Learning in Control

Learning in Control

Algorithms of artificial intelligence and machine learning are of increasing importance for control engineering. At the Chair of Automatic Control, research is mainly directed towards the extension of control methods by learning components.


Prof. Dr.-Ing. Knut Graichen
Tel.: +49 9131 85-27127
E-Mail | Homepage

Learning in Model Design and Identification

Regression methods allow to approximate an unknown function from individual data points. For this purpose, Gaussian process regression uses a mean function that describes the prior knowledge and a covariance function that describes the correlation between data points. The advantage with regard to other regression methods is that by learning the covariance a direct measure of the model accuracy is obtained and thus the reliability of predictions can be assessed.

In the context of control engineering, Gaussian process regression can be used in a variety of ways. One focus of research is the identification of systems, where physical modelling is either poor or requires high effort. Moreover, such learned models can be adapted online in order to reflect effects of aging or wear. A particular challenge is the real-time capable implementation, for which the number of data points must be suitably limited.

If the model includes information about the reliability, this can be used, for example, in a stochastic model predictive controller. In addition to the mean value, it computes a prediction of the uncertainty that allows to satisfy constraints with a given probability.

Embedded learning of combustion models


Stochastic NMPC for collision avoidance with a probability of 99,9%


Learning in Optimization and Optimal Control

Reinforcement learning aims at obtaining an optimal control strategy from repeated interactions with the system. Specifically, for each state, the action that maximizes the expected reward is searched. Formulating this task as an optimization problem shows the conceptual similarity to model predictive control, with the difference that reinforcement learning does not require model knowledge of the system.

Inverse optimal control searches a cost functional, such that the solution of the corresponding optimization problem replicates a desired system behaviour as closely as possible. This allows, for example, to use expert knowledge for the automatic determination of weighting factors for a model predictive controller.

Although many technical tasks can be formulated as optimization problems, there are cases, where the cost function or constraints can only be evaluated by costly numerical simulations. Here, Bayesian optimization allows to solve the complex optimization problem using a limited number of evaluations of the cost function and the constraints. To this end, methods  like Monte Carlo simulation or the approximation of unknown functions by Gaussian process regression can be used.

Reinforcement learning for a hydraulic clutch


Bayesian optimization subject to an unknown equality constraint

Protected: Infinite-Dimensional Systems

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Mechatronics & Automotive

Mechatronik und Automotive

Mechatronic systems, which comprise both mechanical and electrical parts, represent an important application field of control engineering. Due to the limited computing power of the used ECUs, the application of modern control methods in these systems is associated with particular challenges. The Chair of Automatic Control researches control methods for, for example, electric drives, automatic transmissions and vehicles.


Prof. Dr.-Ing. Knut Graichen
Tel.: +49 9131 85-27127
E-Mail | Homepage

Electric drives

Mechatronics is a combination of the classical engineering disciplines of mechanical and electrical engineering. Accordingly a mechatronic system is the conjunction of a mechanical and electrical subsystem. To further increase the performance of the whole system it is of utmost importance to consider and model the separate subsystems as one system. Synchronous machines and power shift transmissions are examples for systems that are studied at our institute.

Permanent magnet synchronous machines (PMSM) play an increasingly important part in modern drive technology. They are used in industrial as well as automotive applications by virtue of their high efficiency and torque density. Besides an energy optimal operation the high performance control of those machines requires the adherence of a variety of nonlinear input and state constraints.

Electric drive test bench

Heavy duty/Off-road applications

Combustion engines

The development of combustion engines has been focused on the improvement of fuel efficiency in the past. Nowadays the compliance with increasingly restrictive exhaust emission regulations affects engine development. As a result, combustion engines have become very complex systems with many degrees of freedom. As the combustion is highly nonlinear, the use of classical control algorithms is evermore sophisticated.

Model predictive control (MPC) is also a suitable approach for this application as the control problem can be easily formulated as constrained optimal control problem. Nevertheless, its solution using accurate models typically leads to a high numerical load. Thus, the real-time feasible applicability on a standard electronic control unit is a challenging. This computational burden can be drastically reduced using suboptimal MPC approaches.

As the name indicates, MPC is based on reliable models. Thus, precise models are needed despite unavoidable model deviations for instance due to engine wear. Computational intelligence techniques that are applied in a wide range of applications can be used to cope with this challenge. This way, suitable engine models can be tracked online.

V12 combustion engine

Powershift transmissions

Because of their higher efficiency and shifting comfort dual clutch transmissions are increasingly used over conventional transmissions. Those advantages are paid for with a significantly more complex shifting process which can hardly be handled without methods of modern control theory. Input constraints in the form of torques and state constraints in the form of shaft revolutions can be taken into account by those methods, thereby decreasing the application costs considerably.

To fulfil those requirements model predictive control strategies for the aforementioned systems are developed at our institute. The real time capability of the control strategies is of key importance with sampling rates typically in the (sub-)millisecond range and available computing capacity severely limited, especially on electric control units. Besides the nonlinearities of the models different control concepts are considered.


Powershift transmission
(Source: ZF Friedrichshafen AG)
Application of powershift transmissions in construction machinery
(Source: ZF Friedrichshafen AG)


Besides the automotive industry, automation of industrial or agricultural vehicles is of increasing importance. By introducing automated driving functions, the driver should be relieved or completely replaced for everyday tasks. Both optimization-based methods of path planning and vehicle control are being researched at the Chair of Automatic Control and developed for real-time use in vehicles.

The challenges in off-road vehicle control are quite different compared to on-road. On the one hand, it is important to consider limitations and actuator dynamics. In addition, there are usually combinations of vehicle and trailer or vehicle and work equipment. Aside from that, the vehicle parameters are permanently varying due to changing loads and environments. In contrast to on-road, the speeds are lower, but the grounds are often unpaved and slippery. This must also be considered by the vehicle controller.

The challenges of global path planning includes manoeuvring in narrow space, such as reverse parking of a trailer truck. In order to be able to react to dynamic obstacles, the local path planning ensures that collision-free and drivable trajectories are generated. In addition, the trajectories have to consider the entire vehicle combination and comply with certain comfort requirements.


Path planning and vehicle control for automated driving functions in agricultural industry
(Source: ZF Friedrichshafen AG)

Automotive applications

An important field of application for control systems is the automotive sector. Today’s high demands on ride comfort, vehicle dynamics and compliance with emission and efficiency targets have made electronic control systems an integral part. Both in vehicle suspension systems and the hybrid powertrains as well as in concepts of e-mobility the increasing complexity of the systems requires the use of appropriate control methods.

In order to meet the high demands, the institute develops model-based control strategies for horizontal dynamics of over-actuated vehicles, vehicle vertical dynamics as well as longitudinal dynamics and drives.


Dr.-Ing. Andreas Michalka
Tel.: +49 9131 85-28592
E-Mail | Homepage

Horizontal dynamics of overactuated vehicles

The increasing electrification of motor vehicles opens the possibility to switch to decentralized actuator configurations. In these, each wheel can be individually driven, braked and steered and a more flexible interior design is made possible. This leads to a system that has more actuators than are required for the specification of even vehicle motion. The control of such overactuated vehicles is the subject of the considerations. By using this overactuation, an increase in driving safety or fault tolerance can be achieved.

Vehicle vertical dynamics

With active suspension systems, the existing conflict between driving comfort and driving safety can be mitigated compared to a passive suspension system design. The control of such systems under changing roadway characteristics and the estimation of these characteristics from the movement of wheels and vehicle body are examined. The improvement of the vehicle response to driver steering and braking interventions with simultaneously reduced vehicle reaction to uneven roads is the goal.

Longitudinal dynamics and drives

Today, the longitudinal dynamic behavior of a vehicle no longer results from the mechanical actuation of the engine and transmission by the driver, but rather from an interaction of complex, highly-automated powertrain structures. On the one hand, control strategies for components (e.g. friction clutches) are developed whose behavior significantly influences this interaction. On the other hand, concepts for automating this interaction are considered, which also include the driver-vehicle interface and, for example, the operating strategy of hybrid drives.

over-actuated vehicle
pFAU: Profile Analysing Unit
friction clutch test bench



Robotics belongs to the largest fields of application for control engineering methods. Besides conventional industrial robots, as known from the automobile production, there is an increasing usage of collaborative and mobile robots, for example as vacuum cleaners or autonomous vehicles. Research projects in this area concern the control of movements and forces on the one hand and the planning of paths and trajectories on the other.


Dr.-Ing. Andreas Völz
Tel.: +49 9131 85-61036
E-Mail | Homepage


Prof. Dr.-Ing. Knut Graichen
Tel.: +49 9131 85-27127
E-Mail | Homepage

Interaction control


When the robot is in contact with its environment, the forces and moments that arise must be taken into account by the control system. The challenges include the contact modelling, e.g. stiffness and friction, the safe handling of contact loss, or the selection of controller parameters for different applications.

In order to meet the demand for versatile and flexibly applicable control methods, the Chair of Automatic Control develops a model predictive interaction controller. Here, differenct objectives such as position control, direct force control, impedance contorl, or hybrid variants can be realized by a generic control framework. Safety aspects can be explicitly considered by limiting the maximum velocities or forces.

One possible field of application is the generic implementation of assembly tasks. The task can be decomposed into a sequence of motion and interaction primitives, where each primitive is represented by a specific parameterization of the model predictive interaction control. In order to reduce the effort for parameterization, the use of learning-based methods is investigated.


  • “Writing on a blackboard with chalk” – Model predictive interaction control for hybrid force/motion control (2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)) DOI: 10.1109/IROS45743.2020.9341168): Video
  • „Admittance Control of the XPlanar System for Human-Mover Interaction“ – Dynamic adaptation of the mover target position due to interaction forces: Video
  • “Object manipulation with an anthropomorphic hand” – Model Predictive Interaction Control for Force Closure Grasping (submitted at the 2021 IEEE Conference on Decision and Control (CDC)): Video
Robot interacts with rigid environment
Xplanar system and Allegro hand

Motion control

One of the basic functions of a robot is to move efficiently between different configurations or along trajectories. A challenge is the predictive control of robot arms taking into account the nonlinear rigid body dynamics as well as constraints. A real-time capable implementation is only possible with specialized algorithms that exploit the structure of the optimization problem.

Another field of research is the development of real-time predictive motion planning methods for driving simulators. By using modern nonlinear model predictive control approaches (MPC), the actuator constraints and the future reference values can be directly incorporated into the motion planning, which is not possible when using the classic filter-based approach. This enables a dynamic prepositioning of the simulator and leads to a better exploitation of the simulator potential. Since the future desired values in the online driver-in-the-loop application are dependent on the driver inputs and thus unknown, the future human driving behavior needs to be estimated in a suitable way in order to fully exploit the predictive potential of the approach. Another aspect in this field is the consideration of perception models to take the mechanism of the human motion perception into account.


  • Predictive motion planning for the Daimler driving simulator in a traffic circle: Video
  • Online motion planning with driver prediction for a driving dynamics maneuver: Video
  • Model Predictive Control for Catching Objects in Flight with a Robot Arm: Video
Daimler driving simulator (Source: Daimler AG)
Model scale truck for planning and control

Collision-free motion planning

If the position of humans and objects in the workspace is detected by sensors, safety can be improved by collision-free motion planning. The challenges are the high number of degrees of freedom of a robot arm, the complex collision detection and the limited computation time, when the environment changes frequently.

Research at the Chair of Automatic Control concerns on the one hand the method of dynamic roadmaps, which enables global path planning in less than 100 milliseconds, and its efficient extension to dual-arm robots. On the other hand, optimization-based methods are investigated, that allow taking constraints into account, e.g. closed kinematics.

Furthermore, collision-free path planning also plays a major role in the fields of mobile robots and autonomous vehicles. The task is particularly challenging when vehicles with multiple trailers are considered, since the computation of feasible motions is very complex for this system class. Research at the chair concerns the method of state lattices, which is based on precomputed motion primitives and an efficient graph search.


  • Collision-free motion planning for a rotating robot with seven degrees of freedom: Video
  • Collision-free motion planning for a dual-arm robot with twelve degrees of freedom: Video
  • Motion planning for a dual-arm robot with closed kinematics: Video
  • Predictive path-following control for continuous replanning with dynamic roadmaps (IEEE RA-L 2019, DOI der Publikation: 1109/LRA.2019.2929990): Video
Mobile dual-arm robot
Global path planning with optimal path in red









2015 and earlier


































  • Regelung von Ring-Resonator-Modulatoren in der optischen Datenübertragung

    (Third Party Funds Single)

    Term: 1. February 2022 - 31. January 2025
    Funding source: Industrie
  • Distributed model predictive control of nonlinear systems with asynchronous communication

    (Third Party Funds Single)

    Term: 1. January 2022 - 31. December 2024
    Funding source: Deutsche Forschungsgemeinschaft (DFG)
  • Anomaly detection and intelligent recalibration of sensorized systems

    (Third Party Funds Single)

    Term: 1. November 2021 - 31. October 2024
    Funding source: Industrie
  • Innovative Regelungs- und Steuerungsstrategien für Druckerhöhungsanlagen - TP Erlangen

    (Third Party Funds Group – Sub project)

    Overall project: Innovative Regelungs- und Steuerungsstrategien für Druckerhöhungsanlagen
    Term: 1. July 2021 - 30. June 2024
    Funding source: Bayerische Forschungsstiftung
  • KI-unterstützte Modellierung zur Steigerung der Regelgüte

    (Third Party Funds Single)

    Term: 1. July 2021 - 30. June 2024
    Funding source: Industrie
  • Kinesthetic teaching and predictive control of interaction tasks in robotics

    (Third Party Funds Single)

    Term: 1. July 2021 - 30. June 2024
    Funding source: Deutsche Forschungsgemeinschaft (DFG)

    Precise interactions as part of industrial manufacturing tasks are typically very complex to characterize and implement. One reason for this is the heterogeneity of the task-specific requirements for the motion and control behavior. A direct implementation of the task into a robot program therefore requires highly qualified specialists and is only profitable for large lot sizes. For a flexible applicability and easy (re-)configuration of the robot system, an approach to programming by kinesthetic demonstration is developed in this project. The robot is guided by the user through the entire manipulation task, while the robot motion as well as the interaction forces are simultaneously recorded. Typically, several repetitions of the demonstration are necessary in order to compensate for the suboptimality and imprecision of the human demonstration.  This is particularly important for complex motion sequences or interaction situations, such as periodic movements or the assembly of components, that are difficult to demonstrate but at the same time are crucial for a successful task execution. 

    The basis for this project is a previously developed general framework for model predictive interaction control (MPIC). The manipulation task is split into a sequence of elementary tasks, so-called manipulation primitives (MPs) with individual motion and control characteristics, which are treated in a holistic manner by a model predictive control approach. The MPIC approach is elaborated in this project regarding the kinesthetic demonstration of manipulation tasks, e.g. by considering the switching between MPs over the prediction horizon of the MPC. A further focus lies on the automatic generation of the MP sequence from the repeated demonstration of the manipulation task without requiring additional expert knowledge. Based on the demonstration, the manipulation task will be iteratively refined by learning the setpoints and the transition conditions of the MPs and finally by optimizing the overall manipulation task.

  • Robust control of modular multi-level converters

    (Third Party Funds Single)

    Term: 16. June 2021 - 31. December 2024
    Funding source: Industrie
  • Bewegungsplanung für Fahrsimulatoren

    (Third Party Funds Single)

    Term: 1. January 2021 - 30. June 2021
    Funding source: Industrie
  • Thermische Umrichtermodellierung für elektrische Antriebssysteme

    (Third Party Funds Single)

    Term: 1. August 2020 - 31. July 2023
    Funding source: Industrie
  • Regelung des Antriebsstrangs beim Kaltwalzen

    (Third Party Funds Single)

    Term: 1. July 2020 - 31. August 2023
    Funding source: Industrie
  • Automated path planning for truck-trailer configurations

    (Third Party Funds Single)

    Term: 1. September 2019 - 31. August 2022
    Funding source: Industrie
  • Modulare und hierarchische Ansätze für die Regelung nebenläufiger zeitbewerteter ereignisdiskreter Systeme

    (Third Party Funds Single)

    Term: 15. July 2019 - 14. July 2022
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)

    Neue Technologien haben zur Entwicklung von Systemen geführt, die weitgehend autonom agieren und typischerweise aus einer Vielzahl vernetzter Komponenten bestehen. Die Komplexität solcher Systeme erfordert neuartige Ansätze zur Modellierung und Reglersynthese, um die gewünschte Funktionalität zu garantieren. Ereignisdiskrete Systeme (discrete-event systems, DES) sind Modelle, deren Dynamik durch das Auftreten asynchroner Ereignisse charakterisiert wird. Solche Modelle eignen sich für viele "man made Systems", wie beispielsweise automatisierte Transportvorrichtungen und flexible Fertigungsanlagen. Die Modellierung ereignisdiskreter Systeme erfolgt mit aus der Informatik bekannten Beschreibungsmitteln, wie etwa endlichen Automaten, formalen Sprachen oder Petri-Netzen. Zur Reglersyn these hat sich die sog. "supervisory control theory" etabliert, bei der der Regler bzw. supervisor aus vergangenen Ereignissen ableitet, welche Ereignisse aktuell unterbunden werden müssen, um einen wunschgemäßen Ablauf des geregelten Systems zu gewährleisten. Eine zentrale Herausforderung ist hierbei die in der Komponentenzahl exponentiell wachsende Zahl von Zuständen des Gesamtsystems. Dieser begegnet man durch modulare oder hierarchische Ansätze, die das explizite Erstellen eines Gesamtmodells umgehen. In ihrer Grundform beschreiben ereignisdiskrete Systeme nur die Reihenfolge der Abfolge von Ereignissen. Dies reicht aus, um Regler zu entwerfen, die einen sicheren und zielführenden Betrieb des geregelten Systems garantieren. In vielen Anwendungen spielt aber neben Sicherheit auch Performanz eine Rolle. Letztere bezieht sich i.A. nicht nur auf die Reihenfolge sondern auch auf die Zeitpunkte, zu denen Ereignisse auftreten. Dazu bietet die Literatur eine Auswahl von Modellformen, die sich hinsichtlich ihrer Ausdrucksstärke deutlich unterscheiden. Am unteren Ende rangieren Ansätze nach Brandin/Wonham, bei denen das Verstreichen von Zeit durch das globale Ereignis "tick" abgebildet wird, sowie sog. zeitbewertete Ereignisgraphen (timed event graphs, TEGs), deren Verhalten sich als Lösungen linearer (max,+)- Gleichungen darstellen lässt. Für beide Ansätze ist die Reglersynthese gut erforscht. Allerdings wird die hier verfügbare Ausdrucksstärke vielen Anwendungen nicht gerecht: Modelliert man nach Brandin-Wonham, so lassen sich nebenläufige Prozesse, die mehrere unabhängige Echtzeituhren erfordern, nicht darstellen; verwendet man zeitbewertete Ereignisgraphen, so können logische Verzweigungen nicht dargestellt werden. In diesem Projekt wollen wir effiziente Methoden zur ereignisdiskreten Regelung für Modellformen untersuchen, die in ihrer Ausdrucksstärke über die beiden genannten Ansätze deutlich hinaus gehen. Wir streben insbesondere an, mit Hilfe modularer und hierarchischer Methoden für sog. (max,+)-Automaten und ausgewählt strukturierte Petri-Netze Regler zu entwerfen, die gegebene Anforderungen hinsichtlich Korrektheit und Performanz garantieren.

  • Agent-based systems for intelligent and robust control of complex energy systems in non-residential buildings as part of a superordinate energy system

    (Third Party Funds Group – Sub project)

    Overall project: Agentensysteme zur intelligenten und robusten Steuerung komplexer Energiesysteme in Nichtwohngebäuden als Bestandteil des übergeordneten Energiesystems
    Term: 1. May 2019 - 30. April 2022
    Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)
  • Formale Verifikation in der Fertigungsautomatisierung (Projektabschnitt B1)

    (Third Party Funds Single)

    Term: 15. April 2019 - 14. April 2020
    Funding source: Siemens AG
  • Compliance for a robotic assistance system

    (Third Party Funds Single)

    Term: 1. April 2019 - 30. September 2022
    Funding source: Industrie
  • Modular distributed model predictive control of nonlinear systems with neighborhood models

    (Third Party Funds Single)

    Term: 1. April 2019 - 31. December 2020
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)

    The steadily growing demands on efficiency and flexibility of modern automation and control systems requires a broader design approach for the overall system that goes beyond the isolated look at and control of single subsystems. Decentral and distributed control schemes follow this holistic design approach by including the interdependencies between the subsystems in the control design.

    Model predictive control (MPC) appears to be a suitable control approach to tackle these kind of systems. In essence, MPC relies on the numerical solution of a finite-horizon dynamic optimization problem that is repetitively solved according to the sampling rate of the system. An extension of MPC to coupled systems is distributed MPC (DMPC), which assigns a single communicating MPC agent to each subsystem. 

    The goal of the project is to develop a DMPC scheme for nonlinear coupled systems, where each MPC agent contains a neighborhood model that anticipates the dynamical behavior of its neighbors in order to enhance the convergence and robustness of the distributed algorithm. Besides the development and mathematical investigation of the methodology, a further goal of the project is the numerical and experimental realization of the control approach. A particular intention of the project is to develop a modular framework that allows for an easy configuration and adaptation of the coupling structure for suitable system classes. 

  • Trajectory planning for off-road applications

    (Third Party Funds Single)

    Term: 1. April 2019 - 31. October 2021
    Funding source: Industrie
  • Formale Verifikation in der Fertigungsautomatisierung (Projektabschnitt A)

    (Third Party Funds Single)

    Term: 15. April 2018 - 14. April 2019
    Funding source: Siemens AG
  • Fehlerdiagnose verteilt-parametrischer Systeme mittels Modulationsfunktionen

    (Third Party Funds Single)

    Term: 1. April 2018 - 31. March 2021
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
  • Quality-aware Co-Design of Responsive Real-Time Control Systems

    (Own Funds)

    Term: 1. September 2015 - 30. September 2021

    A key design goal of safety-critical control systems is the verifiable compliance with a specific quality objective in the sense of the quality of control. Corresponding to these requirements, the underlying real- time operating system has to provide resources and a certain quality of service. However, the relationship between real-time performance and quality of control is nontrivial: First of all, execution load varies considerably with environmental situation and disturbance. Vice versa, the actual execution conditions also have a qualitative influence on the control performance. Typically, substantial overestimations, in particular of the worst-case execution times, have to be made to ensure compliance with the aspired quality of control. This ultimately leads to a significant over-dimension of resources, with the degree disproportionately increasing with the complexity and dynamics of the control system under consideration. Consequently, it is to be expected that pessimistic design patterns and analysis techniques commonly used to date will no longer be viable in the future. Examples of this are complex, adaptive and mixed-critical assistance and autopilot functions in vehicles, where universal guarantees for all driving and environmental conditions are neither useful nor realistic. The issues outlined above can only be solved by an interdisciplinary approach to real-time control systems. This research project emanates from existing knowledge about the design of real-time control systems with soft, firm and hard timing guarantees. The basic assumption is that the control application's performance requirement varies significantly between typical and maximum disturbance and leads to situation-dependent reserves, correspondingly. Consequently, the commonly used pessimistic design and analysis of real-time systems that disregards quality-of- control dynamics is scrutinized. The research objective is the avoidance of pessimism in the design of hard real-time systems for control applications with strict guarantees and thus the resolution of the trade-off between quality-of-control guarantees and good average performance. This proposal pursues a co-design of control application and real-time executive and consists of the following three key aspects: model-based quality-of-control assessment, adaptive and predictive scheduling of control activities, and a hybrid execution model to regain guarantees.

  • Systematischer Entwurf hierarchisch-hybrider Regler

    (Third Party Funds Group – Sub project)

    Overall project: FOR 468: Methods from discrete mathematics for the synthesis and control of chemical processes
    Term: 1. January 2006 - 30. January 2011
    Funding source: DFG / Forschergruppe (FOR)

    Ziel des beschriebenen Forschungsvorhabens ist die Weiterentwicklung eines in der ersten Antragsphase untersuchten Verfahrens zum hierarchischen Entwurf hybrider Regelsysteme. Das genannte Verfahren ermöglicht es, sowohl ingenieurwissenschaftliche Intuition und regelungstechnische Standardverfahren als auch moderne Methoden der diskreten Optimierung auf sichere Weise in einen formalen Entwurfsvorgang einzubinden. Es trägt so zur Beherrschbarkeit der hybriden Regelproblemen innewohnenden Komplexität bei und wurde in der ersten Antragsphase erfolgreich auf eine Mehrprodukt-Batchanlage angewandt. Um das Verfahren zu einer praxistauglichen Entwurfsmethode zu machen, sind eine Reihe von methodischen Weiterentwicklungen notwendig. Diese betreffen strukturelle Fragen hinsichtlich der hierarchischen Reglerarchitektur, Fragen der effizienten Berechnung diskreter Abstraktionen durch sichere Abschätzung erreichbarer Zustandsmengen sowie algorithmische Fragen beim Entwurf ereignisdiskreter Reglerebenen. Die praktische Anwendbarkeit des resultierenden hierarchischen Entwurfsverfahrens soll anhand eines strukturvariablen chromatographischen Trennprozesses nachgewiesen werden.

Control & Optimization

Regelung und Optimierung

One research focus of the Chair of Automatic Control is on the development of nonlinear and (model) predictive control schemes as well as path/trajectory planning for dynamical systems. An important aspect in this regard are real-time feasible algorithms and their embedded hardware implementation for highly dynamical applications.


Prof. Dr.-Ing. Knut Graichen
Tel.: +49 9131 85-27127
E-Mail | Homepage

Model predictive control

Model predictive control (MPC) is a modern control scheme that is particularly suitable for nonlinear systems (NMPC) with multiple control inputs and state/control constraints (e.g. actuator limits, security constraints, etc.). The main research focus at the institute is on the development of highly efficient and real-time feasible MPC schemes as well as the hardware portability of the corresponding algorithms, e.g. for dSPACE, PLC and ECU hardware. Besides the methodological research and algorithmic development, the application of these real-time MPC schemes on different mechatronic systems is subject of various industrial research projects.

The computational efficiency of the (nonlinear) MPC schemes is achieved by tailored suboptimal/real-time implementations that are based on the approximate solution of the underlying dynamic optimization problem with incremental refinement.

Part of the research was implemented within the open-source toolbox GRAMPC that implements an efficient (projected) gradient method with adaptive line search. GRAMPC allows for a convenient setup, tuning and utilization of the MPC scheme for highly dynamical systems with sampling times in the (sub)millisecond range or high-dimensional systems. GRAMPC contains an additional interface (GUI) to MATLAB/Simulink.

Current research extends the existing results to stochastic nonlinear systems (stochastic NMPC) as well as to modular, networked systems.


  • Real-time NMPC-Toolbox GRAMPC: Link
MPC: Moving horizon optimization
Stochastic NMPC for collision avoidance with a probability of 99,9%

Real-time embedded optimization

Complex systems or highly dynamical systems such as mechatronic systems with sampling times in the (sub)millisecond range pose significant challenges for the real-time feasibility of optimization based methods, in particular in the presence of constraints. Focus at the institute therefore concerns memory and computation time efficient algorithms for online optimization and model predictive control that are suitable for hardware implementation with limited resources (embedded design).

The interfacing to standard soft- and hardware allows for a straightforward integration and simulation under Matlab/Simulink as well as the direct implementation on real-time hardware (e.g. dSPACE). The methods are used for efficient implementation on PLC and ECU level within several industrial projects and cooperations.


  • Real-time NMPC of a magnetic levitation system: Video
  • Interactive Java applet for NMPC of an overhead crane with state/control constraints: Java-Applet
  • PLC implementation of NMPC for an overhead crane (lab scale): Video
Connection to standard software
Embedded NMPC design on PLC

Nonlinear control methods

Besides the classical control task of stabilizing set points, the design of tracking controllers is of importance when the exact tracking of reference trajectories or set point changes are required. Typical examples are position changes in robotics (point-to-point control) or start-up and load changes in process engineering. In this regard, the research focus at the institute is on the development of nonlinear feedforward and feedback control schemes for nonlinear systems as well as for distributed/modular systems.

Feedforward controllers are often used in control engineering to realize transitions between set points or to track desired trajectories. Research in this field concerns inversion- and flatness-based methods for nonlinear systems as well as the design of optimal feedforward controllers.

A further research focus is on nonlinear control schemes, for instance, in the context of two-degrees-of-freedom (2dof) control schemes that are often employed in control engineering applications in order to separately design the tracking performance and robustness.


  • Control of a bionic kangaroo: Link
  • Trajectory planning for multiphysics systems: Link
Feedforward control scheme
Two-degrees-of-freedom control scheme
2dof control of a bionic kangaroo

Distributed systems & DMPC

A focus of research is on modular, distributed systems, which are composed by a large number of physically coupled subsystems. An example for this kind of systems is a smart grid. Distributed algorithms are predestinated to control high-scaled distributed systems. A popular way is to adapt model predictive controllers (MPC) for distributed systems. In this case, they are called distributed model predictive controllers (DMPC). The research in the environment of DMPC has several fields for research. One is the development of efficient algorithms, which ensure optimal behavior based on shared information and the investigation of stability guarantees for the controlled system by using decomposition schemes and parallel computation. Another field of research focuses on the consideration of the physical coupling between the subsystems. If information about the dynamical behavior of the neighbor of an agent is given, it can be considered in the optimization algorithm. As the considered system is both compley in dynamics and high-scaled, the implementation of controlling algorithms is challenging. To solve this issue, a framework is developed at the chair of automatic control, which uses the modularity of the network for a clear and simple usage. If the network is changing, the framework is able to automatically adapt its algorithm. This framework is used for the controlling of a scalable spring-mass system. The masses represent agents. Each of the agents are fully actuated and the size of the network is varied for the first simulation example. The simulation result for 100 agents is presented in the following video.

It is numerically shown, that the computational effort for each agent is mostly independent of the number of agents. This shows the predestination of the used algorithm for high-scaled distributed systems. Only the outer agents are actuated for another simulation example. As the agents are not able to directly control their neighbors, the controlling task can only be solved with the usage of communication. This task can be solved by using DMPC as well. The simulation result can be seen in the following video.

The software framework GRAMPC-D has been used to control the robots of the Robotarium¹ for the sake of an experimental validation. At first, a distribution problem was considered, whereby the robots have to maximize their distance. The second scenario evaluated a formation control problem. The robots form the letter “G”. The last scenario considered a platooning scenario whereby the first robot drives to desired positions while the others are following. Thereby, the last robot of the platoon was plugged out and plugged in again.

¹ S.Wilson et al., “The Robotarium: Globally Impactful Opportunities, Challenges, and Lessons Learned in Remote-Access, Distributed Control of Multirobot Systems,” in IEEE Control Systems Magazine, vol. 40, no. 1, pp. 26-44, Feb. 2020.

Distributed system of physically coupled agents.
Distributed algorithms have big advantages for high-sicaled systems considering the computational effort.  It is shown here for a simulation example of a spring-mass system.



Discrete Event Systems

Ereignisdiskrete Systeme

The research group FGDES develops methods for the analysis and sythnesis of discrete-event systems with a particular focus on modular and/or hierarchical architectures.  Here, discrete-event systems are dynamical systems with a finite-range state variable. Prototypical application domains are so called “men made systems”, e.g., for automated manufacturing or logistics, which by construction can be adequately represented by discrete-event models.


Prof. Dr.-Ing. Thomas Moor
Tel.: +49 9131 85-27129
E-Mail | FGDES Homepage


How to generate a PLC-program that operates the plant?

The laboratory model on the right represents a flexible manufacturing system. It consists of 29 interacting electro-mechanical components (conveyor belts, pusher, stack-feeder etc.), equipped with 25 actuators (DC-motors) and 57 sensors (key-switches, inductive sensors). The traditional engineering solution to operate the manufacturing system is to program a logic controller (PLC) such that it activates the appropriate motors in reaction on sensor events. This approach crucially relies on the programmer, who must consider any possible configuration of the system. While methods from software engineering assist the programmer and increase productivity, the process by principle remains error prone and unsafe.

Control Theory for Discrete Event Systems!

The manufacturing system can be formally modelled as a discrete-event system (DES). In contrast to continuous states and continuous time used in physically motivated models, discrete-event systems are characterized by discrete and qualitative changes of (symbolic) state values caused by the occurrence of asynchronous discrete events. In the context of our example, the control theoretic perspective on this system class is of a particular interest: given the formal model of the manufacturing system (plant dynamics) and the desired behaviour (formal specification), how can one systematically derive the required PLC program (controller dynamics) that makes ends meet?

Supervisory control theory (SCT) is a framework that provides an answer to the above question, first proposed by P.J. Ramadge and W.M. Wonham in the late 1980s. Since then, many researchers have contributed, including our group, with a particular focus on hierarchical, decentralized and/or modular control system architectures. At the time of writing, the required controller dynamics for systems of the complexity as our laboratory model can be synthesised easily by methods from supervisory control theory. Ongoing projects address the integration of synthesis algorithms with the work-flow of PLC programming, open questions related to fault detection and diagnosis, as well as network implementations of distributed supervision.

Further Directions

The  research group FGDES provides the software tools  libFAUDES, DESTool, CompileDES and FlexFact, as well asselected Publikationen via the FGDES homepage.


The research at the Chair of Automatic Control focuses on the methodological development and practical applicability of modern control-oriented methods. The research domains thereby can be divided into control and optimization and discrete event systems. An expertise of the chair is to transfer research into practice in various application domains.

Control & Optimization

Regelung und Optimierung
One research focus at the Chair of Automatic Control is on the development and application of nonlinear and (model) predictive control schemes for nonlinear systems. An important aspect in this regard is the applicability of these methods and the corresponding development of real-time feasible algorithms especially for highly dynamical systems and embedded hardware implementations.

Learning in Control

Lernende Verfahren

Algorithms of artificial intelligence and machine learning are of increasing importance for control engineering. At the Chair of Automatic Control, research is mainly directed towards the extension of control methods by learning components.

Discrete Event Systems

Ereignisdiskrete Systeme

The research group FGDES develops methods for the analysis and sythnesis of discrete-event systems with a particular focus on modular and/or hierarchical control architectures. Here, discrete-event systems are dynamical systems with a finite-range state variable. Prototypical application domains are so called “men made systems”, e.g., for automated manufacturing or logistics, which by construction can be adequately represented by discrete-event models.


Robotics belongs to the largest fields of application for control engineering methods. Besides conventional industrial robots, as known from the automobile production, there is an increasing usage of collaborative and mobile robots, for example as vacuum cleaners or autonomous vehicles. Research projects in this area concern the control of movements and forces on the one hand and the planning of paths and trajectories on the other.

Mechatronics & Automotive

Mechatronik und Automotive

Mechatronic systems, which comprise both mechanical and electrical parts, represent an important application field of control engineering. Due to the limited computing power of the used ECUs, the application of modern control methods in these systems is associated with particular challenges. The Chair of Automatic Control researches control methods for, for example, electric drives, automatic transmissions and vehicles.

Projects & Publications

Der Lehrstuhl bearbeitet Forschungsprojekte in Kooperation mit namhaften Industriepartnern und öffentlichen Geldgebern wie beispielsweise der Deutschen Forschungsgemeinschaft (DFG). Eine Übersicht über laufende und abgeschlossene Projekte finden Sie in diesem Bereich.
Der Lehrstuhl veröffentlicht Publikationen in renommierten internationalen Konferenzen und Journale. Eine Liste der am Lehrstuhl entstandenen Publikationen finden Sie hier.