Research Topics

    Semi-Autonomous Consensus Networks

    Network Measures and Adaptive Topology

    We investigate network measures to quantify the effectiveness of the control interfaces with the network, and in particular the average quadratic performance cost (the mean tracking measure) and the open loop norm (the variance damping measure) of the  network dynamics. In fact, when the  network dynamics is diffusive, both measures provide a means of relating topological features of the interaction network which promote manageability of the swarm.

    In situations where the interaction network topology is particularly unsuitable for effective control interfaces, an option is to redesign the network online - where this is possible, for example via the wireless nature of the interactions. In particular, the open loop norm for the network can be employed to dynamically rewire the interaction network topology improving the effectiveness of the controllers' interface with the network.

    Publications:
  • Airlie Chapman, Eric Schoof and Mehran Mesbahi (2013) Distributed Online Topology Design for Disturbance Rejection, 817-821. In Proc. of the IEEE Conference on Decision and Control. Slides
  • Airlie Chapman and Mehran Mesbahi (2013) Semi-Autonomous Consensus: Network Measures and Adaptive Trees, 19-31. In IEEE Transactions on Automatic Control 58 (1).
  • Airlie Chapman and Mehran Mesbahi (2012) System Theoretic Aspects of Influenced Consensus: Single Input Case, 1505-1511. In IEEE Transactions on Automatic Control 57 (6).
  • Airlie Chapman and Mehran Mesbahi (2010) Semi-Autonomous Networks: Network Resilience and Adaptive Trees, 7473-7478. In Proc. of the IEEE Conference on Decision and Control. (Invited Paper) Slides
  • Airlie Chapman, Eric Schoof and Mehran Mesbahi (2010) Semi-Autonomous Networks: Theory and Decentralized Protocols, 1958-1963. In Proc. of the IEEE International Conference on Robotics and Automation. Slides
  • Airlie Chapman, Marzieh Nabi-Abdolyousefi and Mehran Mesbahi (2009) Identification and Infiltration in Consensus-type Networks, 84-89. In 1st IFAC Workshop on Estimation and Control of Networked Systems. (Finalist for the best student paper award) Poster

    UAV Swarming with Wind Gusts

    Dynamic network redesign provides an approach to improve the effectiveness of the human controllers' signal in reducing a wind gust perturbing the UAV swarm. Specifically by rewiring the interaction network topology, we are able to amplify the human controllers' signal, to more effectively dampen the perturbation.  

    Publications:
  • Airlie Chapman and Mehran Mesbahi (2015) "UAV Swarms: Models and Effective Interfaces", 1987-2019. In Handbook of Unmanned Aerial Vehicles, Springer.
  • Airlie Chapman, Ran Dai and Mehran Mesbahi (2011) Network Topology Design for UAV Flocking with Wind Gusts. In Proc. of the AIAA Guidance, Navigation and Control Conference. Slides
  • Airlie Chapman and Mehran Mesbahi (2011) UAV Flocking with Wind Gusts: Adaptive Topology and Model Reduction, 1045-1050. In Proc. of the American Control Conference. (Best session presentation award) Slides  

    Controllability and Observability of Networks

    Symmetry

    Publications:
  • Airlie Chapman and Mehran Mesbahi (2015) State Controllability, Output Controllability and Stabilizability of Networks: A Symmetry Perspective, 4776-4781. In Proc. of the IEEE Conference on Decision and Control. (Invited Paper) Slides Errata
  • Airlie Chapman and Mehran Mesbahi (2014) On Symmetry and Controllability of Multi-Agent Systems, 626-630. In Proc. of the IEEE Conference on Decision and Control.

    Graph Products

    We investigate the Cartesian and Kronecker graph products decompose both the network topology and network dynamics. Moreover, we are able to perform this task efficiently. We employ this decomposition to present large semi-autonomous networks as smaller factor semi-autonomous networks. New tools for network trajectory factorization, controllability and observability follow from the Cartesian product factorization.  

    Publications:
  • Airlie Chapman and Mehran Mesbahi (2014) Kronecker Product of Networked Systems and their Approximates, 1426-1431. In 21st International Symposium on Mathematical Theory of Networks and Systems. Slides
  • Airlie Chapman, Marzieh Nabi-Abdolyousefi and Mehran Mesbahi (2014) Controllability and Observability of Network-of-Networks via Cartesian Products, 2668- 2679. IEEE Transactions on Automatic Control 59 (10). Errata
  • Airlie Chapman, Marzieh Nabi-Abdolyousefi and Mehran Mesbahi (2012) Controllability and Observability of Cartesian Product Networks, 80-85. In Proc. of the IEEE Conference on Decision and Control. (Invited Paper) Slides
  • Structural Controllability

    Publications:
  • Airlie Chapman and Mehran Mesbahi (2013) "Security and Infiltration of Networks: A Structural Controllability and Observability Perspective", 143-160.  Springer's Lecture Notes on Control and Information Sciences 449.
  • Airlie Chapman and Mehran Mesbahi (2013) On Strong Structural Controllability of Networked Systems: A Constrained Matching Approach, 6141-6146. In Proc. of the American Control Conference. Slides

    Network-of-Networks 

    Scalability is a common challenge to modeling large networks. There are many graph based tools that can be exploited to factorize the network interaction topology, but the network interaction dynamics can rarely be decomposed in the same manner. We explore network-of-networks that exhibit this property. 

    Publications:
  • Airlie Chapman, Marzieh Nabi-Abdolyousefi and Mehran Mesbahi (2014) Controllability and Observability of Network-of-Networks via Cartesian Products, 2668- 2679. IEEE Transactions on Automatic Control 59 (10).
  • Airlie Chapman and Mehran Mesbahi (2013) Kronecker Product of Networked Systems and their Approximates, 1426-1431. In 21st International Symposium on Mathematical Theory of Networks and Systems. Slides
  • Airlie Chapman, Marzieh Nabi-Abdolyousefi and Mehran Mesbahi (2012) Controllability and Observability of Cartesian Product Networks, 80-85. In Proc. of the IEEE Conference on Decision and Control. (Invited Paper) Slides
  • Airlie Chapman and Mehran Mesbahi (2012) Cartesian products on Z-Matrix networks: Factorization and interval analysis. In 20th International Symposium on Mathematical Theory of Networks and Systems. Slides

    Online Distributed Optimization

    Publications:
  • Saghar Hosseini, Airlie Chapman, and Mehran Mesbahi (2015) "Online Distributed Estimation via Adaptive Sensor Networks." The IEEE Transactions on Control of Network Systems. (submitted)
  • Saghar Hosseini, Airlie Chapman and Mehran Mesbahi (2014) Online Distributed ADMM via Dual Averaging, 904-909. In Proc. of the IEEE Conference on Decision and Control. (Invited Paper)
  • Airlie Chapman, Eric Schoof and Mehran Mesbahi (2013) Distributed Online Topology Design for Disturbance Rejection, 817-821. In Proc. of the IEEE Conference on Decision and Control. Slides
  • Saghar Hosseini, Airlie Chapman and Mehran Mesbahi (2013) Online Distributed Optimization via Dual Averaging, 1484-1489. In Proc. of the IEEE Conference on Decision and Control. Slides

    Security and Infiltration of Networks

    Network security via topology design (intra-agent security) is a largely unexplored area within a semi-autonomous consensus setting. In addition, this is the only security response available in the case where the agent dynamics and interaction protocol are assumed to be fixed or expensive to alter. Examples of such systems include networks with hardwired dynamics and interactions, for example due to safety and the required performance guarantees, and systems with physically and biologically motivated dynamics and interactions, e.g., diffusion across self assembly units and bio-inspired networks.
    Publications:
  • Airlie Chapman and Mehran Mesbahi (2013) "Security and Infiltration of Networks: A Structural Controllability and Observability Perspective", 143-160.  Springer's Lecture Notes on Control and Information Sciences 449.
  • Airlie Chapman, Marzieh Nabi-Abdolyousefi and Mehran Mesbahi (2009) Identification and Infiltration in Consensus-type Networks, 84-89. In 1st IFAC Workshop on Estimation and Control of Networked Systems. (Finalist for the best student paper award) Poster

    Beyond Linear Consensus

    Advection on Graphs

    Consensus is a popular linear protocol for the network dynamics. Consequently, it is a rich area of research. We explore the advection protocol which shares many characteristics of consensus, facilitating the extension of many of the consensus results to advection. The advection protocol proves advantageous to formation control and load balancing applications. We demonstrate the latter with our robotic platform. 

    Publications:
  • Airlie Chapman, Eric Schoof and Mehran Mesbahi (2012) Advection on Networks with an Application to Decentralized Load Balancing, 2680-2681. In Proc. of the IEEE International Conference on Intelligent Robots and Systems.
  • Airlie Chapman and Mehran Mesbahi (2011) Advection on Graphs, 1461-1466. In Proc. of the IEEE Conference on Decision and Control. Slides

    Z-Matrix Theory

    Linear consensus can also be generalized to nonlinear consensus. The Laplacian matrix, the system matrix at the heart of consensus, lives in the family of Z-matrices. Many results from nonlinear consensus generalize to nonlinear Z-matrix applications. We explore these results, which include the characterization of the set of equilibria and the establishment of asymptotic stability. 

    Publications:
  • Airlie Chapman and Mehran Mesbahi (2012) Cartesian products on Z-Matrix networks: Factorization and interval analysis. In 20th International Symposium on Mathematical Theory of Networks and Systems. Slides
  • Airlie Chapman and Mehran Mesbahi (2012) Stability Analysis of Nonlinear Networks via M-matrix Theory: Beyond Linear Consensus, 6626-6631. In Proc. of the American Control Conference. Slides
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