Biblio

As multi-agent systems become ubiquitous, guaranteeing safety in these systems grows increasingly important. In applications ranging from automated cruise control to safety in robot swarms, barrier functions have emerged as a tool to provably meet safety constraints by guaranteeing forward invariance of a set. However, a single barrier function can rarely satisfy all safety aspects of a system, so there remains a need to address the degree to which multiple barrier functions may be composed through Boolean logic. Utilizing max and min operators represents one such method to accomplish Boolean composition for barrier functions. As such, the main contribution of this work extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions. To validate these results, a Boolean compositional barrier function is deployed onto a team of mobile robots.

We consider linear time-invariant networks with unknown interaction topology where only a subset of the nodes, termed manifest, can be directly controlled and observed. The remaining nodes are termed latent and their number is also unknown. Our goal is to identify the transfer function of the manifest subnetwork and determine whether interactions between manifest nodes are direct or mediated by latent nodes. We show that, if there are no inputs to the latent nodes, then the manifest transfer function can be approximated arbitrarily well in the $H_ınfty}$-norm sense by the transfer function of an auto-regressive model. Motivated by this result, we present a least-squares estimation method to construct the auto-regressive model from measured data. We establish that the least-squares matrix estimate converges in probability to the matrix sequence defining the desired auto-regressive model as the length of data and the model order grow. We also show that the least-squares auto-regressive method guarantees an arbitrarily small $H_ınfty$-norm error in the approximation of the manifest transfer function, exponentially decaying once the model order exceeds a certain threshold. Finally, we show that when the latent subnetwork is acyclic, the proposed method achieves perfect identification of the manifest transfer function above a specific model order as the length of the data increases. Various examples illustrate our results.