This paper investigates a constrained distributed online optimization problem over strongly connected communication networks, where a local cost function of each agent varies in time due to environmental factors. We propose a distributed online projected subgradient method over unbalanced directed networks. The performance of the proposed method is evaluated by a regret which is defined by the error between the cumulative cost over time and the cost of the optimal strategy in hindsight. We show that a logarithmic regret bound can be achieved for strongly convex cost functions. We also demonstrate the validity of the proposed method through a numerical example on distributed estimation over a diffusion field.

The output feedback consensus problem of nonlinear multi-agent systems under a directed network with a time varying communication delay is studied. In order to deal with this problem, the dynamic output feedback controller with an additional low gain parameter that compensates for the effect of nonlinearity and a communication delay is proposed. Also, it is shown that under some assumptions, the proposed controller can always solve the output feedback consensus problem even in the presence of an arbitrarily large communication delay.

This Letter defines thirteen useful correlation measures for directed weighted complex network analysis. First, in-strength and out-strength are defined for each node in the directed weighted network. Then, one node-based strength-strength correlation measure and four arc-based strength-strength correlation measures are defined. In addition, considering that each node is associated with in-degree, out-degree, in-strength and out-strength, four node-based strength-degree correlation measures and four arc-based strength-degree correlation measures are defined. Finally, we use these measures to analyze the world trade network and the food web. The results demonstrate the effectiveness of the proposed measures for directed weighted networks.