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In this article, we develop a general open multiagent systems (OMAS) framework over undirected graphs where the agents' interaction is, in general, nonlinear, time-varying, and heterogeneous, in that the agents interact with different pairwise interaction rules for each link, possibly nonlinear, which may change over time. In particular, assuming the agents interact by exchanging flows, which modify their states, our framework guarantees that the sum of the states of agents participating in the network is preserved. To this end, agents maintain a state variable for each of their neighbors. Upon the disconnection of a neighbor, such a variable is used to completely eliminate the effect of previous interaction with disconnected agents from the overall system. In order to demonstrate the effectiveness of the proposed OMAS framework, we provide a case study focused on average consensus, and, specifically, we develop a sufficient condition on the structure of the agents' interaction guaranteeing asymptotic convergence under the assumption that the network becomes fixed. The article is complemented by simulation results that numerically demonstrate the effectiveness of the proposed method.

In this article, we propose a load balancing problem formulation where agents cooperate with the aim of simultaneously minimizing both the workload disparity among the agents and the overall workload transfer, under network capacity constraints. Notably, in our computational setting, the network is not just a device for the distributed solution of an optimization problem; on the contrary, the problem shares the same sparsity pattern as the network, and this aspect allows us to solve it without the need for the agents to store large amount of data. In particular, while the load balancing process occurs over directed links, agents' communication is assumed to be bidirectional. For this optimization setting, first, an optimality condition is derived; then, a provably convergent distributed algorithm to compute the optimal solution is developed, and an upper bound on the convergence rate is characterized. Simulation results are provided to corroborate the validity and performance of our theoretical findings.