Mechanism Design for Optimal Consensus Problems

Abstract

We consider stationary consensus protocols for networks of dynamic agents with fixed and switching 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 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.

Load balancing over heterogeneous networks with gossip-based algorithms

“…An interesting application in this sense is given by load balancing over networks [1], [5], [7], [11], [13], [21]. This is the reason why our presentation will be carried out within this framework even if the proposed results can also be applied to other application domains.…”

“…We do not provide a bound for such a case 4. This problem has been extensively studied in different fields[8] 5. The case of rings with an odd number of nodes k is upper bounded by the case of rings with k + 1 nodes.…”

Undamped nonlinear consensus using integral Lyapunov functions

“…E-mail: mandreas@kth.se own state were studied in [3] for single integrator dynamics. [2] extended the results to switching communication topologies, where the communication graph always remains connected. Linear consensus for double integrator dynamics were studied in detail in [22] for undirected as well as for directed communication.…”

An LMI approach to optimal consensus seeking in multi-agent systems

“…The author in [10] introduced a method based on passivity for solving the coordination problem. An optimal approach to consensus problem is considered in [11]- [13]. In order to solve the team optimal problem, the authors in [11] have assumed that in evaluating the minimum value of each individual cost, the state of other agents are constant.…”

“…An optimal approach to consensus problem is considered in [11]- [13]. In order to solve the team optimal problem, the authors in [11] have assumed that in evaluating the minimum value of each individual cost, the state of other agents are constant. The works in [12], [13] avoid this restrictive assumption by decomposing the control input of individual agents into local and global components.…”