Networked Control

Advances in computer and communication technology steadily increase the possibilities of dynamical systems interacting via networks. Control of such cyber-physical systems requires explicit consideration of communication aspects and the resulting dynamics of the networked control systems.

Modern control systems, in which information (e.g., measurements or control inputs) between spatially distributed components (e.g., sensor, controllers or actuator) is communicated over shared communication networks (e.g. CAN, Ethernet), are referred to as Networked Control Systems (NCS).

Within the Networked Control group at the IST, we work towards having a more detailed view of the communication system and taking these details into account when designing controllers.

The main concept behind all of our approaches is to describe important aspects and potentials from communication theory in a mathematically rigorous fashion, and use them to address relevant control theoretic questions.

Graph representation of the communication unreliabilities.
Graph representation of the communication unreliabilities.

We develop communication abstractions for network effects and incorporate them into analysis of systems and the design of controllers.

Our goal: theoretic guarantees (such as stability, performance, robustness) on the closed-loop in presence of unreliable communication channels.

Example: switched system with graph-based switching. Unreliability of comunication channels is captured by the combination of a graph and a family of systems.
Interpretation:

  • Vertices encode the current state of the communication un-
    reliability
  • Edges represent the system under network effects like
    losses, e.g., different linear behavior

Applications:
This system class models many important real world problems, e.g., dropouts in NCS, deadline misses in real-time control, resource allocation, ...

Contact Persons: Frank Allgöwer, Michael Hertneck, Simon Lang, Marc Seidel

Publications:

Illustration of the token bucket model
Illustration of the token bucket model.

When information is transmitted over a shared and possibly wireless channel, a number of applications communicate over the same network. Especially in such scenarios, communication resources are limited, such that it is advantageous to use the offered resources in an optimal way. For control applications in particular, a priori designed data transmission schedules (e.g. periodic schedules) are almost always suboptimal: control tasks require a lot of communication during precarious operating conditions, while when in a converged state, a much lower amount of communiation typically suffices.

With our research, we consider the novel approach to use an explicit dynamical model of the network's communication capacity, the token bucket model, to determine when information should be sent. By leveraging Model Predictive Control (MPC) to control both plant and network in a unified manner, both transmissions of new control values are scheduled and the corresponding control values are determined, optimizing a finite-horizon performance criterion. We investigate the interplay between control applications and the network and determine criteria under which desired control objectives, such as stability and a certain level of performance, can be ensured.

Contact Persons: Frank Allgöwer, Stefan Wildhagen

Publications:

Overview graphic over time- event- and self-triggered control
Comparison of different sampling strategies

When communication resources are limited, it may be favourable to determine transmission instants online based on the current system state instead of using traditional periodic sampling with fixed transmission intervals. This leads to a feedback interpretation of the communication process instead of the open loop approach that results from periodic transmissions.

Important questions in this area include not only identifying suitable trigger conditions but also finding appropriate descriptions for the resulting closed-loop system properties, considering network effects, and understanding how these differ between time-triggered, event-triggered, and self-triggered control. In our research, besides developing new triggering concepts, we also focus on better understanding of existing triggering concepts and on the mathematically rigorous analysis and comparison of the performance of event- and self-triggered control to time-triggered control when network effects are taken into account.

In this research direction, we collaborate with Prof. Dragan Nešić from the University of Melbourne, Prof. Duarte Antunes from the Eindhoven Eindhoven University of Technology and Alejandro Maass from the Pontificia Universidad Católica de Chile.

Contact Persons: Frank Allgöwer, Michael Hertneck, David Meister

Possible evolution of the system state with limited bit rate and delay.
Possible evolution of the system state with limited bit rate and delay.

When studying stabilization problems for continuous-time control systems, the state is usually sampled periodically before being coded and sent over a channel. In such a scenario, fundamental bounds on the necessary bit rate for stabilization are known. On the other hand, a study of Kofman and Braslavsky in 2006 showed that using a sampling mechanism that employs state information, the necessary bit rate for stabilizing an unstable control system with one input and one output can be made arbitrarily small. Recently, this initiated research on the influence of such event-based sampling strategies on the necessary bit rates for given control tasks.

In our research, we consider a setup where the controller is assumed to be static and the coder and decoder are assumed to be memoryless. The first control goal that we are interested in is containability. This system property was first introduced by Wong and Brockett in 1997 for a similar scenario but without event-based sampling. Firstly, we analyzed scalar, unstable, linear control systems with time-varying but bounded transmission delays. After extending our results to uncertainties in the system dynamics, our current research focusses on more general system classes.

In this research direction, we collaborate with Prof. Hideaki Ishii from the Tokyo Institute of Technology.

Contact Persons: Frank Allgöwer, Steffen Linsenmayer

Publications:

  • Steffen Linsenmayer, Matthias A. Müller, Hideaki Ishii, Frank Allgöwer
    Event-based Containability for Linear Systems with Arbitrary Small Bit Rates
    in Proc. 8th IFAC Workshop on Distributed Estimation and Control in
    Networked Systems (NecSys), Chicago, IL, USA, 2019, to appear.

  • Steffen Linsenmayer, Hideaki Ishii, and Frank Allgöwer
    Containability with event-based sampling for scalar systems with time-varying delay and uncertainty
    in IEEE Control Systems Letters, Vol. 2, No. 4, pp. 725–730, 2018.

Publications

  1. M. Seidel, M. Hertneck, P. Yu, S. Linsenmayer, D. V. Dimarogonas, and F. Allgöwer, “A Window-based Periodic Event-triggered Consensus Scheme for Multi-agent Systems,” IEEE Transactions on Control of Network Systems, vol. 11, no. 1, Art. no. 1, Mar. 2024, doi: 10.1109/tcns.2023.3285863.
  2. M. Hertneck, A. I. Maass, D. Nesić, and F. Allgöwer, “An $L_p$-norm framework for event-triggered control,” in Proc. European Control Conf. (ECC), in Proc. European Control Conf. (ECC). Stockholm, Sweden, 2024, pp. 2818–2824. doi: 10.23919/ECC64448.2024.10591119.
  3. M. Hertneck, S. Lang, J. Berberich, and F. Allgöwer, “Event-Triggered Control Based on Integral Quadratic Constraints,” IEEE Control Systems Letters, vol. 8, pp. 2039–2044, 2024, doi: 10.1109/LCSYS.2024.3427989.
  4. M. Hertneck and F. Allgöwer, “Robust dynamic self-triggered control for nonlinear systems using hybrid Lyapunov functions,” Nonlinear Analysis: Hybrid Systems, vol. 53, p. 101485, 2024, doi: 10.1016/j.nahs.2024.101485.
  5. D. Meister, F. Aurzada, M. A. Lifshits, and F. Allgöwer, “Time- versus event-triggered consensus of a single-integrator multi-agent system,” Nonlinear Analysis: Hybrid Systems, vol. 53, p. 101494, 2024, doi: 10.1016/j.nahs.2024.101494.
  6. M. Seidel, S. Lang, and F. Allgöwer, “On l2-performance of weakly-hard real-time control systems,” European Journal of Control, p. 101056, Jun. 2024, doi: 10.1016/j.ejcon.2024.101056.
  7. M. Hertneck and F. Allgöwer, “Reverse average dwell time constraints enable arbitrary maximum allowable transmission intervals,” in Proc. 12th IFAC Symp. Nonlinear Control Systems (NOLCOS), in Proc. 12th IFAC Symp. Nonlinear Control Systems (NOLCOS). Canberra, Australia, 2023, pp. 379–384. doi: 10.1016/j.ifacol.2023.02.064.
  8. S. Schlor, R. Strässer, and F. Allgöwer, “Koopman interpretation and analysis of a public-key cryptosystem: Diffie-Hellman key exchange,” in Proc. 22nd IFAC World Congress, in Proc. 22nd IFAC World Congress. Yokohama, Japan, 2023, pp. 984–990. doi: 10.1016/j.ifacol.2023.10.1693.
  9. M. Hertneck and F. Allgöwer, “Self-triggered output feedback control for nonlinear networked control systems based on hybrid Lyapunov functions,” in Proc. 22nd IFAC World Congress, in Proc. 22nd IFAC World Congress. Tokyo, Japan, 2023, pp. 5748–5753. doi: 10.1016/j.ifacol.2023.10.165.
  10. D. Meister and F. Allgöwer, “Performance implications of different p-norms in level-triggered sampling,” in Proc. 62nd IEEE Conf. on Decision and Control (CDC), in Proc. 62nd IEEE Conf. on Decision and Control (CDC). Singapore, Singapore, 2023, pp. 3878–3883. doi: 10.1109/CDC49753.2023.10384009.
  11. D. Meister, F. Dürr, and F. Allgöwer, “Shared Network Effects in Time- versus Event-Triggered Consensus of a Single-Integrator Multi-Agent System,” in 22nd IFAC World Congress, in 22nd IFAC World Congress. Yokohama, Japan, 2023, pp. 5975–5980. doi: 10.1016/j.ifacol.2023.10.636.
  12. D. Antunes, D. Meister, T. Namerikawa, F. Allgöwer, and W. P. M. H. Heemels, “Consistent event-triggered consensus on complete graphs,” in Proc. 62nd IEEE Conf. on Decision and Control (CDC), in Proc. 62nd IEEE Conf. on Decision and Control (CDC). Singapore, Singapore, 2023, pp. 3911–3916. doi: 10.1109/CDC49753.2023.10384026.
  13. D. Meister, F. Aurzada, M. A. Lifshits, and F. Allgöwer, “Analysis of Time- versus Event-Triggered Consensus for a Single-Integrator Multi-Agent System,” in Proc. 61st IEEE Conf. on Decision and Control (CDC), in Proc. 61st IEEE Conf. on Decision and Control (CDC). Cancun, Mexico, 2022, pp. 441–446. doi: 10.1109/CDC51059.2022.9993301.
  14. M. Hertneck and F. Allgöwer, “Dynamic self-triggered control for nonlinear systems with delays,” in Proc. 9th IFAC Conf. on Networked Systems (NECSYS), in Proc. 9th IFAC Conf. on Networked Systems (NECSYS). Zürich, Switzerland, 2022, pp. 312–317. doi: 10.1016/j.ifacol.2022.07.278.
  15. M. Hertneck, S. Linsenmayer, and F. Allgöwer, “Efficient stability analysis approaches for nonlinear  weakly-hard real-time control systems,” Automatica, vol. 133, p. 109868, 2021, doi: https://doi.org/10.1016/j.automatica.2021.109868.
  16. J. Berberich, S. Wildhagen, M. Hertneck, and F. Allgöwer, “Data-driven analysis and control of continuous-time systems under aperiodic sampling,” in Proc. 19th IFAC Symp. System Identification (SYSID), in Proc. 19th IFAC Symp. System Identification (SYSID). Padova, Italy, 2021, pp. 210–215. doi: 10.1016/j.ifacol.2021.08.360.
  17. M. Hertneck and F. Allgöwer, “A Simple Approach to Increase the Maximum Allowable Transmission Interval,” in Proc. 3rd IFAC Conf. on Modelling, Identification and Control of Nonlinear Systems (MICNON), in Proc. 3rd IFAC Conf. on Modelling, Identification and Control of Nonlinear Systems (MICNON). Tokyo, Japan, 2021, pp. 443–448. doi: 10.1016/j.ifacol.2021.10.390.
  18. S. Schlor, M. Hertneck, S. Wildhagen, and F. Allgöwer, “Multi-party computation enables secure polynomial control based solely on secret-sharing,” in Proc. 60th IEEE Conf. Decision and Control (CDC), in Proc. 60th IEEE Conf. Decision and Control (CDC). Austin, TX, USA, 2021, pp. 4882–4887. doi: 10.1109/CDC45484.2021.9683026.
  19. M. Hertneck and F. Allgöwer, “Dynamic self-triggered control for nonlinear systems based on hybrid Lyapunov functions,” in Proc. 60th IEEE Conf. Decision and Control (CDC), in Proc. 60th IEEE Conf. Decision and Control (CDC). Austin, TX, USA, 2021, pp. 533–539. doi: 10.1109/CDC45484.2021.9682784.
  20. S. Linsenmayer, M. Hertneck, and F. Allgöwer, “Linear Weakly Hard Real-Time Control Systems: Time- and Event-Triggered Stabilization,” IEEE Trans.\ Automat.\ Control, vol. 66, no. 4, Art. no. 4, 2021, doi: 10.1109/TAC.2020.3000981.
  21. M. Hertneck, S. Linsenmayer, and F. Allgöwer, “Stabilization of Nonlinear Weakly Hard Real-Time Control Systems,” in Proc. 21st IFAC World Congress, in Proc. 21st IFAC World Congress. Berlin, Germany, 2020, pp. 2632–2637. doi: 10.1016/j.ifacol.2020.12.307.
  22. M. Hertneck, S. Linsenmayer, and F. Allgöwer, “Stability Analysis for Nonlinear Weakly Hard Real-Time Control Systems,” in Proc. 21st IFAC World Congress, in Proc. 21st IFAC World Congress. Berlin, Germany, 2020, pp. 2632–2637. doi: 10.1016/j.ifacol.2020.12.307.
  23. M. Hertneck, S. Linsenmayer, and F. Allgöwer, “Model-Based Nonlinear Periodic Event-Triggered Control for Continuous-Time Systems with Sampled-Data Prediction,” in Proc. European Control Conf. (ECC), in Proc. European Control Conf. (ECC). Saint Petersburg, Russia, 2020, pp. 1814–1819.
  24. M. Hertneck and F. Allgöwer, “Exploiting Information for Decentralized Periodic Event-Triggered Control,” in Proc. 59th IEEE Conf. Decision and Control (CDC), in Proc. 59th IEEE Conf. Decision and Control (CDC). Jeju, South Korea, 2020, pp. 4999–5004. doi: 10.1109/CDC42340.2020.9304456.
  25. M. Hertneck, S. Linsenmayer, and F. Allgöwer, “Nonlinear Dynamic Periodic Event-Triggered Control with Robustness to Packet Loss Based on Non-Monotonic Lyapunov Functions,” in Proc. 58th IEEE Conf. Decision and Control (CDC), in Proc. 58th IEEE Conf. Decision and Control (CDC). Nice, France, 2019, pp. 1680–1685. doi: 10.1109/CDC40024.2019.9029770.
Group picture of the NCS research group at the IST
The NCS research group at the IST (30.01.2024)
Photo: Universität Stuttgart / IST
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