Performance and design of consensus on matrix-weighted and time scaled graphs

In this paper, we consider the $\mathcal{H}_2$-norm of networked systems with multi-time scale consensus dynamics and vector-valued agent states. This allows us to explore how measurement and process noise affect consensus on matrix-weighted graphs by examining edge-state consensus. In particular, we highlight an interesting case where the influences of the weighting and scaling on the $\mathcal{H}_2$ norm can be separated in the design problem. We then consider optimization algorithms for updating the time scale parameters and matrix weights in order to minimize network response to injected noise. Finally, we present an application to formation control for multi-vehicle systems.Comment: 10 pages, 5 figures, accepted to the IEEE Transactions on Control of Network Systems. arXiv admin note: text overlap with arXiv:1909.0786

An H {592}[infinity] dynamic routing control of networked multi-agent systems

This research aims to introduce an analytical solution to the routing problem of Networked Multi-Agent Systems (NMAS) by taking advantage of control theory machinery. Routing problem can be defined as that of finding a route for messages among networked agents by adjusting the output flow of each link according to the traffic information of the network, such that some objective functions are minimized. In this research, a new objective function, namely worst-case queueing length is introduced based on which a novel routing methodology is presented. The propagating, transmitting and processing delays are inevitable characteristics of the queueing dynamics which is considered in the model of the network. The proposed dynamic optimization problem is formulated as a feedback control problem. First, a centralized [Special characters omitted.] optimal control scheme is proposed which can maintain a robust performance of the routing strategy in the presence of multiple and unknown time-varying delays for a fixed network topology. The routing problem is formulated as an [Special characters omitted.] optimal control problem for a time-delayed system. The resulting optimization problem is then recast as a minimization problem involving Linear Matrix Inequality (LMI) constraints. The physical constraints are also formulated as LMI feasibility conditions. The proposed centralized routing scheme is then reformulated in a decentralized framework. This modification yields an algorithm that, obtains the "fastest route", provides robustness against multiple unknown time-varying delays, and enhances the scalability of the algorithm to large scale traffic networks. By stochastically changing the network topology due to the nodes' mobility the overall network model is described by a Markovian jump process. The proposed Markovian jump dynamics can also support changing number of nodes due to adding new nodes to the network or deleting them because of their low energy or faults/failures. The resulting problem which involves Markovian jump dynamics due to the time-varying delays appearing in control is more challenging to solve. The problem is further complicated by the fact that the interconnected terms also change at each switching mode. To stabilize this system, an [Special characters omitted.] controller is presented for the Markovian jump system for mode-dependent interconnected terms. Finally, the LMIs corresponding to the associated physical constrains are properly modified for the mobile networks

Supportive consensus

[EN] The paper is concerned with the consensus problem in a multi-agent system such that each agent has boundary constraints. Classical Olfati-Saber's consensus algorithm converges to the same value of the consensus variable, and all the agents reach the same value. These algorithms find an equality solution. However, what happens when this equality solution is out of the range of some of the agents? In this case, this solution is not adequate for the proposed problem. In this paper, we propose a new kind of algorithms called supportive consensus where some agents of the network can compensate for the lack of capacity of other agents to reach the average value, and so obtain an acceptable solution for the proposed problem. Supportive consensus finds an equity solution. In the rest of the paper, we define the supportive consensus, analyze and demonstrate the network's capacity to compensate out of boundaries agents, propose different supportive consensus algorithms, and finally, provide some simulations to show the performance of the proposed algorithms.The author(s) received specific funding for this work from the Valencian Research Institute for Artificial Intelligence (VRAIN) where the authors are currently working. This work is partially supported by the Spanish Government project RTI2018-095390-B-C31, GVA-CEICE project PROMETEO/2018/002, and TAILOR, a project funded by EU Horizon 2020 research and innovation programme under GA No 952215. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Palomares Chust, A.; Rebollo Pedruelo, M.; Carrascosa Casamayor, C. (2020). Supportive consensus. 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A Decentralized Markovian Jump {cal H}_{\infty } Control Routing Strategy for Mobile Multi-Agent Networked Systems

This paper presents a Markovian jump linear (MJL) system framework for developing routing algorithms in mobile ad hoc networks (MANETs) that encounter changes in the number of nodes and/or the number of destinations. A unified H∞ control strategy is proposed by representing the dynamically changing destination nodes as singular switching control systems. A decentralized routing scheme is proposed and designed for the networked multi-agent system in presence of unknown time-varying delays. To solve the corresponding optimization problem the physical constraints are expressed as linear matrix inequality (LMI) conditions. The resulting decentralized H∞ routing control schemes for both regular and singular MJL systems are shown to formally achieve the desired performance specifications and requirements. Simulation results are presented to illustrate and demonstrate the effectiveness of our proposed novel routing control strategies

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Limits on the Network Sensitivity Function for Multi-Agent Systems on a Graph

This report explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the performance of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems