Dynamical Systems: Reduction, Optimization and Control
Monday, 26 March 2018
2:00pm - 3:30pm
Campus Stuttgart-Vaihingen, Pfaffenwaldring 9
Data-driven Inference of Control Theoretic System Properties
Anne Romer, University of Stuttgart
Since the amount of available data is increasing rapidly, there has been an increasing interest in what is called data-driven control. One complementary approach to the direct controller design from data is to learn and analyze certain system properties from data first, since they allow for the direct application of well-known feedback theorems for controller design. Hence, by learning such properties from data, we obtain insights to the a-priori unknown system, we are not bound to a certain controller structure beforehand while still providing control theoretic guarantees for the closed-loop behavior. Along those lines, we present sampling strategies to iteratively determine the operator gain, the shortage of passivity and conicity of linear time-invariant systems, whose input-output map remains undisclosed. These sampling strategies are based on gradient dynamical systems and saddle point flows, which asymptotically reveal the true system properties.
Analysis of Networked Systems over Switching Topologies
Novel criteria for robust stability and performance analysis are proposed for a class of networked systems with a switching communication structure. In contrast to other approaches, our results are based on recent separation techniques from robust control. These offer substantial extra flexibility and pave the way for covering more general interconnection structures that are affected by heterogeneous uncertainties. The benefits of the proposed approach are illustrated by means of several numerical examples. Moreover, we address the potentials to merge these analysis techniques with distributed controller synthesis algorithms that we recently developed for fixed interconnection structures.
Uncertainty in Controlled Multibody Systems
Andreas Hofmann, University of Stuttgart
Model-based controller design for multibody systems implies exact knowledge of the system dynamics, and the success and the performance are related to the accuracy of the underlying system model. Consequently, a systematically misbehaving controller may arise if model uncertainties are not considered in the design process. In this presentation new methods and ideas for designing model-based robust controllers for multibody systems based on fuzzy arithmetical uncertainty modeling are presented. Fuzzy sets provide a mathematical formulation for possibilisty theory and possibilistic uncertainty models, so that fuzzy arithmetical concepts are well suited for the uncertainty modeling and analysis. Moreover, the presented method allows to incorporate a maximum of available data and knowledge about the shape of the inherent uncertainty into the resulting controller design.
Improved Modeling of Kinematics and Dynamics of Cables for Use in Cable-Driven Parallel Robots
Philipp Tempel, University of Stuttgart
Cable-driven parallel robots make use of elastic cables for force and motion transmission from the driving winches to the mobile platform. The system is inherently susceptible to transversal cable vibration stemming from jerky motion of the platform as well as cable winding and guiding. To improve precision and stiffness of cable robots, the cable motion must explicitly be considered in simulation and control. In this poster, we present different approaches to modeling the cable shape based on the static model first derived by Irvine. Two main approaches are presented, one based on discretization of the cable into segments yielding high dimensional systems, the other being based on Rayleigh-Ritz modal superposition yielding lower dimensional systems. Additionally, the static and dynamic cable force transmission is evaluated against existing models such as four-element or Flory models. Furthermore, overall model validity and applicability to improving accuracy and stiffness is shown.
Feedback Control of Parametrized PDEs via Model Order Reduction and Dynamic Programming Principle
Andreas Schmidt, University of Stuttgart
We investigate infinite horizon optimal control problems for nonlinear parametrized partial differential equations via the famous dynamic programming principle of Bellman by solving Hamilton-Jacobi-Bellman (HJB) equations. Classical discretization techniques for HJB equations are prone to the so-called curse of dimensionality, rendering these methods infeasible already in low-dimensional spaces (say 5−8 dimensions). By combining recent model order reduction techniques for feedback control problems and enhancements like parameter partitioning with efficient approximation schemes for HJB equations, we arrive at reduced problems that can be solved efficiently. Our approach is divided in an offline and online phase, where the online phase is substantially sped up by precalculations that have to performed once in an offline step. Numerical examples for linear and nonlinear flow problems illustrate the effectiveness of the proposed method.
Christian Kleinbach & Jörg Fehr & Oleksandr Martynenko & Syn Schmitt (PP3.045); Dennis Grunert & Kevin Carlberg & Jörg Fehr (PP3.046); Abelardo Rodriguez Pretelin & Wolfgang Nowak (PP3.047); Steffen Linsenmayer & Frank Allgöwer (PP3.048); Ehsan Sharafian Ardakani & Henrik Ebel & Peter Eberhard (PP3.049); Dominik Hamann & Peter Eberhard (PP3.050); Mylena Mordhorst (PP3.051); Johannes Köhler (PP3.052); Fatemeh Ansarieshlaghi & Peter Eberhard (PP3.053); Christian A. Rösinger (PP3.054); Jannik Haas & Wolfgang Nowak (PP3.055); Nehzat Emamy & Pascal Litty & Miriam Mehl (PP3.056); Sergey Oladyshkin & Anneli Guthke & Farid Mohammadi & Rebekka Kopmann & Wolfgang Nowak (PP3.057); Matthias Lorenzen & Frank Allgöwer (PP3.058); Sebastian Most & Wolfgang Nowak & Marco Dentz & Branko Bijeljic & Diogo Bolster (PP3.059); Bastian Hilder (PP3.060); Malte Heckelen (PP3.061); Roman Föll (PP3.062).