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Structural Controllability and Observability of Linear Systems Over Finite Fields With Applications to Multi-Agent Systems.
- Source :
-
IEEE Transactions on Automatic Control . Jan2013, Vol. 58 Issue 1, p60-73. 14p. - Publication Year :
- 2013
-
Abstract
- We develop a graph-theoretic characterization of controllability and observability of linear systems over finite fields. Specifically, we show that a linear system will be structurally controllable and observable over a finite field if the graph of the system satisfies certain properties, and the size of the field is sufficiently large. We also provide graph-theoretic upper bounds on the controllability and observability indices for structured linear systems (over arbitrary fields). We then use our analysis to design nearest-neighbor rules for multi-agent systems where the state of each agent is constrained to lie in a finite set. We view the discrete states of each agent as elements of a finite field, and employ a linear iterative strategy whereby at each time-step, each agent updates its state to be a linear combination (over the finite field) of its own state and the states of its neighbors. Using our results on structural controllability and observability, we show how a set of leader agents can use this strategy to place all agents into any desired state (within the finite set), and how a set of sink agents can recover the set of initial values held by all of the agents. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 58
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 84489491
- Full Text :
- https://doi.org/10.1109/TAC.2012.2204155