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Hierarchical and Cooperative Control

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Description

Hierarchical Control

Complexity represents a major concern in many control problems, and it is common engineering knowledge that suitable decomposition techniques form a necessary ingredient for any systematic treatment of complex control problems. Hierarchical approaches, where several control layers interact, are a particularly attractive way of problem decomposition as they provide an extremely intuitive control architecture. Complexity problems are especially pronounced for hybrid control synthesis problems, and this has motivated the particular line of research described below.

In cooperation with Thomas Moor from Erlangen University and Jen Davoren from Melbourne University, we have developed a formal hierarchical control synthesis framework which is general enough to encompass both continuous and discrete levels [1] and [2]. Unlike heuristic approaches, our synthesis framework guarantees that the control layers interact "properly" and do indeed enforce the overall specifications for the considered plant model. Its elegance stems from the fact that the specifications for lower control levels can be considered suitable abstractions for the plant under low-level control which may be used as a basis for the synthesis of high-level controllers. An essential task within a hierarchical control synthesis procedure is then to come up with a suitable choice of specifications for the individual control layers. Because of the dual role of these specifications, this typically involves a non-trivial trade-off. E.g., imposing a less strict specification for a control layer will facilitate the control synthesis task for this layer, but will make the control synthesis task for higher level control more difficult. In [3], this trade-off was formally investigated for a specific scenario, where the top control layer is only responsible for the timing of certain discrete events, and where the abstraction it is based on can be represented by a timed event graph. A specific two-layer scenario involving a purely discrete top layer control system was developed in [4] and applied to the control of gene regulatory networks. This involves abstractions of gene networks in the form of finite state machines, where each state corresponds to a set of gene expression levels and the events are associated with the activation/repression of genes. To accomplish the top level task, standard supervisory control theory had to be extended to address the so-called state attraction problem.

Consensus-based Cooperative Control

Cooperative control is the attempt to control a process, or a set of interacting processes, via a set of local control agents which share a common goal but lack a central decision unit. Consensus algorithms, which have been used in the field of distributed computing for decades, have recently attracted renewed attention because they can be exploited for cooperative control. Coordination between entities in a group requires that they share information over a network, which is usually modelled as a directed or undirected graph, and develop a consistent view regarding objectives and relevant information on the environment, i.e., reach a consensus. Within this context, we have investigated the following issues.

(i) The first issue concerns a specific class of consensus algorithms, namely max-consensus, which is especially important in applications such as minimum time rendezvous, leader election, and distributed synchronisation of a class of discrete event systems modelled by timed event graphs (TEGs). In particular, we have proposed an approach that uses results from the field of max-plus algebra to analyze max-consensus algorithms in both time-invariant and time-variant communication topologies[5] [6]. Moreover, it was analyzed when the application of a consensus-based control protocol to a network of TEGs leads to a synchronized and stable overall TEG [7] .

(ii) We have also investigated convergence properties of consensus algorithms, characterized by the Laplacian matrix of the communication graph. For agents with double integrator dynamics, we allow position and velocity information to be exchanged between the agents via different undirected communication networks. It turns out that consensus can be achieved even if neither of the two networks is connected [8] [9] [10]. For leader-follower networks, we studied a notion of controllability depending on the structure and the weights of the communication graph [11] [12]. Finally, consensus approaches were applied to synchronization problems in microgrids [13]

People Involved

  • Xavier David-Henriet (now with Evonik)
  • Darina Goldin (now with dojo madness)
  • Behrang Monajemi Nejad (now with Berner & Mattner)
  • Sid Ahmed Attia (now with GE)
  • Johannes Schiffer (now with Leeds University)
  • Jörg Raisch

Cooperation

  • Thomas Moor, Universität Erlangen
  • Jen Davoren, University of Melbourne

Publications

  1. Thomas Moor, Jörg Raisch, Jen M. Davoren. Admissibility Criteria for a Hierarchical Design of Hybrid Control Systems. In Proc. ADHS03 — IFAC Conference on Analysis and Design of Hybrid Systems, pages 389–394, St. Malo, France, 2003.
  2. Jörg Raisch, Thomas Moor. Hierarchical Hybrid Control of a Multiproduct Batch Plant, volume 322 of Lecture Notes in Control and Information Sciences, pages 99–216. Springer-Verlag, 2005.
  3. X. David-Henriet, J. Raisch,, L. Hardouin. Consistent Control Hierarchies with Top Layers Represented by Timed Event Graphs. In Proc. of the 17th International Conference on Methods and Models in Automation and Robotics, IEEE, Międzyzdroje, Poland, 2012.
  4. Baldissera, F.L., Cury, J.E.R., Raisch, J.. A Supervisory Control Theory Approach to Control Gene Regulatory Networks. Automatic Control, IEEE Transactions on, 61 (1):18-33, Jan 2016.
  5. B. Monajemi Nejad, S.A. Attia, J. Raisch. Max-Consensus in a Max-Plus Algebraic Setting: The Case of Fixed Communication Topologies. In in XXII International Symposium on Information, Communication and Automation Technologies, Sarajevo, Bosnia and Herzegovina, 2009.
  6. B. Monajemi Nejad, S.A. Attia, J. Raisch. Max-Consensus in a Max-Plus Algebraic Setting: The Case of Switching Communication Topologies. In in 10th International Workshop on Discrete Event Systems, pages 183-190, Berlin, Germany, August-September 2010.
  7. B. Monajemi Nejad, J. Raisch. Consensus-Based Synchronizing Control for Networks of Timed Event Graphs. In 22nd Mediterranean Conference on Control and Automation, pages 620-627, Palermo, Italy, 2014.
  8. D. Goldin, J. Raisch. Controllability of Second Order Leader-Follower Systems. 2nd IFAC Workshop on Estimation and Control of Networked Systems, 2010.
  9. D. Goldin, S. A. Attia, J. Raisch. Consensus for Double Integrator Dynamics in Heterogeneous Networks. 49th IEEE Conference on Decision and Control (CDC'10), 2010.
  10. D. Goldin, J. Raisch. Consensus for Agents with Double Integrator Dynamics in Heterogeneous Networks. Asian Journal of Control, 16 pages 30-39, 2014.
  11. D.Goldin, J. Raisch. On the Weight Controllability of Consensus Algorithms. In 2013 European Control Conference (ECC2013), pages 233-238, Zuerich, Switzerland, July 2013.
  12. D. Goldin. On the Controllability and Weight Controllability of Double Integrator Leader-Follower Consensus Systems. In Proceedings of the 52nd {IEEE} Conference on Decision and Control, {CDC} 2013, December 10-13, 2013, Firenze, Italy, pages 686–691, 2013.
  13. J. Schiffer, S. Goldin, J. Raisch, T. Sezi. Synchronization of Droop-Controlled Microgrids with Distributed Rotational and Electronic Generation. In Proc. 52nd IEEE Conference on Decision and Control (CDC 2013), pages 2334-2339, Firenze, Italy, December 2013.

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