Finding rigorous and efficient ways to integrate data into control theory has been a problem of great interest for many decades. Since most of the classical contributions in control theory rely on model knowledge, the problem of finding such a model from measured data, i.e., system identification, has become a mature research field. More recently, learning controllers directly from data has received increasing interest, but theoretical guarantees have rarely been addressed. Our research aims at developing modelfree system analysis and control methods, which are only based on measured data. One approach towards this goal is to extract controltheoretic system properties such as dissipativity or nonlinearity measures from data, which can then be used to design controllers via standard methods from the literature. Moreover, we develop controller design methods such as H_{∞}controllers or model predictive control approaches, based directly on measured data.
With the rising amount of data, there has been an increasing interest in what is referred to as datadriven controller design. One complementary approach to this direct controller design from data is to learn and analyze certain dissipation inequalities from data first since they allow for the direct application of wellknown feedback theorems for controller design. Hence, by learning such systemtheoretic inputoutput properties from data, we obtain insights to the apriori unknown system, we are not bound to a certain controller structure beforehand while still providing control theoretic guarantees for the closedloop behavior. Therefore, in this research direction, we study methods to determine dissipation inequalities of the underlying system from available inputoutput data in storage. This leads to, for example, computational methods for general nonlinear systems, and a necessary and sufficient condition from only one inputoutput data sample for linear timeinvariant systems.
Contact Persons: Anne Romer, Julian Berberich, Johannes Köhler, Frank Allgöwer
Selected Publications:
 J. M. Montenbruck and F. Allgöwer.
Some Problems Arising in Controller Design from Big Data via InputOutput Methods.
In Proc. of the 55th Conference on Decision and Control, Las Vegas, USA, 2016.  A. Romer, J. M. Montenbruck and F. Allgöwer.
Determining Dissipation Inequalities from InputOutput Samples.
In Proc. 20th IFAC World Congress, Toulouse, France, 2017.  Anne Romer, Julian Berberich, Johannes Köhler, Frank Allgöwer
Oneshot verification of dissipativity properties from inputoutput data.
IEEE Control Systems Letters, vol. 3, no. 3, 2019.
In this research direction, we seek to determine system properties of an unknown inputoutput system by iteratively conducting (numerical) experiments. In contrast to systems analysis from offline data as introduced above, we hence assume one can apply probing signals to a system and measures the corresponding output. Under this premise, we provide sampling schemes for which we obtain convergence guarantees towards the respective system property for linear timeinvariant systems. These sampling strategies to iteratively determine the operator gain, passivity measures and conicity of linear timeinvariant systems, for example, are based on gradient dynamical systems and saddle point flows, where the respective gradients can be computed from only inputoutput data.
Contact Persons: Anne Romer, Tim Martin, Frank Allgöwer
Selected Publications:
 Anne Romer, Jan Maximilian Montenbruck, Frank Allgöwer
Sampling strategies for datadriven inference of passivity properties.
In Proc. of the 56th IEEE Conference on Decision and Control, Melbourne, Australia, 2017.  Anne Romer, Jan Maximilian Montenbruck, Frank Allgöwer
Datadriven inference of conic relations via saddlepoint dynamics.
In Proc. 9th IFAC Symposium on Robust Control Design, Florianopolis, Brazil, 2018.
In control, linear models are preferable over nonlinear because of their simple structure and the wellinvestigated linear control theory. However, linear models are only valid for systems with mild nonlinear behaviour. Therefore, nonlinearity measures are introduced to quantify the nonlinearity of dynamical systems. These measures give an intuition whether a linear control design is valid. Implicit from the calculation of the nonlinearity measures, a best linear approximation of the nonlinear system behaviour is provided. Since the nonlinearity measures quantify the error of this approximation, results from robust control are applicable. Hence, this linear surrogate model might be preferable over a linear model by Jacobilinearization or by some approaches from linear system identification. Motivated by the connection of nonlinearity measure to conicity of dynamical systems, a characterization of stability for feedback interconnections using nonlinearity measures can be derived by the concept of graph separation and IQC analysis. By obtaining guaranteed bounds for nonlinearity measures from inputoutput samples of a system and the characterization of closedloop stability, nonlinearity measures can be used as a controltheoretic system property for datadriven system analysis and control.
Contact Persons: Tim Martin, Frank Allgöwer
Selected Publications:
 T. Martin and F. Allgöwer.
Nonlinearity measures for datadriven system analysis and control.
In Proc. of the 58th IEEE Conference on Decision and Control, Nice, France, 2019.  T. Schweickhardt and F. Allgöwer
On Systems Gains, Nonlinearity measures: definition, computation and applications.
IEEE Transactions on Automatic Control, 10:113123, 2000.
Although system identification is a wellestablished research field, there are still only few methods which are computationally tractable and yield guarantees on the identification error from noisy data of finite length. This research project circumvents the system identification step by directly characterizing the closedloop behavior under state or outputfeedback, using only measured data. Our goal is to translate modelbased controller design methods to this datadriven framework, while retaining desirable guarantees for the closed loop.
Recently, we developed a purely datadriven parametrization of the closed loop under statefeedback, based on a single noisy openloop trajectory without any model knowledge. Using known results from robust control, this parametrization can be employed to design, e.g., datadriven H_{∞}controllers with endtoendguarantees for the closed loop, thus providing a promising alternative to sequential system identification and robust control. An important open problem is the extension of this approach to outputfeedback design problems, in particular for the case that no statemeasurements are available.
Contact Persons: Julian Berberich, Anne Romer, Frank Allgöwer
Selected Publications:
 J. Berberich, A. Romer, C. W. Scherer, F. Allgöwer
Robust datadriven statefeedback design
American Control Conference, 2020, submitted. [preprint]
Cooperations:
 Carsten W. Scherer, University of Stuttgart, Germany
Model predictive control (MPC) is a powerful control method, which can handle nonlinear systems and constraints. For the implementation of MPC, an accurate model of the plant is required. In this project, we developed an MPC approach, which uses only measured inputoutput data to control an unknown system, without identifying a model. This novel framework for datadriven MPC relies on behavioral system theory, which provides an implicit system description based on past measured data. It is appealing both in terms of theoretical properties as well as practical aspects. The main advantage over existing adaptive or learningbased methods is that it requires only an initially measured, persistently exciting data trajectory as well as an upper bound on the system order, but no (setbased) model description and no online estimation process.
Since neither a model nor statemeasurements of the system are available, the analysis of this MPC is challenging. Using terminal equality constraints, we proved stability and robustness of the closed loop, also in the case of noisy output measurements. Currently, we are investigating several open research directions, which include less conservative stability conditions, extensions to nonlinear systems, as well as practical aspects.
Contact Persons: Julian Berberich, Johannes Köhler, Frank Allgöwer
Selected Publications:

J. Berberich, J. Köhler, M. A. Müller, F. Allgöwer.
Datadriven tracking MPC for changing setpoints
IFAC World Congress, 2020, submitted. [preprint] 
J. Berberich, F. Allgöwer
A trajectorybased framework for datadriven system analysis and control
European Control Conference, 2020, submitted. [preprint]  J. Berberich, J. Köhler, M. A. Müller, F. Allgöwer
Datadriven model predictive control with stability and robustness guarantees
Transactions on Automatic Control, 2019, submitted. [preprint]
Cooperations:
 Matthias A. Müller, Leibniz University Hannover, Germany