Dynamic Average Consensus as Distributed PDE-Based Control for Multi-Agent Systems

This paper delves into the distributed estimator-based Dynamic Average Consensus (DAC) control problem within multi-agent systems (MASs) modeled by Partial Differential Equations (PDEs). The objective of DAC is for agents to converge to time-varying average profiles, referred to as dynamic average reference signals. Unlike prior research, this study will use a distributed estimator to recover the average reference signals for agents to track, which converges to the desired average reference in finite time. The reference signal with compact support employed in this study represents a more generalized signal type compared to previous works. Based on the distributed estimator, this research explores the DAC problem within in-domain PDE control. In-domain control is where input control acts within the governing equation. To assess the stability of the closed-loop system, we employ the Lyapunov technique for analysis. Finally, the proposed control designs' effectiveness in each section of the paper is demonstrated through simulation examples.