[Paper Review] Cooperative Output Regulation with Mixed Time- and Event-triggered Observers.

Shimin Wang, Zhan Shu+1 more|arXiv (Cornell University)|May 5, 2021

Distributed Control Multi-Agent Systems42 references4 citations

TL;DR

This paper proposes a mixed time- and event-triggered observer framework for cooperative output regulation in heterogeneous multi-agent systems. By combining time-triggered state estimation of the leader with event-triggered communication among followers, the method ensures Zeno-free operation and convergence of estimation errors under general positive and convergent triggering functions, including exponential decay.

ABSTRACT

Mixed time- and event-triggered cooperative output regulation for heterogeneous distributed systems is investigated in this paper. A distributed observer with time-triggered observations is proposed to estimate the state of the leader, and an auxiliary observer with event-triggered communication is designed to reduce the information exchange among followers. A necessary and sufficient condition for the existence of desirable time-triggered observers is established, and delicate relationships among sampling periods, topologies, and reference signals are revealed. An event-triggering mechanism based on local sampled data is proposed to regulate the communication among agents; and the convergence of the estimation errors under the mechanism holds for a class of positive and convergent triggering functions, which include the commonly used exponential function as a special case. The mixed time- and event-triggered system naturally excludes the existence of Zeno behavior as the system updates at discrete instants. When the triggering function is bounded by exponential functions, analytical characterization of the relationship among sampling, event triggering, and inter-event behaviour is established. Finally, several examples are provided to illustrate the effectiveness and merits of the theoretical results.

Motivation & Objective

• To address the challenge of efficient and stable information exchange in cooperative output regulation of heterogeneous distributed systems.
• To design a distributed observer using time-triggered sampling to estimate the leader's state with guaranteed convergence.
• To reduce communication burden among followers by introducing an event-triggered auxiliary observer.
• To establish necessary and sufficient conditions for the existence of time-triggered observers based on sampling periods, network topology, and reference signals.
• To ensure Zeno-free behavior and convergence of estimation errors using local sampled data-based event triggering.

Proposed method

• A time-triggered distributed observer is designed to estimate the leader's state at fixed sampling intervals, ensuring stability and convergence.
• An auxiliary event-triggered observer is introduced to minimize communication among followers by triggering updates only when necessary.
• A local sampled-data-based event-triggering mechanism is proposed, which depends on the current state and past samples to decide when to transmit.
• The triggering mechanism uses positive and convergent functions, including exponential functions, to regulate communication frequency.
• Theoretical analysis proves that estimation errors converge under the proposed mechanism, with Zeno behavior excluded due to discrete updates.
• Analytical relationships are derived among sampling period, event-triggering behavior, and the upper bound of the triggering function when bounded by exponential functions.

Experimental results

Research questions

• RQ1 What conditions guarantee the existence of a time-triggered distributed observer for leader state estimation in heterogeneous systems?
• RQ2 How can communication among followers be minimized while maintaining estimation accuracy and system stability?
• RQ3 What is the relationship between sampling period, network topology, and reference signal dynamics in the observer design?
• RQ4 Under what conditions does the event-triggering mechanism prevent Zeno behavior and ensure convergence of estimation errors?
• RQ5 How do the parameters of the triggering function, particularly exponential-type functions, affect the inter-event time and system performance?

Key findings

• A necessary and sufficient condition is established for the existence of time-triggered observers, explicitly linking sampling period, network topology, and reference signal dynamics.
• The proposed event-triggering mechanism ensures convergence of estimation errors for a broad class of positive and convergent triggering functions.
• Zeno behavior is naturally excluded because the system updates only at discrete time instants, even under dense event triggering.
• When the triggering function is bounded by an exponential function, the inter-event time can be analytically characterized in relation to sampling period and system parameters.
• Theoretical analysis confirms that the mixed time- and event-triggered framework maintains system stability and estimation accuracy with reduced communication.
• Numerical examples demonstrate the effectiveness and advantages of the proposed method in reducing communication while ensuring convergence.