Regelungssysteme (Control Systems)

Abstraction-Based, Hierarchical, and Distributed Control

Summary

Contact Person:
Jörg Raisch

Abstraction-based, hierarchical, and distributed control can be seen as different, but related, attempts to handle complex control synthesis problems. Abstraction-based control aims at providing approximations, or abstractions, of given plant models such that a controller that "works" for an abstraction will, provably, also "work" for the underlying, more complex model. Hierarchical control can be interpreted as a multi-level decomposition of a given control problem, where solutions of low-level problems are "tied together" by higherlevel control, with the latter typically based on abstractions of the plant under the respective low-level control. Finally, distributed control refers to a scenario where a process, or a set of interacting processes, is to be controlled via a set of local controllers which share a common goal but lack a central decision unit.

Abstraction-Based Control

l-complete approximation [Moor and Raisch, 1999; Moor et al., 2002], and its extension, asynchronous l-complete approximation [Schmuck and Raisch, 2014b], were developed to facilitate control synthesis for hybrid dynamical systems, i.e., systems where continuous and discrete-event components interact. They provide purely discrete conservative approximations of the considered hybrid system, where conservativeness is in the sense of overapproximating the latter's external behaviour. In [Schmuck et al., 2015], the relation between different realisations of this class of abstractions and widely used quotient based abstractions (QBA) was investigated. It was shown that, in general, they are incomparable both in terms of behavioural inclusion and similarity relations.

Based on l-complete (asynchronous) approximations, standard methods from discrete event systems theory can be used to synthesise least restrictive control. This scenario was extended in [Park and Raisch, 2015] to cover the case where some of the external signals included in the abstraction are not visible for the controller.

If controller synthesis on the basis of the employed abstraction fails, l-complete (asynchronous) approximation allows for global abstraction refinement. This, however, may be computationally infeasible. For this reason, we have investigated a method for local refinement that focuses on aspects of the current abstraction preventing the controller synthesis step from being successful [Yang et al., 2018, 2020].

Hierarchical Control

A formal hierarchical control synthesis framework which is general enough to encompass both continuous and discrete levels was outlined in [Moor et al., 2003;  Raisch and Moor, 2005]. It 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 dificult. In [David-Henriet et al., 2012], 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 [Baldissera et al., 2016] 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.

Consensus-Based Distributed Control

In a distributed control scenario, a process, or a set of interacting processes, is to be controlled via a set of local control agents which share a common goal but lack a central decision unit.


Consensus plays an important role in distributed control. We have investigated a number of different consensus scenarios. For example, in [Goldin and Raisch, 2014], agents with double integrator dynamics exchange position and velocity information via different undirected communication networks. It turns out that consensus can then be achieved even if neither of the two networks is connected. In [Arun Kumar et al., 2017], we have investigated consensus problems where information is only exchanged when triggered by discrete events and the triggering mechanism may either be static or dynamic. We have proposed an approach that uses results from the field of max-plus algebra to analyse max-consensus, which is especially important in applications such as minimum time rendezvous, leader election, and distributed synchronisation, for both timeinvariant and time-variant communication topologies [Monajemi Nejad et al., 2009, 2010]. Moreover, it was analysed when the application of a consensusbased control protocol to a network of Timed Event Graphs (TEGs) leads to a synchronised and stable overall TEG [Monajemi Nejad and Raisch, 2014].


In the context of the DFG priority programme 1914 (Cyber-Physical Networking), in two joint projects with S. Stanczak from the Network Information Theory Group at TU Berlin, we have investigated the interplay between control and wireless communication in consensus problems for multi-agent systems. In particular, we have been interested in how to exploit the wireless superposition property to dramatically reduce information exchange for different consensus algorithms. Results for linear consensus were reported in [Molinari et al., 2018a]. Results for max-consensus problems can be found in [Molinari et al., 2018b, 2021, 2022]. The superposition property of the wireless channel was also exploited to obtain efficient consensus-based formation control for multi-agent systems [Molinari and Raisch, 2019] and for distributively solving systems of linear equations [Molinari and Raisch, 2020].


In a case study [Molinari and Raisch, 2018], we investigated the use of consensus-based auction algorithms for the automation of road intersections. In [Molinari et al., 2019b; Molinari et al., 2020], these results were extended and combined with local model-predictive control to obtain a distributed control scheme for road intersections. Average consensus, consensus-based auctioning, and distributed model-predictive control were also combined to automate lane changes and collision avoidance on highways [Molinari et al., 2019a].
The application of consensus-based methods to control problems in electrical power grids has been explored in [Schiffer et al., 2013, 2016; Parada Contzen and Raisch, 2015, 2016; Krishna et al., 2018, 2020].

People involved, projects and cooperations

Group members

Previous group members

  • Anne-Kathrin Schmuck (joined Max-Planck-Institut für Softwaresysteme, Kaiserslautern)
  • Fabio Baldissera (joined Federal University of Santa Catarina)
  • Thomas Seel (joined Friedrich-Alexander Universität Erlangen-Nürnberg)
  • Johannes Schiffer (joined Brandenburgisch-Technische Universität Cottbus)
  • Miguel Parada Contzen (joined Universidad del Bío Bío)
  • Behrang Monajemi Nejad (joined Volkswagen)
  • Ajay Krishna (joined Brandenburgisch-Technische Universität Cottbus)

Running projects

Completed Projects

Cooperations

  • Thomas Moor, Friedrich-Alexander Universität Erlangen-Nürnberg
  • Slawomir Stanczak, TU Berlin
  • Jung-Min Yang, Kyungpook National University
  • Seong-Jin Park, Ajou University
  • José Cury, Federal University of Santa Catarina
  • Pawel Romanczuk, HU Berlin
  • Oliver Brock, TU Berlin

Publications related to this research area

2022

Molinari, Fabio; Agrawal, Navneet; Stańczak, Sławomir; Raisch, Jörg
Over-The-Air Max-Consensus in Clustered Networks Adopting Half-Duplex Communication Technology
IEEE Transactions on Control of Network Systems
2022

2021

Molinari, Fabio; Agrawal, Navneet; Stańczak, Sławomir; Raisch, Jörg
Max-Consensus Over Fading Wireless Channels
IEEE Transactions on Control of Network Systems, 8 (2) :791-802
2021
Herausgeber: IEEE

2020

Molinari, Fabio; Raisch, Jörg
Exploiting Wireless Interference For Distributively Solving Linear Equations
IFAC-PapersOnLine, 53 (2) :2999-3006
2020
ISSN: 2405-8963
Molinari, Fabio; Katriniok, Alexander; Raisch, Jörg
Real-Time Distributed Automation Of Road Intersections
IFAC-PapersOnLine, 53 (2) :2606-2613
2020
ISSN: 2405-8963
Yang, Jung-Min; Moor, Thomas; Raisch, Jörg
Refinements of behavioural abstractions for the supervisory control of hybrid systems
Discrete Event Dynamic Systems, 30 (3) :533–560
2020

2019

Molinari, F.; Raisch, J.
Efficient Consensus-based Formation Control With Discrete-Time Broadcast Updates
2019 IEEE 58th Conference on Decision and Control (CDC), Seite 4172-4177
Dezember 2019
Molinari, F.; Dethof, A. M.; Raisch, J.
Traffic Automation in Urban Road Networks Using Consensus-based Auction Algorithms For Road Intersections
2019 18th European Control Conference (ECC), Seite 3008-3015
Juni 2019
Molinari, F.; Grapentin, A.; Charalampidis, A.; Raisch, J.
Automating lane changes and collision avoidance on highways via distributed agreement
at-Automatisierungstechnik, 67 (12) :1047–1057
2019
Herausgeber: De Gruyter Oldenbourg

2018

Molinari, F.; Raisch, J.
Automation Of Road Intersections Using Consensus-based Auction Algorithms
2018 Annual American Control Conference (ACC), Seite 5994-6001
IEEE
Juni 2018
Molinari, F.; Stanczak, S.; Raisch, J.
Exploiting the Superposition Property of Wireless Communication for Average Consensus Problems in Multi-Agent Systems
2018 European Control Conference (ECC), Seite 1766-1772
Juni 2018
Yang, Jung–Min; Moor, Thomas; Raisch, Jörg
Local Refinement of l-complete Approximations for Supervisory Control of Hybrid Systems
IFAC-PapersOnLine, 51 (7) :472 - 479
2018
ISSN: 2405-8963

2017

Kumar, S. Arun; Chowdhury, N.R.; Srikant, S.; Raisch, J.
Consensus analysis of systems with time-varying interactions : An event-triggered approach
IFAC-PapersOnLine, 50 (1) :9349 - 9354
2017
ISSN: 2405-8963

2016

Baldissera, Fabio; Cury, Jose; Raisch, Jörg
A Supervisory Control Theory Approach to Control Gene Regulatory Networks
IEEE Transactions on Automatic Control, 61 (1) :18–33
Januar 2016
ISSN: 0018-9286
Contzen, Miguel Parada; Raisch, Jörg
Reactive Power Consensus in Microgrids
European Control Conference (ECC) 2016,
Herausgeber: Aalborg, Denmark
2016
Schiffer, J.; Seel, T.; Raisch, J.; Sezi, T.
Voltage Stability and Reactive Power Sharing in Inverter-Based Microgrids With Consensus-Based Distributed Voltage Control
Control Systems Technology, IEEE Transactions on, 24 (1) :96-109
Januar 2016
ISSN: 1063-6536

2015

Schmuck, Anne-Kathrin; Tabuada, Paulo; Raisch, Jörg
Comparing asynchronous l-complete approximations and quotient based abstractions
54th IEEE Conference on Decision and Control (CDC), Seite 6823-6829
Herausgeber: Osaka, Japan
Dezember 2015
Park, Seong-Jin; Raisch, Jörg
Supervisory Control of Hybrid Systems Under Partial Observation Based on l -Complete Approximations
IEEE Transactions on Automatic Control, 60 (5) :1404-1409
Mai 2015
ISSN: 0018-9286
Contzen, Miguel Parada; Raisch, Jörg
Active Power Consensus in Microgrids
International Symposium on Smart Electric Distribution Systems and Technologies (EDST),
Herausgeber: Vienna, Austria
2015

2014

Schmuck, A.-K.; Raisch, J.
Asynchronous l-Complete Approximations
Systems and Control Letters :67-75
2014
Goldin, D.; Raisch, J.
Consensus for Agents with Double Integrator Dynamics in Heterogeneous Networks
Asian Journal of Control, 16 :30-39
2014
Nejad, B. Monajemi; Raisch, J.
Consensus-Based Synchronizing Control for Networks of Timed Event Graphs
22nd Mediterranean Conference on Control and Automation, Seite 620-627
Herausgeber: Palermo, Italy
2014
Schmuck, A.-K.; Raisch, J.
Constructing (Bi)Similar Finite State Abstractions using Asynchronous l-Complete Approximations
53rd IEEE Conference on Decision and Control, Los Angeles, USA, Seite 6744–6751
2014
Schmuck, A.-K.; Raisch, J.
Simulation and Bisimulation over Multiple Time Scales in a Behavioral Setting
Proceedings of the 22nd Mediterranean Conference on Control and Automation, Palermo, Italy, Seite 517–524
2014

2012

David-Henriet, Xavier; Raisch, Jörg; Hardouin, Laurent
Consistent Control Hierarchies with Top Layers Represented by Timed Event Graphs
Proc. of the 17th International Conference on Methods and Models in Automation and Robotics, IEEE
Herausgeber: Miedzyzdroje, Poland
2012

2010

Nejad, B. Monajemi; Attia, S.A.; Raisch, J.
Max-Consensus in a Max-Plus Algebraic Setting: The Case of Switching Communication Topologies
in 10th International Workshop on Discrete Event Systems, Seite 183-190
Herausgeber: Berlin, Germany
2010