Non-linear protocols for optimal distributed consensus in networks of dynamic agents |
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Authors: | D Bauso L Giarr R Pesenti |
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Affiliation: | aDipartimento di Ingegneria dell’Automazione e dei Sistemi, Università di Palermo, Viale Delle Scienze, 90128 Palermo, Italy;bDipartimento di Ingegneria Informatica, Università di Palermo, Viale Delle Scienze, 90128 Palermo, Italy |
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Abstract: | We consider stationary consensus protocols for networks of dynamic agents with fixed topologies. At each time instant, each agent knows only its and its neighbors’ state, but must reach consensus on a group decision value that is function of all the agents’ initial state. We show that the agents can reach consensus if the value of such a function is time-invariant when computed over the agents’ state trajectories. We use this basic result to introduce a non-linear protocol design rule allowing consensus on a quite general set of values. Such a set includes, e.g., any generalized mean of order p of the agents’ initial states. As a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents. This notion suggests a game theoretic interpretation of consensus problems as mechanism design problems. Under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives. We prove that such objectives can be chosen so that rational agents have a unique optimal protocol, and asymptotically reach consensus on a desired group decision value. We use a Lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time-invariant undirected network. Finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles. |
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Keywords: | Consensus protocols Decentralized control Optimal control Networks |
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