants Abdelkader
More informationDO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED.
EE 539 Homeworks Sprng 08 Updated: Tuesday, Aprl 7, 08 DO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED. For full credt, show all work. Some problems requre hand calculatons.
More informationOutline. Communication. Bellman Ford Algorithm. Bellman Ford Example. Bellman Ford Shortest Path [1]
DYNAMIC SHORTEST PATH SEARCH AND SYNCHRONIZED TASK SWITCHING Jay Wagenpfel, Adran Trachte 2 Outlne Shortest Communcaton Path Searchng Bellmann Ford algorthm Algorthm for dynamc case Modfcatons to our algorthm
More informationAsynchronous Periodic Event-Triggered Coordination of Multi-Agent Systems
017 IEEE 56th Annual Conference on Decson and Control (CDC) December 1-15, 017, Melbourne, Australa Asynchronous Perodc Event-Trggered Coordnaton of Mult-Agent Systems Yaohua Lu Cameron Nowzar Zh Tan Qng
More informationFormation Flight Control of Multi-UAV System with Communication Constraints
do: 105028/jatmv8208 Formaton Flght Control of Mult-UAV System wth Communcaton Constrants Rubn Xue 1, Gaohua Ca 2 Abstract: Three dmensonal formaton control problem of mult-uav system wth communcaton constrants
More informationIntroduction. - The Second Lyapunov Method. - The First Lyapunov Method
Stablty Analyss A. Khak Sedgh Control Systems Group Faculty of Electrcal and Computer Engneerng K. N. Toos Unversty of Technology February 2009 1 Introducton Stablty s the most promnent characterstc of
More informationDecentralized Event-Triggered Cooperative Control with Limited Communication
Decentralzed Event-Trggered Cooperatve Control wth Lmted Communcaton Abstract Ths note studes event-trggered control of Mult-Agent Systems (MAS) wth frst order ntegrator dynamcs. It extends prevous work
More informationDistributed Multi-Agent Coordination: A Comparison Lemma Based Approach
2011 Amercan Control Conference on O'Farrell Street, San Francsco, CA, USA June 29 - July 01, 2011 Dstrbuted Mult-Agent Coordnaton: A Comparson Lemma Based Approach Yongcan Cao and We Ren Abstract In ths
More informationLossy Compression. Compromise accuracy of reconstruction for increased compression.
Lossy Compresson Compromse accuracy of reconstructon for ncreased compresson. The reconstructon s usually vsbly ndstngushable from the orgnal mage. Typcally, one can get up to 0:1 compresson wth almost
More informationINTO CHAINED FORM USING DYANMIC FEEDBACK D. TILBURY, O. SRDALEN, L. BUSHNELL; S. SASTRY
A MULTI-STEERING TRAILER SYSTEM: CONVERSION INTO CHAINED FORM USING DYANMIC FEEDBACK D. TILBURY, O. SRDALEN, L. BUSHNELL; S. SASTRY Electroncs Research Laboratory, Department of Electrcal Engneerng and
More informationVoronoi Based Coverage Control for Nonholonomic Mobile Robots
Vorono Based Coverage Control for onholonomc Moble Robots Alreza Drafzoon, Mohammad B. Menhaj, and Ahmad Afshar Abstract In ths paper we deal wth the problem of coverng an envronment usng a group of moble
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationContainment Control of Multi-Agent Systems with Dynamic Leaders Based on a P I n -Type Approach
Contanment Control of Mult-Agent Systems wth Dynamc Leaders Based on a P I n -Type Approach 1 arxv:1411.4346v1 [cs.sy] 17 Nov 214 Yunpeng Wang, Long Cheng, We Ren, Zeng-Guang Hou, and Mn Tan Abstract Ths
More informationConsensus of Multi-Agent Systems by Distributed Event-Triggered Control
Preprnts of the 19th World Congress The Internatonal Federaton of Automatc Control Consensus of Mult-Agent Systems by Dstrbuted Event-Trggered Control Wenfeng Hu, Lu Lu, Gang Feng Department of Mechancal
More informationThis article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and
Ths artcle appeared n a ournal publshed by Elsever The attached copy s furnshed to the author for nternal non-commercal research and educaton use, ncludng for nstructon at the authors nsttuton and sharng
More informationCooperative output regulation of multi-agent systems coupled by dynamic edges. Title. Xiang, J; Li, Y; Hill, DJ
Ttle Cooperatve output regulaton of mult-agent systems coupled by dynamc edges Author(s) Xang, J; L, Y; Hll, DJ Ctaton The 19th World Congress of the Internatonal Federaton of Automatc Control (IFAC),
More informationFormation Control of Nonholonomic Multi-Vehicle Systems based on Virtual Structure
Proceedngs of the 7th World Congress The Internatonal Federaton of Automatc Control Seoul, Korea, July 6-, 8 Formaton Control of Nonholonomc Mult-Vehcle Systems based on Vrtual Structure Chka Yoshoka Toru
More informationPattern Generation with Multiple Robots
Pattern Generaton wth Multple Robots Mong-yng A. Hseh and Vjay Kumar GRASP Laboratory Unversty of Pennsylvana Phladelpha, PA 1914 Emal: {mya, kumar}@grasp.cs.upenn.edu Abstract We develop decentralzed
More informationDISTRIBUTED SENSOR FUSION USING DYNAMIC CONSENSUS. California Institute of Technology
DISTRIBUTED SENSOR FUSION USING DYNAMIC CONSENSUS Demetr P. Spanos Rchard M. Murray Calforna Insttute of Technology Abstract: Ths work s an extenson to a companon paper descrbng consensustrackng for networked
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationIN RECENT years, there has been an increasing research interest
IEEE/ASME TRASACTIOS O MECHATROICS, VOL. 4, O. 2, APRIL 2009 29 Robust Fnte-Tme Consensus Trackng Algorthm for Multrobot Systems Suyang Khoo, Lhua Xe, Fellow, IEEE, and Zhhong Man, Member, IEEE Abstract
More information3 Riccati Design for Synchronization of Continuous-Time Systems
3 Rccat Desgn for Synchronzaton of Contnuous-Tme Systems Ths chapter studes cooperatve trackng control of mult-agent dynamcal systems nterconnected by a fxed communcaton graph topology. Each agent or node
More informationOff-policy Reinforcement Learning for Robust Control of Discrete-time Uncertain Linear Systems
Off-polcy Renforcement Learnng for Robust Control of Dscrete-tme Uncertan Lnear Systems Yonglang Yang 1 Zhshan Guo 2 Donald Wunsch 3 Yxn Yn 1 1 School of Automatc and Electrcal Engneerng Unversty of Scence
More informationThe equation of motion of a dynamical system is given by a set of differential equations. That is (1)
Dynamcal Systems Many engneerng and natural systems are dynamcal systems. For example a pendulum s a dynamcal system. State l The state of the dynamcal system specfes t condtons. For a pendulum n the absence
More informationController Design for Networked Control Systems in Multiple-packet Transmission with Random Delays
Appled Mehans and Materals Onlne: 03-0- ISSN: 66-748, Vols. 78-80, pp 60-604 do:0.408/www.sentf.net/amm.78-80.60 03 rans eh Publatons, Swtzerland H Controller Desgn for Networed Control Systems n Multple-paet
More informationAdaptive Flocking Control for Dynamic Target Tracking in Mobile Sensor Networks
The 29 IEEE/RSJ Internatonal Conference on Intellgent Robots and Systems October -5, 29 St. Lous, USA Adaptve Flockng Control for Dynamc Target Trackng n Moble Sensor Networks Hung Manh La and Wehua Sheng
More informationOn simultaneous parameter identification and state estimation for cascade state affine systems
Amercan Control Conference Westn Seattle Hotel, Seattle, Washngton, USA June 11-13, WeAI1.9 On smultaneous parameter dentfcaton and state estmaton for cascade state affne systems M. GHANES, G. ZHENG and
More informationROBUST ATTITUDE COORDINATION CONTROL OF FORMATION FLYING SPACECRAFT UNDER CONTROL INPUT SATURATION
Internatonal Journal of Innovatve Computng, Informaton and Control ICIC Internatonal c 011 ISSN 1349-4198 Volume 7, Number 7(B, July 011 pp. 43 435 ROBUST ATTITUDE COORDINATION CONTROL OF FORMATION FLYING
More informationCommunication-efficient Distributed Solutions to a System of Linear Equations with Laplacian Sparse Structure
Communcaton-effcent Dstrbuted Solutons to a System of Lnear Equatons wth Laplacan Sparse Structure Peng Wang, Yuanq Gao, Nanpeng Yu, We Ren, Janmng Lan, and D Wu Abstract Two communcaton-effcent dstrbuted
More informationControl of Uncertain Bilinear Systems using Linear Controllers: Stability Region Estimation and Controller Design
Control of Uncertan Blnear Systems usng Lnear Controllers: Stablty Regon Estmaton Controller Desgn Shoudong Huang Department of Engneerng Australan Natonal Unversty Canberra, ACT 2, Australa shoudong.huang@anu.edu.au
More informationChapter 7 Channel Capacity and Coding
Wreless Informaton Transmsson System Lab. Chapter 7 Channel Capacty and Codng Insttute of Communcatons Engneerng atonal Sun Yat-sen Unversty Contents 7. Channel models and channel capacty 7.. Channel models
More informationIrregular vibrations in multi-mass discrete-continuous systems torsionally deformed
(2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected
More informationContainment Control for First-Order Multi-Agent Systems with Time-Varying Delays and Uncertain Topologies
Commun. heor. Phys. 66 (06) 49 55 Vol. 66, No., August, 06 Contanment Control for Frst-Order Mult-Agent Systems wth me-varyng Delays and Uncertan opologes Fu-Yong Wang ( ), Hong-Yong Yang ( ), Shu-Nng
More informationTokyo Institute of Technology Periodic Sequencing Control over Multi Communication Channels with Packet Losses
oyo Insttute of echnology Fujta Laboratory oyo Insttute of echnology erodc Sequencng Control over Mult Communcaton Channels wth acet Losses FL6-7- /8/6 zwrman Gusrald oyo Insttute of echnology Fujta Laboratory
More informationOn Non-Consensus Motions of Dynamical Linear Multi-Agent Systems
On Non-Consensus Motons of Dynamcal Lnear Mult-Agent Systems Ca, Nng 1, 2, 4 Deng, Chun-Ln 1, 3 Wu, Qu-Xuan 4 1 School of Electrcal Engneerng, Northwest Unversty for Natonaltes, Lanzhou, Chna 2 Key Laboratory
More informationAutomatica. Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Mou Chen a,c, Shuzhi Sam Ge b,c,, Beibei Ren c
Automatca 47 (0) 45 465 Contents lsts avalable at ScenceDrect Automatca ournal homepage: www.elsever.com/locate/automatca Adaptve trackng control of uncertan MIMO nonlnear systems wth nput constrants Mou
More informationDistributed event-triggered coordination for average consensus on weight-balanced digraphs
Dstrbuted event-trggered coordnaton for average consensus on weght-balanced dgraphs Cameron Nowzar a Jorge Cortés b a Department of Electrcal and Systems Engneerng, Unversty of Pennsylvana, Phladelpha,
More informationContainment Control of Multi-Agent Systems with Dynamic Leaders Based on a P I n -Type Approach
Contanment Control of Mult-Agent Systems wth Dynamc Leaders Based on a P I n -Type Approach Long Cheng, Yunpeng Wang, We Ren, Zeng-Guang Hou, and Mn Tan arxv:4446v [cssy] 27 Aug 25 Abstract Ths paper studes
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationFlocking Control of a Mobile Sensor Network to Track and Observe a Moving Target
29 IEEE Internatonal Conference on Robotcs and Automaton Kobe Internatonal Conference Center Kobe, Japan, May 12-17, 29 Flockng Control of a Moble Sensor Network to Track and Observe a Movng Target Hung
More informationPeriodic Event-Triggered Average Consensus over Directed Graphs
05 IEEE 54th Annual Conference on Decson and Control CDC) December 5-8, 05 Osaka, Japan Perodc Event-Trggered Average Consensus over Drected Graphs Xangyu Meng, Lhua Xe, Yeng Cha Soh, Cameron Nowzar, and
More informationCHAPTER 6. LAGRANGE S EQUATIONS (Analytical Mechanics)
CHAPTER 6 LAGRANGE S EQUATIONS (Analytcal Mechancs) 1 Ex. 1: Consder a partcle movng on a fxed horzontal surface. r P Let, be the poston and F be the total force on the partcle. The FBD s: -mgk F 1 x O
More informationDistributed Self-triggered Control for Multi-agent Systems
49th IEEE Conference on Decson and Control December 15-17, 21 Hlton Atlanta Hotel, Atlanta, GA, USA Dstrbuted Self-trggered Control for Mult-agent Systems Dmos V. Dmarogonas, Emlo Frazzol and Karl H. Johansson
More informationA graph is a pair G= (V,E) with V a nonempty finite set of nodes or vertices V { v1 a set of edges or arcs E V V. We assume ( vi, vi) E,
Prepared by FL Lews Updated: hursday, October 6, 008 Graphs A graph s a par G= (V,E) wth V a nonempty fnte set of nodes or vertces V { v,, v N } and a set of edges or arcs E V V We assume ( v, v) E,, e
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationA revised adaptive fuzzy sliding mode controller for robotic manipulators
A revsed adaptve fuzzy sldng mode controller for robotc manpulators Xaosong Lu* Department of Systems and Computer Engneerng, Carleton Unversty, 5 Colonel By Drve, Ottawa, Ontaro, Canada E-mal: luxaos@sce.carleton.ca
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationcoordinates. Then, the position vectors are described by
Revewng, what we have dscussed so far: Generalzed coordnates Any number of varables (say, n) suffcent to specfy the confguraton of the system at each nstant to tme (need not be the mnmum number). In general,
More informationEEE 241: Linear Systems
EEE : Lnear Systems Summary #: Backpropagaton BACKPROPAGATION The perceptron rule as well as the Wdrow Hoff learnng were desgned to tran sngle layer networks. They suffer from the same dsadvantage: they
More informationEnergy Storage Elements: Capacitors and Inductors
CHAPTER 6 Energy Storage Elements: Capactors and Inductors To ths pont n our study of electronc crcuts, tme has not been mportant. The analyss and desgns we hae performed so far hae been statc, and all
More informationEvent-triggered Coordination for Formation Tracking Control in Constrained Space with Limited Communication
IEEE TRASACTIO O CYBERETICS Event-trggered Coordnaton for Formaton Trackng Control n Constraned Space wth Lmted Communcaton Xaome Lu, Shuzh Sam Ge, Fellow, IEEE, Cher-Hang Goh, Senor Member, IEEE, and
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationA Fuzzy-Neural Adaptive Iterative Learning Control for Freeway Traffic Flow Systems
Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 016 Vol I, IMECS 016, March 16-18, 016, Hong Kong A Fuzzy-Neural Adaptve Iteratve Learnng Control for Freeway Traffc Flow
More informationWavelet chaotic neural networks and their application to continuous function optimization
Vol., No.3, 04-09 (009) do:0.436/ns.009.307 Natural Scence Wavelet chaotc neural networks and ther applcaton to contnuous functon optmzaton Ja-Ha Zhang, Yao-Qun Xu College of Electrcal and Automatc Engneerng,
More informationDistributed Cooperative Control System Algorithms Simulations and Enhancements
Po Wu and P.J. Antsakls, Dstrbuted Cooperatve Control System Algorthms: Smulatons and Enhancements, ISIS Techncal Report, Unversty of Notre Dame, ISIS-2009-001, Aprl 2009. (http://www.nd.edu/~ss/tech.html)
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
More informationRobust Sliding Mode Observers for Large Scale Systems with Applications to a Multimachine Power System
Robust Sldng Mode Observers for Large Scale Systems wth Applcatons to a Multmachne Power System Mokhtar Mohamed, Xng-Gang Yan,*, Sarah K. Spurgeon 2, Bn Jang 3 Instrumentaton, Control and Embedded Systems
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationPhysics 181. Particle Systems
Physcs 181 Partcle Systems Overvew In these notes we dscuss the varables approprate to the descrpton of systems of partcles, ther defntons, ther relatons, and ther conservatons laws. We consder a system
More informationCoverage Control with Information Decay in Dynamic Environments
Coverage Control wth Informaton ecay n ynamc Envronments Nco Hübel S. Hrche A. Gusrald T. Hatanaka M. Fujta O. Sawodny Insttute for System ynamcs, Unverstät Stuttgart Fujta Laboratory, ept. of Mechancal
More informationA class of event-triggered coordination algorithms for multi-agent systems on weight-balanced digraphs
2018 Annual Amercan Control Conference (ACC) June 27 29, 2018. Wsconsn Center, Mlwaukee, USA A class of event-trggered coordnaton algorthms for mult-agent systems on weght-balanced dgraphs Png Xu Cameron
More informationAppendix B. The Finite Difference Scheme
140 APPENDIXES Appendx B. The Fnte Dfference Scheme In ths appendx we present numercal technques whch are used to approxmate solutons of system 3.1 3.3. A comprehensve treatment of theoretcal and mplementaton
More informationDecentralized Adaptive Regulation for Nonlinear Systems with iiss Inverse Dynamics
Vol. 3, No. ACTA AUTOMATICA SINICA February, 8 Decentralzed Adaptve Regulaton for Nonlnear Systems wth ISS Inverse Dynamcs YAN Xue-Hua, XIE Xue-Jun, LIU Ha-Kuan Abstract Ths paper consders the decentralzed
More informationStudy on Active Micro-vibration Isolation System with Linear Motor Actuator. Gong-yu PAN, Wen-yan GU and Dong LI
2017 2nd Internatonal Conference on Electrcal and Electroncs: echnques and Applcatons (EEA 2017) ISBN: 978-1-60595-416-5 Study on Actve Mcro-vbraton Isolaton System wth Lnear Motor Actuator Gong-yu PAN,
More informationFormation Control for Nonlinear Multi-agent Systems with Linear Extended State Observer
IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 1, NO. 2, APRIL 2014 171 Formaton Control for Nonlnear Mult-agent Systems wth Lnear Extended State Observer Wen Qn Zhongxn Lu Zengqang Chen Abstract Ths paper
More informationExperience with Automatic Generation Control (AGC) Dynamic Simulation in PSS E
Semens Industry, Inc. Power Technology Issue 113 Experence wth Automatc Generaton Control (AGC) Dynamc Smulaton n PSS E Lu Wang, Ph.D. Staff Software Engneer lu_wang@semens.com Dngguo Chen, Ph.D. Staff
More informationHierarchical State Estimation Using Phasor Measurement Units
Herarchcal State Estmaton Usng Phasor Measurement Unts Al Abur Northeastern Unversty Benny Zhao (CA-ISO) and Yeo-Jun Yoon (KPX) IEEE PES GM, Calgary, Canada State Estmaton Workng Group Meetng July 28,
More informationTracking with Kalman Filter
Trackng wth Kalman Flter Scott T. Acton Vrgna Image and Vdeo Analyss (VIVA), Charles L. Brown Department of Electrcal and Computer Engneerng Department of Bomedcal Engneerng Unversty of Vrgna, Charlottesvlle,
More informationVQ widely used in coding speech, image, and video
at Scalar quantzers are specal cases of vector quantzers (VQ): they are constraned to look at one sample at a tme (memoryless) VQ does not have such constrant better RD perfomance expected Source codng
More informationU.C. Berkeley CS294: Beyond Worst-Case Analysis Luca Trevisan September 5, 2017
U.C. Berkeley CS94: Beyond Worst-Case Analyss Handout 4s Luca Trevsan September 5, 07 Summary of Lecture 4 In whch we ntroduce semdefnte programmng and apply t to Max Cut. Semdefnte Programmng Recall that
More informationStabilization and Performance Analysis for Networked Flight Control System with Random Time Delays via a LMI Gridding Approach
Sensors & ransducers ol. 58 Issue November 23 pp. 32-38 Sensors & ransducers 23 by IFSA http://www.sensorsportal.com Stablzaton and Performance Analyss for Networed Flght Control System wth Random me Delays
More informationDigital Signal Processing
Dgtal Sgnal Processng Dscrete-tme System Analyss Manar Mohasen Offce: F8 Emal: manar.subh@ut.ac.r School of IT Engneerng Revew of Precedent Class Contnuous Sgnal The value of the sgnal s avalable over
More informationAdaptive sliding mode reliable excitation control design for power systems
Acta Technca 6, No. 3B/17, 593 6 c 17 Insttute of Thermomechancs CAS, v.v.. Adaptve sldng mode relable exctaton control desgn for power systems Xuetng Lu 1, 3, Yanchao Yan Abstract. In ths paper, the problem
More informationStability analysis for class of switched nonlinear systems
Stablty analyss for class of swtched nonlnear systems The MIT Faculty has made ths artcle openly avalable. Please share how ths access benefts you. Your story matters. Ctaton As Publshed Publsher Shaker,
More informationA Dioid Linear Algebra Approach to Study a Class of Continuous Petri Nets
A Dod Lnear Algebra Approach to Study a Class of Contnuous Petr Nets Duan Zhang, Huapng Da, Youxan Sun Natonal Laboratory of Industral Control Technology, Zhejang Unversty, Hangzhou, P.R.Chna, 327 {dzhang,
More informationMore metrics on cartesian products
More metrcs on cartesan products If (X, d ) are metrc spaces for 1 n, then n Secton II4 of the lecture notes we defned three metrcs on X whose underlyng topologes are the product topology The purpose of
More informationCOOPERATIVE CONTROL OF MULTI-AGENT SYSTEMS STABILITY, OPTIMALITY AND ROBUSTNESS KRISTIAN HENGSTER MOVRIĆ
COOPERAIVE COROL OF MULI-AGE SYSEMS SABILIY, OPIMALIY AD ROBUSESS by KRISIA HEGSER MOVRIĆ Presented to the Faculty of the Graduate School of he Unversty of exas at Arlngton n Partal Fulfllment of the Requrements
More informationMicrowave Diversity Imaging Compression Using Bioinspired
Mcrowave Dversty Imagng Compresson Usng Bonspred Neural Networks Youwe Yuan 1, Yong L 1, Wele Xu 1, Janghong Yu * 1 School of Computer Scence and Technology, Hangzhou Danz Unversty, Hangzhou, Zhejang,
More informationProjective change between two Special (α, β)- Finsler Metrics
Internatonal Journal of Trend n Research and Development, Volume 2(6), ISSN 2394-9333 www.jtrd.com Projectve change between two Specal (, β)- Fnsler Metrcs Gayathr.K 1 and Narasmhamurthy.S.K 2 1 Assstant
More informationχ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body
Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown
More informationContinuous Time Markov Chain
Contnuous Tme Markov Chan Hu Jn Department of Electroncs and Communcaton Engneerng Hanyang Unversty ERICA Campus Contents Contnuous tme Markov Chan (CTMC) Propertes of sojourn tme Relatons Transton probablty
More informationAppendix B: Resampling Algorithms
407 Appendx B: Resamplng Algorthms A common problem of all partcle flters s the degeneracy of weghts, whch conssts of the unbounded ncrease of the varance of the mportance weghts ω [ ] of the partcles
More informationThe Quadratic Trigonometric Bézier Curve with Single Shape Parameter
J. Basc. Appl. Sc. Res., (3541-546, 01 01, TextRoad Publcaton ISSN 090-4304 Journal of Basc and Appled Scentfc Research www.textroad.com The Quadratc Trgonometrc Bézer Curve wth Sngle Shape Parameter Uzma
More informationDistributed event-triggered control for multi-agent formation stabilization and tracking
strbuted event-trggered control for mult-agent formaton stablzaton and trackng Chrstophe Vel, Sylvan Bertrand, Mchel Keffer, Hélène Pet-Lahaner o cte ths verson: Chrstophe Vel, Sylvan Bertrand, Mchel Keffer,
More informationDecentralized Feedback Stabilization of Multiple Nonholonomic Agents
Decentralzed Feedback Stablzaton of Multple Nonholonomc Agents Invted Paper Savvas G. Lozou Dmos V. Dmarogonas Kostas J. Kyrakopoulos Control Systems Lab., Natonal Techncal Unversty of Athens, Athens,
More informationEvent-Triggering in Distributed Networked Systems with Data Dropouts and Delays
Event-Trggerng n Dstrbuted Networked Systems wth Data Dropouts and Delays Xaofeng Wang and Mchael D. Lemmon Unversty of Notre Dame, Department of Electrcal Engneerng, Notre Dame, IN, 46556, USA, xwang13,lemmon@nd.edu
More informationPower law and dimension of the maximum value for belief distribution with the max Deng entropy
Power law and dmenson of the maxmum value for belef dstrbuton wth the max Deng entropy Bngy Kang a, a College of Informaton Engneerng, Northwest A&F Unversty, Yanglng, Shaanx, 712100, Chna. Abstract Deng
More informationChapter 7 Channel Capacity and Coding
Chapter 7 Channel Capacty and Codng Contents 7. Channel models and channel capacty 7.. Channel models Bnary symmetrc channel Dscrete memoryless channels Dscrete-nput, contnuous-output channel Waveform
More informationA PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS
HCMC Unversty of Pedagogy Thong Nguyen Huu et al. A PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS Thong Nguyen Huu and Hao Tran Van Department of mathematcs-nformaton,
More informationParameter Estimation for Dynamic System using Unscented Kalman filter
Parameter Estmaton for Dynamc System usng Unscented Kalman flter Jhoon Seung 1,a, Amr Atya F. 2,b, Alexander G.Parlos 3,c, and Klto Chong 1,4,d* 1 Dvson of Electroncs Engneerng, Chonbuk Natonal Unversty,
More informationFINITE-TIME BOUNDEDNESS AND STABILIZATION OF SWITCHED LINEAR SYSTEMS
K Y BERNETIKA VOLUM E 46 21, NUMBER 5, P AGES 87 889 FINITE-TIME BOUNDEDNESS AND STABILIZATION OF SWITCHED LINEAR SYSTEMS Habo Du, Xangze Ln and Shhua L In ths paper, fnte-tme boundedness and stablzaton
More informationC. Nowzari, J. Cortés, and G. J. Pappas: Event-triggered communication and control for multi-agent average consensus Chap /1/23 11:26 page 1
consensus Chap. 0 2017/1/23 11:26 page 1 1 0.1 Introducton In ths chapter we look at one of the canoncal drvng examples for mult-agent systems: average consensus. In ths scenaro, a group of agents seek
More informationProceedings of Australasian Conference on Robotics and Automation, 2-4 Dec 2013, University of New South Wales, Sydney Australia
Proceedngs of Australasan Conference on Robotcs and Automaton 2-4 Dec 2013 Unversty of ew South Wales Sydney Australa Robust Optmal Atttude Control of Multrotors Hao Lu Behang Unversty School of Astronautcs
More informationChapter 2 Robust Covariance Intersection Fusion Steady-State Kalman Filter with Uncertain Parameters
Chapter 2 Robust Covarance Intersecton Fuson Steady-State Kalman Flter wth Uncertan Parameters Wenjuan Q, Xueme Wang, Wenqang Lu and Zl Deng Abstract For the lnear dscrete tme-nvarant system wth uncertan
More informationScroll Generation with Inductorless Chua s Circuit and Wien Bridge Oscillator
Latest Trends on Crcuts, Systems and Sgnals Scroll Generaton wth Inductorless Chua s Crcut and Wen Brdge Oscllator Watcharn Jantanate, Peter A. Chayasena, and Sarawut Sutorn * Abstract An nductorless Chua
More information