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.

Recent advances in computer and communication technology have encouraged a shift towards a spatially distributed actuation, control and sensing of technical processes. Often, the involved communication and computation devices serve a number of processes instead of, as is the traditional view in control research, being dedicated to one process alone. These developments gave rise to the concept of Networked Control Systems: instead of assuming ideal communication channels, the control loop is closed over packet-based (and often shared and/or wireless) communication networks, as they are used in real-world applications. Such packet based networks, however, introduce a limited bandwidth and possibly a probability of packet loss and delay, which might jeopardize the fulfillment of intended control goals, such as stability or control performance.

At the IST, we work towards having a more detailed view of the communication system and taking these details into account when designing the controller. This research direction within the field of Networked Control Systems is motivated by the observation that the communication system is built by engineers too, i.e., it can be optimized to support the control specific requirements. The main concept behind all of our approaches is to formulate important aspects and potentials from communication theory in a mathematically rigorous fashion, in order to address relevant control theoretic questions. A more specific and detailed description of the research topics within our group can be found below.

Illustration of the communication abstraction. (c)
Illustration of the communication abstraction.

In Networked Control Systems, a predominant goal is bridging the gap between control systems and communication systems. In particular, this includes the design of network models that can serve as a basis for control systems providing a guaranteed quality of control. On the other hand, these network models should allow for an efficient implementation in communication infrastructures. To achieve results of such interdisciplinary value, appropriate network models play a key role.

One example for such a model is the communication abstraction, which was developed in our group in collaboration with the Distributed Systems group of the Institute for Parallel and Distributed Systems at the University of Stuttgart (Head: Prof. Rothermel). The major characteristic of this abstraction is the distinction between deterministic (reliable) transmissions for guaranteeing stability, and opportunistic (unreliable) transmissions for optimizing quality of control. The mathematical formulation of such an abstraction is closely related to the concept of weakly hard real-time constraints, a specification concept from the real-time systems area. We are constantly working on improving and extending this model as well as on characterizing research questions for classical control theoretic results that are of particular interest under such an abstraction.

Contact Persons: Frank Allgöwer, Steffen Linsenmayer, Stefan Wildhagen, Michael Hertneck

Publications:

Illustration of the token bucket model (c)
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:

Time evolution of a non-monotonic Lyapunov function with event-triggered control updates. (c)
Time evolution of a non-monotonic Lyapunov function with event-triggered control updates.

When several processes share a communication medium with limited bandwidth, a new challenge that arises is the design of sampling and control strategies that use the communication medium as little as possible, to keep it available for other processes. Nevertheless, stability and performance goals like a certain convergence rate of the system state need to be guaranteed.

An approach to reduce the usage of the communication medium, while still guaranteeing stability and performance, is event-triggered control. Here, control updates are not sent over the communication medium periodically as in (traditional) time-triggered control, but according to a state dependent trigger rule.

The research in our group focuses mainly on periodic event-triggered control (PETC). In PETC, the trigger rule is evaluated periodically at fixed sampling times, which eases the implementation on digital hardware in comparison to a continuous-time evaluation.

We develop novel dynamic PETC mechanisms for linear and nonlinear systems and investigate new methods, such as non-monotonic Lyapunov functions, to derive theoretical properties for PETC mechanisms. In the design of the PETC mechanisms, we take into account typical aspects that arise in the field of Networked Control Systems, as e.g. network induced delays and packet loss.

In this research direction, we collaborate with Prof. Dimos V. Dimarogonas from the KTH Royal Institute of Technology, Stockholm.

Contact Persons: Frank Allgöwer, Steffen Linsenmayer, Michael Hertneck

Publications:

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