Leader-Following Synchronization in Singular Multi-Agent Systems Under Signed and Uncertain Network Graphs

Abstract

This article considers the problem of leader-following synchronization in a singular multi-agent system. Two different types of network topologies are considered, one is signed and another is uncertain. A unified reduced-order observer with a distributed feedback control scheme is proposed for both types of network topologies to achieve synchronization. In particular, the following objectives are achieved in the closed-loop: i) the system is impulse-free, ii) the estimated states of the agents converge to their respective actual states, and iii) the follower states synchronize with the leader states, satisfying a pre-specified decay rate (helps to regulate the synchronization speed). The developed algorithm provides flexibility to independently design the associated gain parameters. Further, the algorithm utilizes only orthogonal matrices for transformations at various stages, and hence, it is numerically efficient. The effectiveness of the proposed design approach is demonstrated with some examples. Note to Practitioners—Most of the industry-favorable modeling and simulation software, such as OpenModelica, Simcenter Amesim, and MATLAB Simscape, produce a singular model for a physical system. A network of such singular systems is referred to as singular multi-agent system (SMAS). An important control objective of an SMAS is leader-following synchronization, which has potential applications in areas such as vehicle platoons, robotic systems, defense, space, and smart power grids. Such a synchronization objective is achieved through the implementation of a distributed control architecture, where the control action is over a communication network. The communication network, however, is always prone to cyber attacks and uncertainty within communication channels. The attacker may compromise the network and send conflicting signals to make some of the agents behave antagonistically. In this work, we provide a methodology to select control gains and network parameters appropriately so that synchronization can still be achieved despite such network-related issues. Our approach uses a distributed observer-based control strategy that allows practitioners to design the controller when sensor data and communication are limited. Moreover, singular dynamics often exhibits impulsive behavior, which is undesirable in practice. The proposed control architecture also obviates such undesirable behavior and allows regulating the synchronization speed. Since the control gain parameters are designed offline and independently, the proposed control structure is well-suited for real-time implementation in industrial networked systems.