Decentralized and Distributed Control of Large-scale Interconnected Multi-Agent Systems in Prescribed Time

Interactions and communication between individuals and individuals, individuals and groups, as well as groups and groups are common in both the natural and applied sciences. In this paper, we investigate the control problem of large-scale systems composed of multiple individuals and groups, where there are interactions among these individuals and groups, as well as potential communication exchanges. Each plant is modeled as a high-order mismatched uncertain nonlinear system, and only a subset of plants can access output measurements from their limited neighbors. In this situation, decentralized and distributed output-feedback controllers are designed to regulate the states of all plants to the equilibrium point within a prescribed time. The stability analysis is based upon a blend of graph-theoretic, matrix-theoretic, and system-theoretic tools with the application of matrix pencil and time-varying feedback playing a central role. In particular, the control objective is divided into two sub-objectives where the first is decentralized prescribed-time regulation and the second is distributed prescribed-time leader-following consensus tracking. In addition, we integrate the analysis within a formal framework of classical Lyapunov theory by stretching the time axis. Numerical simulations are given to show the effectiveness and performance of the proposed control schemes.