Dynamic Periodic Event-triggered Multi-agent Consensus Using Relative-state Measurements: A Hybrid System Approach

Abstract

Driven by technological advances in emerging fields such as autonomous vehicles, robots, and industrial internet-of-things, multi-agent systems (MASs) continue to be a prominent research area within Control Systems. Often, in practical applications, the agents employ information obtained from sensors, on-board and/or off-board, to accomplish complex tasks, asynchronously. Moreover, given the wide accessibility to electronic hardware and infrastructure, modern agents generally employ digital sensors and processors and coordinate wirelessly. The agents may even operate under a power storage device to allow for remote deployment. For modern agents, it is essential to emphasize that resources are often limited and access to information for control updates are only available when sampled. Given these potential resource constraints, there is significant interest in further studying control protocols, which incorporate the characteristics of digital hardware, to reduce resource consumption while still achieving the control objectives. In this thesis, two problem formations are considered. Firstly, we consider the problem of distributed MAS consensus where the agents' dynamics follow a single-integrator. The control protocol of each agent employs local relative-state measurements, at their own sampling frequencies, and a dynamic periodic event-triggered protocol to dictate when control updates occur. Unlike continuous-time event-triggered protocols, the periodic event-triggered protocol only checks for events at discrete event-monitoring instants. Between subsequent event-monitoring instants, the agents have no access to information regarding its neighbours. In our formulation, the event-monitoring instants are governed by sampling periods whose bounds are explicitly pre-computed, individually, for each agent. As a result, the designed control protocol is inherently asynchronous, even when the event-trigger mechanism is redundant, and avoids Zeno-behaviour by design. To unify the continuous-time agents' dynamics and both the discrete-time sensing and controller updates, the overall MAS is modelled and analyzed within the hybrid system framework.

Our second problem formulation aims to encompass a broader range of implementations. As such, we extend the agents' dynamics within the first problem formulation from a single-integrator to linear time-invariant systems. However, it is worth noting that since reaching consensus by stabilizing to the origin is trivial, we instead focus on achieving consensus to a new stabilizing set other than the origin. Furthermore, within our second problem formulation, we explore two constructions of the dynamic periodic event-triggered protocol, where the second construction is aimed at reducing the event frequency through incorporating an independently tunable term.

For both problem formulations, we prove consensus of the MAS utilizing the Lyapunov stability theorem within the hybrid system framework. We also provide sufficient conditions on the construction of the dynamic periodic event-trigger mechanisms and bound between event-monitoring instants such that consensus is guaranteed. Numerical examples, simulations, and comparisons are provided to demonstrate the utility and effectiveness of the results.