Solvability conditions and design for H∞ & H2 almost state synchronization of homogeneous multi-agent systems

This paper studies the H∞ and H2 almost state synchronization problem for homogeneous multi-agent systems with general linear agents affected by external disturbances and with a directed communication topology. Agents are connected via diffusive full-state coupling or diffusive partial-state coupling. A necessary and sufficient condition is developed for the solvability of the H∞ and H2 almost state synchronization problem. Moreover, a family of protocols based on either an algebraic Riccati equation (ARE) method or a directed eigen structure assignment method are developed such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H∞ and H2 norm of the corresponding closed-loop transfer function, is reduced to any arbitrarily small value. The protocol for full-state coupling is static, while for partial-state coupling it is dynamic

H∞ & H2 almost state synchronization with full-state coupling for homogeneous multi-agent systems

This paper studies the H∞ and H2 almost state synchronization problem for homogeneous multi-agent systems with general linear agents affected by external disturbances and a directed communication topology. Agents are connected via diffusive full-state coupling, i.e. agents are coupled through states. A necessary and sufficient condition is developed for the solvability of the H∞ and H2 almost state synchronization problem. Moreover, a family of static protocols are developed such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H∞ and H2 norm of the corresponding closed-loop transfer function, is reduced to any arbitrarily small value. The protocol design is based on two methods: algebraic Riccati equation (ARE) or asymptotic time-scale eigenstructure assignment (ATEA)

Scale-free Protocol Design for Output Synchronization of Heterogeneous Multi-agent subject to Unknown, Non-uniform and Arbitrarily Large Input Delays

This paper studies output synchronization problems for heterogeneous networks of continuous- or discrete-time right-invertible linear agents in presence of unknown, non-uniform and arbitrarily large input delay based on localized information exchange. It is assumed that all the agents are introspective, meaning that they have access to their own local measurements. Universal linear protocols are proposed for each agent to achieve output synchronizations. Proposed protocols are designed solely based on the agent models using no information about communication graph and the number of agents or other agent models information. Moreover, the protocols can tolerate arbitrarily large input delays.Comment: 9 pages, 3 figures, short version of this paper will be presented at Chinese Control Conference 2020. arXiv admin note: text overlap with arXiv:2002.06577, arXiv:2001.02117, arXiv:1908.06535, arXiv:2004.0949

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control

Event-based synchronisation of linear discrete-time dynamical networks

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