December  2007, 2(4): 627-646. doi: 10.3934/nhm.2007.2.627

On rendezvous control with randomly switching communication graphs

1. 

Department of Information Engineering, Via Gradenigo 6/b, Padova, 35131, Italy, Italy

Received  June 2007 Revised  September 2007 Published  September 2007

In this paper we analyze randomized coordination control strategies for the rendezvous problem of multiple agents with unknown initial positions. The performance of these control strategies is measured in terms of three metrics: average relative agents’ distance, total input energy consumption, and number of packets per unit time that each agent can receive from the other agents. By considering an LQ-like performance index, we show that a-priori knowledge about the first and second order statistics of agents’ initial position can greatly improve performance as compared to rendezvous control strategies based only on relative distance feedback. Moreover, we show that randomly switching communication topologies, as compared to static communication topologies, require very little information exchange to achieve high performance even when the number of agents grows very large.
Citation: Luca Schenato, Sandro Zampieri. On rendezvous control with randomly switching communication graphs. Networks & Heterogeneous Media, 2007, 2 (4) : 627-646. doi: 10.3934/nhm.2007.2.627
[1]

Monique Chyba, Geoff Patterson, Gautier Picot, Mikael Granvik, Robert Jedicke, Jeremie Vaubaillon. Designing rendezvous missions with mini-moons using geometric optimal control. Journal of Industrial & Management Optimization, 2014, 10 (2) : 477-501. doi: 10.3934/jimo.2014.10.477

[2]

Ying Wu, Zhaohui Yuan, Yanpeng Wu. Optimal tracking control for networked control systems with random time delays and packet dropouts. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1343-1354. doi: 10.3934/jimo.2015.11.1343

[3]

GuanLin Li, Sebastien Motsch, Dylan Weber. Bounded confidence dynamics and graph control: Enforcing consensus. Networks & Heterogeneous Media, 2020, 15 (3) : 489-517. doi: 10.3934/nhm.2020028

[4]

Rui Li, Yingjing Shi. Finite-time optimal consensus control for second-order multi-agent systems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 929-943. doi: 10.3934/jimo.2014.10.929

[5]

Suoqin Jin, Fang-Xiang Wu, Xiufen Zou. Domain control of nonlinear networked systems and applications to complex disease networks. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2169-2206. doi: 10.3934/dcdsb.2017091

[6]

Lijuan Wang, Qishu Yan. Optimal control problem for exact synchronization of parabolic system. Mathematical Control & Related Fields, 2019, 9 (3) : 411-424. doi: 10.3934/mcrf.2019019

[7]

Jitka Machalová, Horymír Netuka. Optimal control of system governed by the Gao beam equation. Conference Publications, 2015, 2015 (special) : 783-792. doi: 10.3934/proc.2015.0783

[8]

Thomas I. Seidman. Optimal control of a diffusion/reaction/switching system. Evolution Equations & Control Theory, 2013, 2 (4) : 723-731. doi: 10.3934/eect.2013.2.723

[9]

Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control & Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185

[10]

Thalya Burden, Jon Ernstberger, K. Renee Fister. Optimal control applied to immunotherapy. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 135-146. doi: 10.3934/dcdsb.2004.4.135

[11]

Ellina Grigorieva, Evgenii Khailov. Optimal control of pollution stock. Conference Publications, 2011, 2011 (Special) : 578-588. doi: 10.3934/proc.2011.2011.578

[12]

Hang-Chin Lai, Jin-Chirng Lee, Shuh-Jye Chern. A variational problem and optimal control. Journal of Industrial & Management Optimization, 2011, 7 (4) : 967-975. doi: 10.3934/jimo.2011.7.967

[13]

Qun Lin, Ryan Loxton, Kok Lay Teo. The control parameterization method for nonlinear optimal control: A survey. Journal of Industrial & Management Optimization, 2014, 10 (1) : 275-309. doi: 10.3934/jimo.2014.10.275

[14]

Changjun Yu, Shuxuan Su, Yanqin Bai. On the optimal control problems with characteristic time control constraints. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021021

[15]

Cristiana J. Silva, Helmut Maurer, Delfim F. M. Torres. Optimal control of a Tuberculosis model with state and control delays. Mathematical Biosciences & Engineering, 2017, 14 (1) : 321-337. doi: 10.3934/mbe.2017021

[16]

Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019

[17]

Sandra Ricardo, Witold Respondek. When is a control system mechanical?. Journal of Geometric Mechanics, 2010, 2 (3) : 265-302. doi: 10.3934/jgm.2010.2.265

[18]

Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020107

[19]

Fabio Bagagiolo. Optimal control of finite horizon type for a multidimensional delayed switching system. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 239-264. doi: 10.3934/dcdsb.2005.5.239

[20]

Mourad Azi, Mohand Ouamer Bibi. Optimal control of a dynamical system with intermediate phase constraints and applications in cash management. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021005

2019 Impact Factor: 1.053

Metrics

  • PDF downloads (43)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]