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State Agreement for Continuous‐Time Coupled Nonlinear Systems
Abstract
Two related problems are treated in continuous time. First, the state agreement problem is studied for coupled nonlinear differential equations. The vector fields can switch within a finite family. Associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems. Generalizing the work of Moreau, under the assumption that the vector fields satisfy a certain subtangentiality condition, it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time. The proof uses nonsmooth analysis. Second, the rendezvous problem for kinematic point‐mass mobile robots is studied when the robots’ fields of view have a fixed radius. The circumcenter control law of Ando et al. [IEEE Trans. Robotics Automation, 15 (1999), pp. 818–828] is shown to solve the problem. The rendezvous problem is a kind of state agreement problem, but the interaction structure is state dependent.
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Cites
Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
Olfati-Saber, R., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834113 · Cited by 12,788
Coordination of groups of mobile autonomous agents using nearest neighbor rules
Jadbabaie, A., Lin, J., & Morse, A. S. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.812781 · Cited by 8,339
Cited by
Consensus Problems on Networks With Antagonistic Interactions
Altafini, C. (2013) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2012.2224251 · Cited by 2,109
Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms
Bullo, F., Cortés, J., & Martínez, S. (2009) · Princeton University Press eBooks · doi:10.1515/9781400831470 · Cited by 1,509
A tutorial on modeling and analysis of dynamic social networks. Part I
Proskurnikov, A. V., & Tempo, R. (2017) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2017.03.002 · Cited by 553
On the Bipartite Consensus for Generic Linear Multiagent Systems With Input Saturation
Qin, J., Fu, W., Zheng, W. X., & Gao, H. (2017) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2016.2612482 · Cited by 373
Yang, X., Cao, J., & Yang, Z. (2013) · SIAM Journal on Control and Optimization · doi:10.1137/120897341 · Cited by 360
Metadata
- Authors
- Lin, Z., Francis, B., & Maggiore, M.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 2007-01
- Volume
- 46
- Issue
- 1
- Pages
- 288-307
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W2024571424
- Cited by
- 508
- References
- 2
- FWCI
- 33.98
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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