Consensus algorithms have been studied in the field of distributed computing for decades. Recently consensus algorithms have attracted renewed attention because they can be exploited for distributed cooperative control. The purpose of this paper is the analysis of a specific class of consensus algorithms called max-consensus. This class of algorithms is needed for applications such as minimum time rendezvous and leader election. A new approach using max-plus algebra is proposed to analyze convergence of max-consensus algorithm. In this paper we focus on the problem of achieving max-consensus in time-invariant communication topologies. Conditions to achieve max-consensus are discussed and the convergence rate of the algorithm for different communication topologies is studied.

Abstract. In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagintype Maximum Principle (MP) for optimal control processes governed by hybrid dynamics with autonomous location transitions, we extend the necessary optimality conditions to a class of Impulsive Hybrid Optimal Control Problems (IHOCPs). For these problems, we obtain a concise characterization of the Impulsive Hybrid MP (IHMP), namely, the corresponding boundary-value problem and some additional relations. As in the classical case, the proposed IHMP provides a basis for diverse computational algorithms for the treatment of IHOCPs.

In this paper we study topological properties of consensus algorithms for agents with double integrator dynamics communicating over networks modeled by undirected graphs. Unlike existing work we drop the assumption that the positions and the velocities of the agents are shared along homogeneous communication networks. In fact, our main result is that consensus can be achieved even though the networks along which position and velocity information is shared are different, and not even connected. We further provide insights on consensus rate based only on the topological properties of the network and show that unlike in homogeneous networks, consensus type cannot be changed by introducing gains.

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