Structural controllability and observability of linear systems over finite fields with applications to multiagent systems
Date
2013Source
IEEE Transactions on Automatic ControlVolume
58Issue
1Pages
6073Google Scholar check
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We develop a graphtheoretic 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 graphtheoretic upper bounds on the controllability and observability indices for structured linear systems (over arbitrary fields). We then use our analysis to design nearestneighbor rules for multiagent 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 timestep, 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. © 2012 IEEE.
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