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In this paper we propose a novel method to establish stability and, in addition, convergence to a consensus state for a class of discrete-time Multi-Agent System (MAS) evolving according to nonlinear heterogeneous local interaction rules which is not based on Lyapunov function arguments. In particular, we focus on a class of discrete-time MASs whose global dynamics can be represented by sub-homogeneous and order-preserving nonlinear maps. This paper directly generalizes results for sub-homogeneous and order-preserving linear maps which are shown to be the counterpart to stochastic matrices thanks to nonlinear Perron-Frobenius theory. We provide sufficient conditions on the structure of local interaction rules among agents to establish convergence to a fixed point and study the consensus problem in this generalized framework as a particular case. Examples to show the effectiveness of the method are provided to corroborate the theoretical analysis.
In this paper, an optimal output consensus problem is studied for discrete-time linear multiagent systems subject to external disturbances. Each agent is assigned with a local cost function which is known only to itself. Distributed protocols are to
This paper investigates an optimal consensus problem for a group of uncertain linear multi-agent systems. All agents are allowed to possess parametric uncertainties that range over an arbitrarily large compact set. The goal is to collectively minimiz
In this paper, a distributed learning leader-follower consensus protocol based on Gaussian process regression for a class of nonlinear multi-agent systems with unknown dynamics is designed. We propose a distributed learning approach to predict the re
This paper studies synchronization of homogeneous and heterogeneous discrete-time multi-agent systems. A class of linear dynamic protocol design methodology is developed based on localized information exchange with neighbors which does not need any k
Discrete abstractions have become a standard approach to assist control synthesis under complex specifications. Most techniques for the construction of discrete abstractions are based on sampling of both the state and time spaces, which may not be ab