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Dr. Andreas Rauh
ENSTA Bretagne, Lab-STICC, 29806 Brest, France

Basic Info


Research Keywords & Expertise

0 Optimization
0 Robust Control
0 State Estimation
0 interval analysis
0 Stochastic filtering techniques

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Optimization
Robust Control
State Estimation
interval analysis

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Short Biography

Andreas Rauh was born in Munich, Germany, on March 25, 1977. He received his diploma degree in electrical engineering and information technology from the Technische Universität München, Munich, Germany, in 2001, his PhD degree (Dr.-Ing.) from the University of Ulm, Germany, in 2008, and his habilitation (Dr.-Ing. habil.) in Measurement Technology and Automatic Control from the University of Rostock, Germany, in 2017. He has published more than 160 articles and chapters in edited books, international conferences and peer-reviewed journals with a focus on modeling, control, as well as state and parameter estimation for systems with stochastic and set-valued uncertainty. Since 2008 he has been a member of the IEEE 1788 Working Group for the Standardization of Interval Arithmetic.

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Journal article
Published: 07 July 2021 in Algorithms
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Most research activities that utilize linear matrix inequality (LMI) techniques are based on the assumption that the separation principle of control and observer synthesis holds. This principle states that the combination of separately designed linear state feedback controllers and linear state observers, which are independently proven to be stable, results in overall stable system dynamics. However, even for linear systems, this property does not necessarily hold if polytopic parameter uncertainty and stochastic noise influence the system’s state and output equations. In this case, the control and observer design needs to be performed simultaneously to guarantee stabilization. However, the loss of the validity of the separation principle leads to nonlinear matrix inequalities instead of LMIs. For those nonlinear inequalities, the current paper proposes an iterative LMI solution procedure. If this algorithm produces a feasible solution, the resulting controller and observer gains ensure robust stability of the closed-loop control system for all possible parameter values. In addition, the proposed optimization criterion leads to a minimization of the sensitivity to stochastic noise so that the actual state trajectories converge as closely as possible to the desired operating point. The efficiency of the proposed solution approach is demonstrated by stabilizing the Zeeman catastrophe machine along the unstable branch of its bifurcation diagram. Additionally, an observer-based tracking control task is embedded into an iterative learning-type control framework.

ACS Style

Andreas Rauh; Robert Dehnert; Swantje Romig; Sabine Lerch; Bernd Tibken. Iterative Solution of Linear Matrix Inequalities for the Combined Control and Observer Design of Systems with Polytopic Parameter Uncertainty and Stochastic Noise. Algorithms 2021, 14, 205 .

AMA Style

Andreas Rauh, Robert Dehnert, Swantje Romig, Sabine Lerch, Bernd Tibken. Iterative Solution of Linear Matrix Inequalities for the Combined Control and Observer Design of Systems with Polytopic Parameter Uncertainty and Stochastic Noise. Algorithms. 2021; 14 (7):205.

Chicago/Turabian Style

Andreas Rauh; Robert Dehnert; Swantje Romig; Sabine Lerch; Bernd Tibken. 2021. "Iterative Solution of Linear Matrix Inequalities for the Combined Control and Observer Design of Systems with Polytopic Parameter Uncertainty and Stochastic Noise." Algorithms 14, no. 7: 205.

Journal article
Published: 10 May 2021 in Axioms
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When modeling real-life applications, uncertainty appears in the form of, for example, modeling approximations, measurement errors, or simply physical restrictions. Those uncertainties can either be treated as stochastic or as bounded, with known limits in the form of intervals. The latter is considered in this paper for a real-life application in the form of an electrical circuit. This is reasonable because the electrical circuit is subject to uncertainties, mainly due to circuit element tolerances and variable load conditions. Since conservative worst-case limits for such parameters are commonly known, interval methods can be applied. The aim of this paper is to demonstrate a possible overall handling of the given uncertain system. Firstly, this includes a control and a reliable computation of the states’ interval enclosures. On the one hand, this can be used to predict the system’s behavior, and on the other hand to verify the control numerically. Here, the implemented feedback control is based on linear matrix inequalities (LMIs) and the states are predicted using an interval enclosure technique based on cooperativity. Since the original system is not cooperative, a transformation is performed. Finally, an observer is implemented as a diagnosis tool regarding faulty measurements or component failures. Since adding a state-of-the-art observer would destroy this structure, a cooperativity-preserving method is applied. Overall, this paper combines methods from robust control design and interval-based evaluations, and presents a suitable observer technique to show the applicability of the presented methods.

ACS Style

Julia Kersten; Andreas Rauh; Harald Aschemann. Analyzing Uncertain Dynamical Systems after State-Space Transformations into Cooperative Form: Verification of Control and Fault Diagnosis. Axioms 2021, 10, 88 .

AMA Style

Julia Kersten, Andreas Rauh, Harald Aschemann. Analyzing Uncertain Dynamical Systems after State-Space Transformations into Cooperative Form: Verification of Control and Fault Diagnosis. Axioms. 2021; 10 (2):88.

Chicago/Turabian Style

Julia Kersten; Andreas Rauh; Harald Aschemann. 2021. "Analyzing Uncertain Dynamical Systems after State-Space Transformations into Cooperative Form: Verification of Control and Fault Diagnosis." Axioms 10, no. 2: 88.

Journal article
Published: 10 May 2021 in Sensors
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Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either H2 or H measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller—which was jointly optimized with a linear derivative estimator—with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

ACS Style

Andreas Rauh; Swantje Romig. Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty. Sensors 2021, 21, 3285 .

AMA Style

Andreas Rauh, Swantje Romig. Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty. Sensors. 2021; 21 (9):3285.

Chicago/Turabian Style

Andreas Rauh; Swantje Romig. 2021. "Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty." Sensors 21, no. 9: 3285.

Journal article
Published: 14 March 2021 in Algorithms
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Thick ellipsoids were recently introduced by the authors to represent uncertainty in state variables of dynamic systems, not only in terms of guaranteed outer bounds but also in terms of an inner enclosure that belongs to the true solution set with certainty. Because previous work has focused on the definition and computationally efficient implementation of arithmetic operations and extensions of nonlinear standard functions, where all arguments are replaced by thick ellipsoids, this paper introduces novel operators for specifically evaluating quasi-linear system models with bounded parameters as well as for the union and intersection of thick ellipsoids. These techniques are combined in such a way that a discrete-time state observer can be designed in a predictor-corrector framework. Estimation results are presented for a combined observer-based estimation of state variables as well as disturbance forces and torques in the sense of an unknown input estimator for a hovercraft.

ACS Style

Andreas Rauh; Auguste Bourgois; Luc Jaulin. Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design. Algorithms 2021, 14, 88 .

AMA Style

Andreas Rauh, Auguste Bourgois, Luc Jaulin. Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design. Algorithms. 2021; 14 (3):88.

Chicago/Turabian Style

Andreas Rauh; Auguste Bourgois; Luc Jaulin. 2021. "Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design." Algorithms 14, no. 3: 88.

Journal article
Published: 08 March 2021 in Algorithms
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Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.

ACS Style

Andreas Rauh; Julia Kersten. Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters. Algorithms 2021, 14, 85 .

AMA Style

Andreas Rauh, Julia Kersten. Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters. Algorithms. 2021; 14 (3):85.

Chicago/Turabian Style

Andreas Rauh; Julia Kersten. 2021. "Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters." Algorithms 14, no. 3: 85.

Journal article
Published: 01 March 2021 in Clean Technologies
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The electric power characteristic of solid oxide fuel cells (SOFCs) depends on numerous influencing factors. These are the mass flow of supplied hydrogen, the temperature distribution in the interior of the fuel cell stack, the temperatures of the supplied reaction media at the anode and cathode, and—most importantly—the electric current. Describing all of these dependencies by means of analytic system models is almost impossible. Therefore, it is reasonable to identify these dependencies by means of stochastic filter techniques. One possible option is the use of Kalman filters to find locally valid approximations of the power characteristics. These can then be employed for numerous online purposes of dynamically operated fuel cells such as maximum power point tracking or the maximization of the fuel efficiency. In the latter case, it has to be ensured that the fuel cell operation is restricted to the regime of Ohmic polarization. This aspect is crucial to avoid fuel starvation phenomena which may not only lead to an inefficient system operation but also to accelerated degradation. In this paper, a Kalman filter-based, real-time implementable optimization of the fuel efficiency is proposed for SOFCs which accounts for the aforementioned feasibility constraints. Essentially, the proposed strategy consists of two phases. First, the parameters of an approximation of the electric power characteristic are estimated. The measurable arguments of this function are the hydrogen mass flow and the electric stack current. In a second stage, these inputs are optimized so that a desired stack power is attained in an optimal way. Simulation results are presented which show the robustness of the proposed technique against inaccuracies in the a-priori knowledge about the power characteristics. For a numerical validation, three different models of the electric power characteristic are considered: (i) a static neural network input/output model, (ii) a first-order dynamic system representation and (iii) the combination of a static neural network model with a low-order fractional differential equation model representing transient phases during changes between different electric operating points.

ACS Style

Andreas Rauh. Kalman Filter-Based Real-Time Implementable Optimization of the Fuel Efficiency of Solid Oxide Fuel Cells. Clean Technologies 2021, 3, 206 -226.

AMA Style

Andreas Rauh. Kalman Filter-Based Real-Time Implementable Optimization of the Fuel Efficiency of Solid Oxide Fuel Cells. Clean Technologies. 2021; 3 (1):206-226.

Chicago/Turabian Style

Andreas Rauh. 2021. "Kalman Filter-Based Real-Time Implementable Optimization of the Fuel Efficiency of Solid Oxide Fuel Cells." Clean Technologies 3, no. 1: 206-226.

Journal article
Published: 21 February 2021 in Fractal and Fractional
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Verified simulation techniques have been investigated intensively by researchers who are dealing with ordinary and partial differential equations. Tasks that have been considered in this context are the solution to initial value problems and boundary value problems, parameter identification, as well as the solution of optimal control problems in cases in which bounded uncertainty in parameters and initial conditions are present. In contrast to system models with integer-order derivatives, fractional-order models have not yet gained the same attention if verified solution techniques are desired. In general, verified simulation techniques rely on interval methods, zonotopes, or Taylor model arithmetic and allow for computing guaranteed outer enclosures of the sets of solutions. As such, not only the influence of uncertain but bounded parameters can be accounted for in a guaranteed way. In addition, also round-off and (temporal) truncation errors that inevitably occur in numerical software implementations can be considered in a rigorous manner. This paper presents novel iterative and series-based solution approaches for the case of initial value problems to fractional-order system models, which will form the basic building block for implementing state estimation schemes in continuous-discrete settings, where the system dynamics is assumed as being continuous but measurements are only available at specific discrete sampling instants.

ACS Style

Andreas Rauh; Luc Jaulin. Novel Techniques for a Verified Simulation of Fractional-Order Differential Equations. Fractal and Fractional 2021, 5, 17 .

AMA Style

Andreas Rauh, Luc Jaulin. Novel Techniques for a Verified Simulation of Fractional-Order Differential Equations. Fractal and Fractional. 2021; 5 (1):17.

Chicago/Turabian Style

Andreas Rauh; Luc Jaulin. 2021. "Novel Techniques for a Verified Simulation of Fractional-Order Differential Equations." Fractal and Fractional 5, no. 1: 17.

Conference paper
Published: 11 January 2021 in Electronic Proceedings in Theoretical Computer Science
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ACS Style

Andreas Rauh; Julia Kersten. Verification and Reachability Analysis of Fractional-Order Differential Equations Using Interval Analysis. Electronic Proceedings in Theoretical Computer Science 2021, 331, 18 -32.

AMA Style

Andreas Rauh, Julia Kersten. Verification and Reachability Analysis of Fractional-Order Differential Equations Using Interval Analysis. Electronic Proceedings in Theoretical Computer Science. 2021; 331 ():18-32.

Chicago/Turabian Style

Andreas Rauh; Julia Kersten. 2021. "Verification and Reachability Analysis of Fractional-Order Differential Equations Using Interval Analysis." Electronic Proceedings in Theoretical Computer Science 331, no. : 18-32.

Journal article
Published: 22 October 2020 in Acta Cybernetica
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In many fields of engineering as well as computational physics, it is necessary to describe dynamic phenomena which are characterized by an infinitely long horizon of past state values. This infinite horizon of past data then influences the evolution of future state trajectories. Such phenomena can be characterized effectively by means of fractional-order differential equations. In contrast to classical linear ordinary differential equations linear fractional-order models have frequency domain characteristics with amplitude responses that deviate from the classical integer multiples of ±20 dB per frequency decade and, respectively, deviate from integer multiples of ±π/2 in the limit values of their corresponding phase response. Although numerous simulation approaches have been developed in recent years for the numerical evaluation of fractional-order models with point-valued initial conditions and parameters, the robustness analysis of such system representations is still a widely open area of research. This statement is especially true if interval uncertainty is considered with respect to initial states and parameters. Therefore, this paper summarizes the current state-of-the-art concerning the simulation-based analysis of fractional-order dynamics with a restriction to those approaches that can be extended to set-valued (interval) evaluations for models with bounded uncertainty. Especially, it is shown how verified simulation techniques for integer-order models with uncertain parameters can be extended toward fractional counterparts. Selected linear as well as nonlinear illustrating examples conclude this paper to visualize algorithmic properties of the suggested interval-based simulation methodology and point out directions of ongoing research.

ACS Style

Andreas Rauh; Julia Kersten. Toward the Development of Iteration Procedures for the Interval-Based Simulation of Fractional-Order Systems. Acta Cybernetica 2020, 25, 21 -48.

AMA Style

Andreas Rauh, Julia Kersten. Toward the Development of Iteration Procedures for the Interval-Based Simulation of Fractional-Order Systems. Acta Cybernetica. 2020; 25 (1):21-48.

Chicago/Turabian Style

Andreas Rauh; Julia Kersten. 2020. "Toward the Development of Iteration Procedures for the Interval-Based Simulation of Fractional-Order Systems." Acta Cybernetica 25, no. 1: 21-48.

Journal article
Published: 07 April 2020 in IEEE Transactions on Control Systems Technology
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This article develops an iterative learning control (ILC) design for a class of multiple-input-multiple-output systems where a distributed heating system is used as a particular example to experimentally validate the design. The class of systems considered is described by a parabolic partial differential equation, which, for control design, is approximated by a finite-dimensional state-space model obtained by applying the method of integro-differential relations combined with a projection approach. In some cases, including the distributed heating system, this approximation may result in a nonminimum phase system and, hence, pose an additional design challenge. In this work, the ILC law is computed in the frequency domain by solving a convex optimization problem, and its performance is evaluated in both simulation and experiment.

ACS Style

Slawomir Mandra; Krzysztof Galkowski; Andreas Rauh; Harald Aschemann; Eric Rogers. Iterative Learning Control for a Class of Multivariable Distributed Systems With Experimental Validation. IEEE Transactions on Control Systems Technology 2020, 29, 949 -960.

AMA Style

Slawomir Mandra, Krzysztof Galkowski, Andreas Rauh, Harald Aschemann, Eric Rogers. Iterative Learning Control for a Class of Multivariable Distributed Systems With Experimental Validation. IEEE Transactions on Control Systems Technology. 2020; 29 (3):949-960.

Chicago/Turabian Style

Slawomir Mandra; Krzysztof Galkowski; Andreas Rauh; Harald Aschemann; Eric Rogers. 2020. "Iterative Learning Control for a Class of Multivariable Distributed Systems With Experimental Validation." IEEE Transactions on Control Systems Technology 29, no. 3: 949-960.

Journal article
Published: 25 March 2020 in Algorithms
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Solid oxide fuel cell systems such as those presented in this paper are not only applicable for a pure supply with electric energy, they can typically also be used in decentralized power stations, i.e., as micro-cogeneration systems for houses, where both electric and thermal energy are required. For that application, obviously, the electric power need is not constant but rather changes over time. In such a way, it essentially depends on the user profiles of said houses which can refer to e.g., private households as well as offices. The power use is furthermore not predefined. For an optimal operation of the fuel cell, we want to adjust the power, to match the need with sufficiently small time constants without the implementation of mid- or long-term electrical storage systems such as battery buffers. To adapt the produced electric power a simple, however, sufficiently robust feedback controller regulating the hydrogen mass flow into the cells is necessary. To achieve this goal, four different controllers, namely, a PI output-feedback controller combined with a feedforward control, an internal model control (IMC) approach, a sliding-mode (SM) controller and a state-feedback controller, are developed and compared in this paper. As the challenge is to find a controller ensuring steady-state accuracy and good tracking behavior despite the nonlinearities and uncertainties of the plant, the comparison was done regarding these requirements. Simulations and experiments show that the IMC outperforms the alternatives with respect to steady-state accuracy and tracking behavior.

ACS Style

Wiebke Frenkel; Andreas Rauh; Julia Kersten; Harald Aschemann. Experiments-Based Comparison of Different Power Controllers for a Solid Oxide Fuel Cell Against Model Imperfections and Delay Phenomena. Algorithms 2020, 13, 76 .

AMA Style

Wiebke Frenkel, Andreas Rauh, Julia Kersten, Harald Aschemann. Experiments-Based Comparison of Different Power Controllers for a Solid Oxide Fuel Cell Against Model Imperfections and Delay Phenomena. Algorithms. 2020; 13 (4):76.

Chicago/Turabian Style

Wiebke Frenkel; Andreas Rauh; Julia Kersten; Harald Aschemann. 2020. "Experiments-Based Comparison of Different Power Controllers for a Solid Oxide Fuel Cell Against Model Imperfections and Delay Phenomena." Algorithms 13, no. 4: 76.

Journal article
Published: 19 March 2020 in Acta Cybernetica
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One of the most important advantages of interval observers is their capability to provide estimates for a given dynamic system model in terms of guaranteed state bounds which are compatible with measured data that are subject to bounded uncertainty. However, the inevitable requirement for being able to produce such verified bounds is the knowledge about a dynamic system model in which possible uncertainties and inaccuracies are themselves represented by guaranteed bounds. For that reason, classical point-valued parameter identification schemes are often not sufficient or should, at least, be handled with sufficient care if safety critical applications are of interest. This paper provides an application-oriented description of the major steps leading from a control-oriented system model with an associated verified parameter identification to a verified design of interval observers which provide the basis for the development and implementation of cooperativity-preserving feedback controllers. The corresponding computational steps are described and visualized for the temperature control of a laboratory-scale test rig available at the Chair of Mechatronics at the University of Rostock.

ACS Style

Andreas Rauh; Julia Kersten. From Verified Parameter Identification to the Design of Interval Observers and Cooperativity-Preserving Controllers. Acta Cybernetica 2020, 24, 509 -537.

AMA Style

Andreas Rauh, Julia Kersten. From Verified Parameter Identification to the Design of Interval Observers and Cooperativity-Preserving Controllers. Acta Cybernetica. 2020; 24 (3):509-537.

Chicago/Turabian Style

Andreas Rauh; Julia Kersten. 2020. "From Verified Parameter Identification to the Design of Interval Observers and Cooperativity-Preserving Controllers." Acta Cybernetica 24, no. 3: 509-537.

Journal article
Published: 18 March 2020 in Acta Cybernetica
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In real-life applications, dynamic systems are often subject to uncertainty due to model simplifications, measurement inaccuracy or approximation errors which can be mapped to specific parameters. Uncertainty in dynamic systems can come either in stochastic forms or as interval representations, when they are considered as bounded as it will be done in this paper. The main idea, here, is to find a joint approach for an interval-based gain scheduling controller while simultaneously reducing overestimation by enclosing state intervals with the least amount of conservativity. The robust and/ or optimal control design is realized using linear matrix inequalities (LMIs) to find an efficient solution and aims at a guaranteed stabilization of the system dynamics over a predefined time horizon. Since the resulting system is assumed to be asymptotically stable, a temporal reduction of the widths of intervals representing worst-case bounds of the system states at a specific point of time should occur. However, for commonly used approaches in the computation of interval enclosures those interval widths seemingly blow up due to the wrapping effect in many cases. To avoid this, we provide two interval enclosure techniques --- an exploitation of cooperativity and an exponential approach --- and discuss their applicability taking into account two real-life applications, a high-bay rack feeder and an inverse pendulum.

ACS Style

Julia Kersten; Andreas Rauh; Harald Aschemann. Verified Interval Enclosure Techniques for Robust Gain Scheduling Controllers. Acta Cybernetica 2020, 24, 467 -491.

AMA Style

Julia Kersten, Andreas Rauh, Harald Aschemann. Verified Interval Enclosure Techniques for Robust Gain Scheduling Controllers. Acta Cybernetica. 2020; 24 (3):467-491.

Chicago/Turabian Style

Julia Kersten; Andreas Rauh; Harald Aschemann. 2020. "Verified Interval Enclosure Techniques for Robust Gain Scheduling Controllers." Acta Cybernetica 24, no. 3: 467-491.

Journal article
Published: 16 March 2020 in Acta Cybernetica
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The Summer Workshop on Interval Methods (SWIM) is an annual meeting initiated in 2008 by the French MEA working group on Set Computation and Interval Techniques of the French research group on Automatic Control. A special focus of the MEA group is on promoting interval analysis techniques and applications to a broader community of researchers, facilitated by such multidisciplinary workshops. Since 2008, SWIM has become a keystone event for researchers dealing with various aspects of interval and set-based methods. In 2018, the 11th edition in this workshop series was held at the University of Rostock, Germany, with a focus on research topics in the fields of engineering, computer science, and mathematics. A total of 31 talks were given during this workshop, covering the following areas: verified solution of initial value problems for ordinary differential equations, differential-algebraic system models, and partial differential equations, scientific computing with guaranteed error bounds, design of robust and fault-tolerant control systems, modeling and quantification of errors in engineering tasks, implementation of software libraries, and usage of the aforementioned approaches for system models in control engineering, data analysis, signal and image processing. After a peer-review process, 15 high-quality articles were selected for publication in this special issue. They are roughly divided into two thematic groups: Uncertainty Modeling, Software, Verified Computing and Optimization as well as Interval Methods in Control and Robotics. The first part, Uncertainty Modeling, Software, Verified Computing and Optimization, contains methodological aspects concerning reliable modeling of dynamic systems as well as visualization and quantification of uncertainty in the fields of measurement and simulation. Moreover, existence proofs for solutions of partial differential equations and their reliable optimal control synthesis are considered. A paper making use of quantifier elimination for robust linear output feedback control by means of eigenvalue placement concludes this section. The second part of this special issue, Interval Methods in Control and Robotics, is focused on the design as well as numerical and experimental validation of robust state observation and control procedures along with reliable parameter and state estimation approaches in the fields of control for thermal systems, robotics, localization of drones and global positioning systems.

ACS Style

Ekaterina Auer; Julia Kersten; Andreas Rauh. Preface. Acta Cybernetica 2020, 24, 265 -266.

AMA Style

Ekaterina Auer, Julia Kersten, Andreas Rauh. Preface. Acta Cybernetica. 2020; 24 (3):265-266.

Chicago/Turabian Style

Ekaterina Auer; Julia Kersten; Andreas Rauh. 2020. "Preface." Acta Cybernetica 24, no. 3: 265-266.

Journal article
Published: 16 March 2020 in Acta Cybernetica
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Magnet resonance imaging does not only have a large number of applications in the field of medical examinations. In addition, several promising applications were also reported for the measurement of technical fluid flows and for the measurement of temperature fields in technical devices which do not allow for a classical access by either arrays of flow meters on the one hand or by arrays of temperature sensors such as thermocouples on the other hand. Due to the fact that magnet resonance imaging can be performed in a non-invasive manner, it has the advantage to provide relevant data without disturbing the velocity and temperature fields by external sensor devices. Moreover, measurement information can also be obtained for scenarios in which a direct access to the media under investigation is hardly possible due to constructive limitations. To make this kind of measurement applicable also for dynamic scenarios, not only the spatial resolution but also the temporal one needs to be sufficiently accurate. If the temporal resolution is of interest, an acceleration of the measurement process becomes possible by compressed sensing techniques which make use of an undersampling of the so-called $k$-space. However, such compressed sensing approaches require a reconstruction of the original fields of the physical variables to be measured. In this paper, it is shown how interval arithmetic approaches can be employed to solve the necessary optimality criteria for the fluid velocity reconstruction under the assumption of bounded measurement errors.

ACS Style

Kristine John; Andreas Rauh; Martin Bruschewski; Sven Grundmann. Towards Analyzing the Influence of Measurement Errors in Magnetic Resonance Imaging of Fluid Flows. Acta Cybernetica 2020, 24, 343 -372.

AMA Style

Kristine John, Andreas Rauh, Martin Bruschewski, Sven Grundmann. Towards Analyzing the Influence of Measurement Errors in Magnetic Resonance Imaging of Fluid Flows. Acta Cybernetica. 2020; 24 (3):343-372.

Chicago/Turabian Style

Kristine John; Andreas Rauh; Martin Bruschewski; Sven Grundmann. 2020. "Towards Analyzing the Influence of Measurement Errors in Magnetic Resonance Imaging of Fluid Flows." Acta Cybernetica 24, no. 3: 343-372.

Journal article
Published: 02 March 2020 in Algorithms
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High-temperature fuel cells are one of the devices currently investigated for an integration into distributed power supply grids. Such distributed grids aim at the simultaneous production of thermal energy and electricity. To maximize the efficiency of fuel cell systems, it is reasonable to track the point of maximum electric power production and to operate the system in close vicinity to this point. However, variations of gas mass flows, especially the concentration of hydrogen contained in the anode gas, as well as variations of the internal temperature distribution in the fuel cell stack module lead to the fact that the maximum power point changes in dependence of the aforementioned phenomena. Therefore, this paper first proposes a real-time capable stochastic filter approach for the local identification of the electric power characteristic of the fuel cell. Second, based on this estimate, a maximum power point tracking procedure is derived. It is based on an iteration procedure under consideration of the estimation accuracy of the stochastic filter and adjusts the fuel cell’s electric current so that optimal operating points are guaranteed. Numerical simulations, based on real measured data gathered at a test rig available at the Chair of Mechatronics at the University of Rostock, Germany, conclude this paper.

ACS Style

Andreas Rauh; Wiebke Frenkel; Julia Kersten. Kalman Filter-Based Online Identification of the Electric Power Characteristic of Solid Oxide Fuel Cells Aiming at Maximum Power Point Tracking. Algorithms 2020, 13, 58 .

AMA Style

Andreas Rauh, Wiebke Frenkel, Julia Kersten. Kalman Filter-Based Online Identification of the Electric Power Characteristic of Solid Oxide Fuel Cells Aiming at Maximum Power Point Tracking. Algorithms. 2020; 13 (3):58.

Chicago/Turabian Style

Andreas Rauh; Wiebke Frenkel; Julia Kersten. 2020. "Kalman Filter-Based Online Identification of the Electric Power Characteristic of Solid Oxide Fuel Cells Aiming at Maximum Power Point Tracking." Algorithms 13, no. 3: 58.

Articles
Published: 04 January 2020 in International Journal of Control
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For simulations of dynamic systems with uncertain interval-valued initial states, it is possible to compute lower and upper bounds for the sets of possible state trajectories independently if the respective ordinary differential equations (ODEs) satisfy the structural property of cooperativity. Then, the domain of all reachable states is fully determined by the solutions of two decoupled initial value problems (IVPs). Each of these IVPs is characterized by point-valued initial conditions, where the simplest type of control signal of these ODEs is given as a purely time-dependent feedforward control sequence which is known a-priori. Especially for applications from the field of thermo-fluidic systems, such cooperative ODEs are obtained directly by means of first-principle modeling. The simulation task described before becomes more challenging if the IVPs are, furthermore, subject to uncertain parameters. The simplest subclass of such systems, to which this paper is restricted, are linear ODE models with interval uncertainty in the coefficients of both the system and input matrices. From the perspective of modeling, this class of systems firstly comprises state-space representations of dynamic processes with actually linear dynamics and imprecisely known physical parameters. Secondly, also nonlinear input-affine state-space representations can be accounted for by this class of systems if they are embedded into a linear polytopic uncertainty model which represents a conservative convex combination of extremal system realizations. To be able to forecast the range of reachable states without significant computational effort in the case that a closed-loop controller is applied to the system, it is reasonable to impose structural constraints on the respective gain matrices so that the observer-based closed-loop control system remains cooperative. Suitable design procedures based on linear matrix inequality techniques are derived in this paper. They are validated in simulations and experiments for a prototypical heat transfer process.

ACS Style

Andreas Rauh; Julia Kersten; Harald Aschemann. Interval and linear matrix inequality techniques for reliable control of linear continuous-time cooperative systems with applications to heat transfer. International Journal of Control 2020, 93, 2771 -2788.

AMA Style

Andreas Rauh, Julia Kersten, Harald Aschemann. Interval and linear matrix inequality techniques for reliable control of linear continuous-time cooperative systems with applications to heat transfer. International Journal of Control. 2020; 93 (11):2771-2788.

Chicago/Turabian Style

Andreas Rauh; Julia Kersten; Harald Aschemann. 2020. "Interval and linear matrix inequality techniques for reliable control of linear continuous-time cooperative systems with applications to heat transfer." International Journal of Control 93, no. 11: 2771-2788.

Journal article
Published: 01 January 2020 in IFAC-PapersOnLine
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Interval-based state estimation techniques represent promising approaches for the quantification of worst-case bounds of those sets of state variables that are reachable over a finitely long time horizon under the consideration of bounded uncertainty. In previous work, it has been shown that such estimation techniques cannot only be employed for the class of linear uncertain systems but also for nonlinear ones if they are reformulated in terms of quasi-linear state-space representations. However, naive polytopic uncertainty models may lead to quite conservative enclosures of the reachable states. Those, in turn, lead to conservative control strategies if the aforementioned interval enclosures are combined with strategies for the design of robust feedforward and feedback controllers. Therefore, this paper aims at the reduction of pessimism during interval-based state estimation by means of novel uncertainty models, relying on a parameter bounding approach that is implemented by means of a correlation analysis as well as a suitable principle axes transformation of the parameter space. The practical applicability of the proposed procedure is visualized for an experimentally validated thermal model of a solid oxide fuel cell stack, for which the computed interval bounds of reachable states represent a fundamental requirement for the design of a combined feedforward and feedback control allowing for preventing the violation of upper temperature limits in a guaranteed way.

ACS Style

Noël Cont; Wiebke Frenkel; Julia Kersten; Andreas Rauh; Harald Aschemann. Interval-Based Modeling of High-Temperature Fuel Cells for a Real-Time Control Implementation Under State Constraints. IFAC-PapersOnLine 2020, 53, 12542 -12547.

AMA Style

Noël Cont, Wiebke Frenkel, Julia Kersten, Andreas Rauh, Harald Aschemann. Interval-Based Modeling of High-Temperature Fuel Cells for a Real-Time Control Implementation Under State Constraints. IFAC-PapersOnLine. 2020; 53 (2):12542-12547.

Chicago/Turabian Style

Noël Cont; Wiebke Frenkel; Julia Kersten; Andreas Rauh; Harald Aschemann. 2020. "Interval-Based Modeling of High-Temperature Fuel Cells for a Real-Time Control Implementation Under State Constraints." IFAC-PapersOnLine 53, no. 2: 12542-12547.

Journal article
Published: 01 January 2020 in IFAC-PapersOnLine
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Interval observers have been investigated by many researchers during the last decade, especially for those classes of systems that can be described by finite-dimensional continuous-time ordinary differential equations, discrete-time difference equations, and sets of partial differential equations in which both, system parameters and external disturbances, may be subject to bounded uncertainty. In contrast to this, only preliminary investigations were performed for fractional-order models. Due to the fact that many electro-chemical processes such as the charging and discharging dynamics of batteries can be described in good accuracy by using fractional-order models, this paper focuses on the design and numerical validation of interval observers for such systems. Here, we present a cooperativity-enforcing observer structure leading directly to decoupled lower and upper bounding systems for the sets of reachable states. This is visualized by a battery model with interval uncertainty in the output equation.

ACS Style

Erik Hildebrandt; Julia Kersten; Andreas Rauh; Harald Aschemann. Robust Interval Observer Design for Fractional-Order Models with Applications to State Estimation of Batteries. IFAC-PapersOnLine 2020, 53, 3683 -3688.

AMA Style

Erik Hildebrandt, Julia Kersten, Andreas Rauh, Harald Aschemann. Robust Interval Observer Design for Fractional-Order Models with Applications to State Estimation of Batteries. IFAC-PapersOnLine. 2020; 53 (2):3683-3688.

Chicago/Turabian Style

Erik Hildebrandt; Julia Kersten; Andreas Rauh; Harald Aschemann. 2020. "Robust Interval Observer Design for Fractional-Order Models with Applications to State Estimation of Batteries." IFAC-PapersOnLine 53, no. 2: 3683-3688.

Journal article
Published: 01 January 2020 in IFAC-PapersOnLine
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A nonlinear model of heat transfer in a solid structure controlled by a Peltier element is considered. The thermoelectrical converter in between two cylindrical bodies regulates temperature distribution in one cylinder, while the other body is used as the thermal capacitor. An optimal control problem is stated to minimize heat losses in the electrical circuit of the Peltier element in a given time interval. A feedforward piecewise constant control signal is designed to reach the vicinity of a desired steady state by using the a-priori prediction of variations of the external temperature. Additionally, feedback loops are designed for model linearization, trajectory stabilization, and compensation of changes in the ambient air temperature.

ACS Style

Alexander Gavrikov; Georgy Kostin; Harald Aschemann; Andreas Rauh. Modeling and Control of a Thermoelectric Structure with a Peltier Element Subject to External Disturbances. IFAC-PapersOnLine 2020, 53, 7771 -7776.

AMA Style

Alexander Gavrikov, Georgy Kostin, Harald Aschemann, Andreas Rauh. Modeling and Control of a Thermoelectric Structure with a Peltier Element Subject to External Disturbances. IFAC-PapersOnLine. 2020; 53 (2):7771-7776.

Chicago/Turabian Style

Alexander Gavrikov; Georgy Kostin; Harald Aschemann; Andreas Rauh. 2020. "Modeling and Control of a Thermoelectric Structure with a Peltier Element Subject to External Disturbances." IFAC-PapersOnLine 53, no. 2: 7771-7776.