In this paper, leader-following consensus of the discrete-time heterogenous multi-agent system with bounded communication delays is studied. The heterogeneous multi-agent system is composed of first-order and second-order integrator agents. By applying the graph theory and the algebra theory, sufficient consensus criteria are obtained to guarantee that each agent can track the leader. Despite there exist bounded time delays among agents, consensus can also be realised under fixed and switching topologies. Event-triggered control laws are designed to reduce the frequency of individual actuation updating. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

We describe a method for removing the effect of confounders in order to reconstruct a latent quantity of interest. The method, referred to as half-sibling regression, is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification and illustrate the potential of the method in a challenging astronomy application.