Structural Controllability and Observability of Linear Systems Over Finite Fields With Applications to Multi-Agent Systems
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 si...
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Veröffentlicht in: | IEEE transactions on automatic control 2013-01, Vol.58 (1), p.60-73 |
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description | 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. |
doi_str_mv | 10.1109/TAC.2012.2204155 |
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N.</creator><creatorcontrib>Sundaram, S. ; Hadjicostis, C. N.</creatorcontrib><description>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. 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N.</creatorcontrib><title>Structural Controllability and Observability of Linear Systems Over Finite Fields With Applications to Multi-Agent Systems</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>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. 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N.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Structural Controllability and Observability of Linear Systems Over Finite Fields With Applications to Multi-Agent Systems</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2013-01</date><risdate>2013</risdate><volume>58</volume><issue>1</issue><spage>60</spage><epage>73</epage><pages>60-73</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><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><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TAC.2012.2204155</doi><tpages>14</tpages></addata></record> |
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subjects | Agents (artificial intelligence) Algorithms Controllability Design engineering Distributed consensus distributed function calculation Expert systems finite fields Graph theory linear system theory Linear systems Mathematical analysis multi-agent systems Multiagent systems Observability Polynomials Quantization quantized control Strategy structural controllability structural observability structured system theory Studies Vegetation |
title | Structural Controllability and Observability of Linear Systems Over Finite Fields With Applications to Multi-Agent Systems |
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