With a single stochastic extremum seeking control signal, we steer multiple autonomous vehicles, modeled as nonholonomic unicycles, toward the maximum of an unknown, spatially distributed signal field. The vehicles, whose angular velocities are constant and distinct, travel at the same forward velocity, which is controlled by the stochastic extremum seeking controller. To determine the vehicles’ velocity, the controller uses measurements of the signal field at the respective vehicle positions and excitation based on filtered white noise. The positions of the vehicles are not measured. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source and provide a numerical example to illustrate the effectiveness of the algorithm.
Issue Section:
Research Papers
References
1.
Wang
, J.
, and Gao
, W.
, 2012
, “Nano/Microscale Motors: Biomedical Opportunities and Challenges
,” ACS Nano
, 6
(7
), pp. 5745
–5751
.10.1021/nn30289972.
Gao
, W.
, Pei
, A.
, and Wang
, J.
, 2012
, “Water-Driven Micromotors
,” ACS Nano
, 6
(9
), pp. 8432
–8438
.10.1021/nn303309z3.
Garcia-Gradilla
, V.
, Orozco
, J.
, Sattayasamitsathit
, S.
, Soto
, F.
, Kuralay
, F.
, Pourazary
, A.
, Katzenberg
, A.
, Gao
, W.
, Shen
, Y.
, and Wang
, J.
, 2013
, “Functionalized Ultrasound-Propelled Magnetically Guided Nanomotors: Toward Practical Biomedical Applications
,” ACS Nano
, 7
(10
), pp. 9232
–9240
.10.1021/nn403851v4.
Ariyur
, K. B.
, and Krstic
, M.
, 2003
, Real-Time Optimization by Extremum Seeking Control
, Wiley-Interscience
, Hoboken, NJ
.5.
Liu
, S.-J.
, and Krstic
, M.
, 2010
, “Stochastic Averaging in Continuous Time and Its Applications to Extremum Seeking
,” IEEE Trans. Autom. Control
, 55
(10
), pp. 2235
–2250
.10.1109/TAC.2010.20432906.
Krstic
, M.
, and Wang
, H. H.
, 2000
, “Stability of Extremum Seeking Feedback for General Nonlinear Dynamic Systems
,” Automatica
, 36
(4
), pp. 595
–601
.10.1016/S0005-1098(99)00183-17.
Choi
, J.-Y.
, Krstic
, M.
, Ariyur
, K. B.
, and Lee
, J. S.
, 2002
, “Extremum Seeking Control for Discrete Time Systems
,” IEEE Trans. Autom. Control
, 47
(2
), pp. 318
–323
.10.1109/9.9833708.
Tan
, Y.
, Nešić
, D.
, and Mareels
, I.
, 2006
, “On Non-Local Stability Properties of Extremum Seeking Control
,” Automatica
, 42
(6
), pp. 889
–903
.10.1016/j.automatica.2006.01.0149.
Stanković
, M. S.
, and Stipanović
, D. M.
, 2010
, “Extremum Seeking Under Stochastic Noise and Applications to Mobile Sensors
,” Automatica
, 46
(8
), pp. 1243
–1251
.10.1016/j.automatica.2010.05.00510.
Nešić
, D.
, Tan
, Y.
, Moase
, W. H.
, and Manzie
, C.
, 2010
, “A Unifying Approach to Extremum Seeking: Adaptive Schemes Based on Estimation of Derivatives
,” 49th IEEE Conference on Decision and Control
(CDC
), Atlanta, GA, December 15–17, pp. 4625
–4630
.10.1109/CDC.2010.571792911.
Liu
, S.-J.
, and Krstic
, M.
, 2011
, “Stochastic Nash Equilibrium Seeking for Games With General Nonlinear Payoffs
,” SIAM J. Control Optim.
, 49
(4
), pp. 1659
–1679
.10.1137/10081173812.
Ghaffari
, A.
, Krstic
, M.
, and Nešić
, D.
, 2012
, “Multivariable Newton-Based Extremum Seeking
,” Automatica
, 48
(8
), pp. 1759
–1767
.10.1016/j.automatica.2012.05.05913.
Frihauf
, P.
, Krstic
, M.
, and Başar
, T.
, 2012
, “Nash Equilibrium Seeking in Noncooperative Games
,” IEEE Trans. Autom. Control
, 57
(5
), pp. 1192
–1207
.10.1109/TAC.2011.217341214.
Scheinker
, A.
, and Krstic
, M.
, 2013
, “Minimum-Seeking for CLFs: Universal Semiglobally Stabilizing Feedback Under Unknown Control Directions
,” IEEE Trans. Autom. Control
, 58
(5
), pp. 1107
–1122
.10.1109/TAC.2012.222551415.
Wang
, H. H.
, Yeung
, S.
, and Krstic
, M.
, 2000
, “Experimental Application of Extremum Seeking on an Axial-Flow Compressor
,” IEEE Trans. Control Syst. Technol.
, 8
(2
), pp. 300
–309
.10.1109/87.82680116.
Banaszuk
, A.
, Ariyur
, K. B.
, Krstic
, M.
, and Jacobson
, C. B.
, 2004
, “An Adaptive Algorithm for Control of Combustion Instability
,” Automatica
, 40
(11
), pp. 1965
–1972
.10.1016/j.automatica.2004.06.00817.
Schuster
, E.
, Torres
, N.
, and Xu
, C.
, 2006
, “Extremum Seeking Adaptive Control of Beam Envelope in Particle Accelerators
,” IEEE Conference on Control Applications
, Munich, Germany, October 4–6, pp. 1837
–1842
.10.1109/CACSD-CCA-ISIC.2006.477692018.
Killingsworth
, N. J.
, and Krstic
, M.
, 2006
, “PID Tuning Using Extremum Seeking—Online, Model-Free Performance Optimization
,” IEEE Control Syst. Mag.
, 26
(1
), pp. 70
–79
.10.1109/MCS.2006.158015519.
Luo
, L.
, and Schuster
, E.
, 2009
, “Mixing Enhancement in 2D Magnetohydrodynamic Channel Flow by Extremum Seeking Boundary Control
,” American Control Conference
(ACC '09
), St. Louis, MO, June 10–12, pp. 1530–1535
.10.1109/ACC.2009.516060120.
Moase
, W. H.
, Manzie
, C.
, and Brear
, M. J.
, 2009
, “Newton-Like Extremum-Seeking Part I: Theory
,” 48th IEEE Conference on Decision and Control
(CDC
), Shanghai, December 15–18, pp. 3839
–3844
.10.1109/CDC.2009.540019821.
Moase
, W. H.
, Manzie
, C.
, and Brear
, M. J.
, 2009
, “Newton-Like Extremum-Seeking Part II: Simulation and Experiments
,” 48th IEEE Conference on Decision and Control
(CDC
), Shanghai, December 15–18, pp. 3845
–3850
.10.1109/CDC.2009.540019522.
Stanković
, M. S.
, Johansson
, K. H.
, and Stipanović
, D. M.
, 2012
, “Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks
,” IEEE Trans. Autom. Control
, 57
(4
), pp. 904
–919
.10.1109/TAC.2011.217467823.
King
, R.
, Becker
, R.
, Feuerbach
, G.
, Henning
, L.
, Petz
, R.
, Nitsche
, W.
, Lemke
, O.
, and Neise
, W.
, 2006
, “Adaptive Flow Control Using Slope Seeking
,” 14th IEEE Mediterranean Conference on Control and Automation
(MED '06
), Ancona, Italy, June 28–30.10.1109/MED.2006.32875324.
Li
, Y.
, Rotea
, M. A.
, Chiu
, G. T.-C.
, Mongeau
, L. G.
, and Paek
, I. S.
, 2005
, “Extremum Seeking Control of a Tunable Thermoacoustic Cooler
,” IEEE Trans. Control Syst. Technol.
, 13
(4
), pp. 527
–536
.10.1109/TCST.2005.84733425.
Ou
, Y.
, Xu
, C.
, Schuster
, E.
, Luce
, T. C.
, Ferron
, J. R.
, Walker
, M. L.
, and Humphreys
, D. A.
, 2008
, “Design and Simulation of Extremum-Seeking Open-Loop Optimal Control of Current Profile in the DIII-D Tokamak
,” Plasma Phys. Control Fusion
, 50
(11
), p. 115001
.10.1088/0741-3335/50/11/11500126.
Wehner
, W.
, and Schuster
, E.
, 2009
, “Stabilization of Neoclassical Tearing Modes in Tokamak Fusion Plasmas Via Extremum Seeking
,” IEEE Control Applications (CCA
) & Intelligent Control (ISIC), St. Petersburg, Russia, July 8–10, pp. 853–860.10.1109/CCA.2009.528094327.
Porat
, B.
, and Nehorai
, A.
, 1996
, “Localizing Vapor-Emitting Sources by Moving Sensors
,” IEEE Trans. Signal Process.
, 44
(4
), pp. 1018
–1021
.10.1109/78.49256028.
Ögren
, P.
, Fiorelli
, E.
, and Leonard
, N.
, 2004
, “Cooperative Control of Mobile Sensor Networks: Adaptive Gradient Climbing in a Distributed Environment
,” IEEE Trans. Autom. Control
, 49
(8
), pp. 1292
–1302
.10.1109/TAC.2004.83220329.
Zhang
, C.
, Arnold
, D.
, Ghods
, N.
, Siranosian
, A.
, and Krstic
, M.
, 2007
, “Source Seeking With Nonholonomic Unicycle Without Position Measurement and With Tuning of Forward Velocity
,” Syst. Control Lett.
, 56
(3
), pp. 245
–252
.10.1016/j.sysconle.2006.10.01430.
Cochran
, J.
, and Krstic
, M.
, 2009
, “Nonholonomic Source Seeking With Tuning of Angular Velocity
,” IEEE Trans. Autom. Control
, 54
(4
), pp. 717
–731
.10.1109/TAC.2009.201492731.
Ghods
, N.
, Frihauf
, P.
, and Krstic
, M.
, 2010
, “Multi-Agent Deployment in the Plane Using Stochastic Extremum Seeking
,” 49th IEEE Conference on Decision and Control
(CDC
), Atlanta, GA, December 15–17, pp. 5505
–5510
.10.1109/CDC.2010.571728232.
Liu
, S.-J.
, and Krstic
, M.
, 2010
, “Stochastic Source Seeking for Nonholonomic Unicycle
,” Automatica
, 46
(9
), pp. 1443
–1453
.10.1016/j.automatica.2010.05.02533.
Liu
, S.-J.
, Frihauf
, P.
, and Krstic
, M.
, 2012
, “Stochastic Source Seeking With Tuning of Forward Velocity
,” 31st Chinese Control Conference
(CCC
), Hefei, China, July 25–27, pp. 4424
–4429
.34.
Fax
, J. A.
, and Murray
, R. M.
, 2004
, “Information Flow and Cooperative Control of Vehicle Formations
,” IEEE Trans. Autom. Control
, 49
(9
), pp. 1465
–1476
.10.1109/TAC.2004.83443335.
Lin
, Z.
, Francis
, B.
, and Maggiore
, M.
, 2005
, “Necessary and Sufficient Graphical Conditions for Formation Control of Unicycles
,” IEEE Trans. Autom. Control
, 50
(1
), pp. 121
–127
.10.1109/TAC.2004.84112136.
Lafferriere
, G.
, Williams
, A.
, Caughman
, J.
, and Veerman
, J. J. P.
, 2005
, “Decentralized Control of Vehicle Formations
,” Syst. Control Lett
., 54
(9
), pp. 899
–910
.10.1016/j.sysconle.2005.02.00437.
Marshall
, J. A.
, Broucke
, M. E.
, and Francis
, B. A.
, 2004
, “Formations of Vehicles in Cyclic Pursuit
,” IEEE Trans. Autom. Control
, 49
(11
), pp. 1963
–1974
.10.1109/TAC.2004.83758938.
Pavone
, M.
, and Frazzoli
, E.
, 2007
, “Decentralized Policies for Geometric Pattern Formation and Path Coverage
,” ASME J. Dyn. Syst.
, Meas.
, Control
, 129
(5
), pp. 633
–643
.10.1115/1.276765839.
Cortés
, J.
, Martínez
, S.
, Karataş
, T.
, and Bullo
, F.
, 2004
, “Coverage Control for Mobile Sensing Networks
,” IEEE Trans. Robot. Autom.
, 20
(2
), pp. 243
–255
.10.1109/TRA.2004.82469840.
Olfati-Saber
, R.
, 2006
, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
,” IEEE Trans. Autom. Control
, 51
(3
), pp. 401
–420
.10.1109/TAC.2005.86419041.
Hsieh
, M. A.
, Kumar
, V.
, and Chaimowicz
, L.
, 2008
, “Decentralized Controllers for Shape Generation With Robotic Swarms
,” Robotica
, 26
(5
), pp. 691
–701
.10.1017/S026357470800432342.
Choi
, J.
, Oh
, S.
, and Horowitz
, R.
, 2009
, “Distributed Learning and Cooperative Control for Multi-Agent Systems
,” Automatica
, 45
(12
), pp. 2802
–2814
.10.1016/j.automatica.2009.09.02543.
Mesquita
, A. R.
, Hespanha
, J. P.
, and Åström
, K.
, 2008
, “Optimotaxis: A Stochastic Multi-Agent Optimization Procedure With Point Measurements
,” 11th International Workshop on Hybrid Systems: Computation and Control (HSCC 2008
), St. Louis, MO, April 22–24, pp. 358
–371
.10.1007/978-3-540-78929-1_2644.
Becker
, A.
, and McLurkin
, J.
, 2013
, “Exact Range and Bearing Control of Many Differential-Drive Robots With Uniform Control Inputs
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
(IROS
), Tokyo, November 3–7, pp. 3338–3343
.10.1109/IROS.2013.669683145.
Becker
, A.
, Habibi
, G.
, Werfel
, J.
, Rubenstein
, M.
, and McLurkin
, J.
, 2013
, “Massive Uniform Manipulation: Controlling Large Populations of Simple Robots With a Common Input Signal
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
(IROS
), Tokyo, November 3–7, pp. 520–527
.10.1109/IROS.2013.669640146.
Tao
, G.
, 2003
, Adaptive Control Design and Analysis
, Wiley-Interscience
, Hoboken, NJ
.Copyright © 2014 by ASME
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