Observer-based Event-Triggered Control of Multi-Agent Systems under Time-Varying Delays

Abstract

A multi-agent system (MAS) consists of agents that collaborate through local interactions to solve complex tasks, offering advantages such as efficiency, flexibility, and reduced cost. MASs have broad applications in fields such as robotics, smart grids, unmanned aerial vehicle (UAV), etc., effectively addressing problems that are challenging for single agents. However, communication among agents often occurs over networks, introducing challenges such as network congestion, delays, and packet loss, which can adversely affect system performance and stability. In order to reduce the need for constant communication, and mitigate network issues, event-triggering control (ETC) systems are introduced. Nonetheless, communication delays are inevitable and must be considered when designing control algorithms to maintain stability in MASs. This study focuses on developing control strategies for MASs with time-varying communication delays, utilizing ETC to minimize network load. In the first part of the research, we propose a new observer-based asynchronous periodic event-triggered control approach for the consensus of linear MASs to reduce the communication load in both sensor-observer (S-O) and controller-actuator (C-A) channels. In order to deal with the time-varying delays, each agent uses a set of observers to estimate its states as well as its neighbors' states. We demonstrate that all agents' states and observed states converge asymptotically to an agreement point in the presence of time-varying communication delays in both channels. The results show the efficiency of the observer-based ETC in terms of efficient use of communication resources and lower settling time. In the second part, we address the challenge of time-varying formation control in MASs in the presence of time-varying intra- and inter-agent communication delays. We explicitly consider distinct, time-varying delays between each agent and its neighbors, and such delay patterns are more reflective of the intricate delay patterns encountered in real-world MASs. We employ a dynamic event-triggering mechanism (DETM) in S-O and C-A channels, and in the design stage, we guarantee that the closed-loop system of all agents is stable and agents reach the desired formation. Numerical simulations demonstrate that our approach achieves a balance by reducing inter-agent communication frequency while maintaining the desired formation. We address the challenge of asynchronous periodic event-triggered consensus control framework for MASs with general linear dynamics. Achieving consensus in MASs without a shared clock poses a significant challenge due to the asynchronous nature of communication and event-triggering mechanisms. We establish theoretical conditions under which consensus can be reached despite the absence of synchronized communication among agents. Our analysis demonstrates the effectiveness of the proposed approach in achieving consensus while minimizing communication overhead. Finally, we extend the framework of event-triggered control of MASs with time-varying delays to address the scenarios where the communication topology switches based on semi-Markovian rules, which provides a broader design approach for handling more complex MAS environments. We consider the case where transition rates in the switching topologies are partially unknown and implement DETMs on both the S-O and C-A channels to minimize unnecessary data transmissions within the network, which involves utilizing locally triggered sampled data in a distributed manner to optimize resource efficiency. We formulate the event-triggering parameters to ensure the stability of the closed-loop system comprising all agents, thereby achieving consensus. Through numerical simulations and experiments, we demonstrate that our approach effectively balances reducing the frequency of inter-agent communication with ensuring that the agents reach consensus. In addition to the theoretical contributions outlined in this research, we conducted a series of experiments using a multi-agent system consisting of e-puck robots to validate the proposed control strategies. These experiments provided empirical evidence supporting the effectiveness of the event-triggered control frameworks across different scenarios. The results demonstrated the ability of the agents to achieve consensus and maintain the desired formation, aligning with our theoretical findings. The validations highlight the practical applicability of our approaches in achieving efficient and stable coordination among agents in dynamic environments