# 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.

Accepted for publication

This paper addresses the problem of exponential practical stabilization of linear time-invariant systems with disturbances using event-triggered control and bounded communication bit rate. We consider both the case of instantaneous communication with finite precision data at each transmission and the case of non-instantaneous communication with bounded communication rate. Given a prescribed rate of convergence, the proposed event-triggered control implementations opportunistically determine the transmission instants and the finite precision data to be transmitted on each transmission. We show that our design exponentially practically stabilizes the origin while guaranteeing a uniform positive lower bound on the inter-transmission and inter-reception times, ensuring that the number of bits transmitted on each transmission is upper bounded uniformly in time, and allowing for the possibility of transmitting fewer bits at any given time if more bits than prescribed were transmitted earlier. We also characterize the necessary and sufficient average data rate for exponential practical stabilization. Several simulations illustrate the results.

This paper addresses the problem of event-triggered control of linear time-invariant systems over time-varying rate limited communication channels, including the possibility of channel blackouts, which are intervals of time when the communication channel is unavailable for feedback. In order to design an effective event-triggered controller that operates successfully even in the presence of blackouts, we analyze the channel data capacity, which is the total maximum number of bits that could be communicated over a given time interval. We provide an efficient real-time algorithm to estimate the channel capacity for a time-slotted model of channel evolution. Equipped with this algorithm we then propose an event-triggering scheme, which using prior knowledge of the channel information, guarantees exponential stabilization at a desired convergence rate despite intermittent channel blackouts. The contributions are the notion of channel blackouts, the effective control despite their occurrence, and the analysis and quantification of the data capacity for a class of time-varying continuous-time channels.

This paper addresses the problem of asymptotic stabilization for linear time-invariant (LTI) systems using event-triggered control under finite data rate communication - both in the sense of finite precision data at each transmission and finite average data rate. Given a prescribed rate of convergence for asymptotic stability, we introduce an event-triggered control implementation that opportunistically determines the transmission instants and the finite precision data to be transmitted at each transmission. We show that our design exponentially stabilizes the origin while guaranteeing a positive lower bound on the inter-transmission times, ensuring that the number of bits transmitted at each transmission is upper bounded, and allowing for the possibility of transmitting fewer bits at any given time if more bits than prescribed were transmitted on a previous transmission. In our technical approach, we consider both the case of instantaneous and non-instantaneous transmissions. Several simulations illustrate the results.