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    Stochastic Optimal Control and MPC - Dissipativity, Risk, and Performance
    It stands to reason that three of the most impactful concepts in systems and control in the 20th century have been the optimal control siblings – i.e. the Pontryagin Maximum Principle (PMP) and Dynamic Programming together with the Hamilton-Jacobi-Bellman approach – as well as the dissipativity framework for dynamic systems coined by Jan Willems. Moreover, Model Predictive Control (MPC) can be regarded as a successful attempt to alleviate the curse of dimensionality in solving the Hamilton-Jacobi-Bellman Equation (HJBE) by resorting to a receding-horizon application of open-loop optimal inputs – either obtained directly via the PMP or via direct solution methods for optimal control. The last decades have seen significant progress, for example, in terms of stability and performance analysis of MPC considering nonlinear prediction models, real-time implementation of MPC, MPC accounting for uncertainty surrounding system dynamics and exogenous disturbances. To this end, disturbances may be treated in a stochastic or in a worst-case manner. While the usual control-centered approach to MPC considers underlying tasks such as setpoint stabilization and trajectory tracking, in the last years several breakthroughs were obtained in analyzing MPC with generic, i.e. economic cost functions, which do not express control tasks directly. Indeed, the analysis of these schemes uses concepts from the PMP, Dynamic Programming, and dissipativity notions. Moreover, these approaches are of major interest for directly optimizing process economics via closed-loop control in various applications ranging from process industries to energy systems and economics. Yet, from a systems and control point of view, the combination of stochastic uncertainty descriptions with economic objective formulations is not well-explored, despite the fact that combining both approaches promises great potential for applications. In this context, the present project develops new tools for analysis and numerical solution of stochastic optimal control problems and MPC. The proposed research enables the development of novel tools for economic optimization-based control of stochastic nonlinear systems. The focus of the project is on the development and understanding of stochastic dissipativity concepts and their use in analysing the closed-loop performance of stochastic economic MPC schemes. In addition to standard cost functions based on expectation and variance we also investigate risk-aware formulations. The methods are tested on benchmark problems for multi-energy systems, particularly on scheduling problems for energy storage populations under uncertainty.
      18
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    Urbane Lufttransportsimulation: Simulationsbasierte Entwicklung von Infrastruktur- und Betriebskonzepten zur Bewertung der Chancen und Risiken des Aufbaus urbaner Luftmobilität am Beispiel der Metropolregion Hamburg
    Ziel des Projektes ULTRAS ist die Bewertung von Möglichkeiten und Risiken bei der Entwicklung eines integrierten Lösungsvorschlags für ein urbanes Lufttransportsystems (UAM) in der Metropolregion Hamburg. Dazu werden für konkreten Transportbedarf und Routen von Lufttaxies mit ihren Kapazitätsbeschränkungen 4D-Trajektorien geplant. Die Trajektorien werden in eine Schnellzeitsimulation überführt, in der sich die unbemannten Lufttaxis trotz ihrer Ortungstoleranzen autonom seperieren können um Kollisionen auszuschließen. Fahrzeugdynamik und Flugregler werden ebenso simuliert wie redundante Sensoren und Echtzeitkommunikation zwischen den Fahrzeugen und mit einem Kontrollzentrum am Boden. Die Simulationsergebnisse werden unter verschiedenen technischen Aspekten, dem wirtschaftlichen Nutzen sowie den Kosten und Umweltauswirkungen bewertet. Unter den Kriterien der Akzeptanz und Wirtschaftlichkeit wird eine volkswirtschaftliche Bewertung vorgenommen und Handlungsempfehlungen abgeleitet.
      195  16
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    HIR3X Helmholtz International Laboratory on Reliability, Repetition, Results at the most Advanced X-Ray Sources
    Analytical methods based on radiation produced by particle accelerators play a key role in many fields of science. Their intense radiation that is tunable over a wide wavelength range in the X-ray regime allows for the determination of the atomic and element specific electronic structure and dynamics of matter not only of bulk materials but also for extremely small samples or surface layers of less than one atomic layer. Synchrotron radiation sources of the newest generation and the envisaged upcoming generation will boost the limit even further in the study of even smaller sample regions and non-crystalline samples. While storage-ring-based sources are able to access the static structure and slow dynamics in materials that are characteristic for e.g. the movement of larger atomic groups during a molecular reaction, Free Electron Lasers (FELs) opened up a totally new field in ultrafast science to capture fast atomic movements and electronic changes on the relevant time scales of several femtoseconds, and enabling totally new experiments by their extremely high single pulse intensities like single-shot imaging. Both institutions, SLAC and DESY, are pioneers at the forefront of FEL research. The FLASH facility at DESY was the first FEL in the VUV and soft X-ray regime, which started user operation in 2005 to mainly study ultrafast electronic properties and processes in matter and imaging at the nanometer scale. The LCLS at SLAC was the first FEL to operate in the harder X-ray regime, which brought such studies of the dynamics and structure of matter to atomic distances. FELs can be categorized in two main classes: 1) FELs based on normal conducting linear accelerators like LCLS, FERMI@ELLETTRA, SACLA@SPRING-8, PAL-FEL and SwissFEL@PSI with pulse repetition rates in the 30-120 Hz regime and 2) FELs based on superconducting linac technology like FLASH, the European XFEL and the upcoming LCLS II (now under construction) that are able to deliver pulse repetition rates in the 5 – 1000 kHz range. The latter facilities allow several FEL undulators to be served by one linac and thus have dramatically increased throughput. Together with their extremely high average brightness produced by the high pulse repetitions rates, this allows rapid measurement of large datasets that are required to investigate extremely dilute targets like gas phase reactions or capture rare events such as the transition state in a chemical reaction. The optimum operation of a FEL is still far from routine due to the immense complexity of these installations. Changes of beam parameters can be time consuming even for expert operators. However, to fully exploit the capabilities of these FEL sources not only the operation of the accelerator facilities is a major challenge but also the transport of the photon beam, the handling and ultrafast delivery of samples as well as coping with the huge amounts of data that these facilities produce. Especially in the latter case, quick online evaluations of the measured data are desperately needed to steer the course of the experiments. Since these challenges are similar for LCLS and LCLS II at SLAC and for FLASH and European XFEL in Hamburg, SLAC and DESY have already a long tradition of collaboration on various levels in the field of accelerators, FEL physics, and photon science. Both institutions are key players in the field in the world. Based on the existing collaboration SLAC and DESY want to tackle jointly the challenges mentioned above, which are growing more urgent with the rise of high repetition rate FELs. In addition to a closer collaboration in search for sustainable technical solutions with respect to beam transport and sample delivery one of the main collaboration tasks will be the further development of artificial-intelligence-based techniques for the control of the FEL facilities that require ten thousand to thirty thousand control parameters to be adjusted for optimum and reliable systems operation. Artificial intelligence (AI) and machine learning algorithms will also e developed for the quasi real-time assessment of data quality and first evaluation. The hope is that by utilizing suitable AI software vetoes or triggers it will be possible to effectively reduce the data volume to a sustainable and meaningful level. All these measures are intended to stabilize and optimize the operation of high repetition rate FELs and the corresponding experimental stations and as such to make the analytical techniques that they make available to a larger community of non-expert users.
      29
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    SPP 1914: Cyber-Physical Networking: Cooperative and Topology Control for Tightly Coupled Large-Scale Wireless Networked Autonomous Agents
    In this project we consider cooperative control of mobile agents that interact over a wireless network. The network is set up by the nodes, i.e. no external communication infrastructure is assumed. The project goal is to develop analysis and synthesis tools that allow joint design of distributed cooperative control and communication strategies for large homogeneous groups of mobile agents which interact via a wireless network. The overall control performance expressed in terms of a suitably defined l2 performance channel depends on the local dynamic control of individual agents as well as on flow of information between agents. It is restricted by imperfections of the communication network, in particular by packet loss and time delay, as well as possibly quantization effects resulting from low bit rates. The goal is to derive conditions on the stability and the performance of multi-agent systems that depend on the decision variables of the design. These variables are the control gains, the communication network parameters and the network topology. The project will continue with our study of time-triggered distributed control of wireless networked agents. We develop tools for trading network demands against control demands in an architecture which facilitates the decoupling of stochastic aspects of wireless networks and deterministic control of agent dynamics. We study with distributed consensus and flocking two core building blocks for control of multi-agent systems. In addition to concepts well understood for time-triggered control, we will explore the potential of event-triggered control as well as event-triggered model predictive control for more efficient use of channel capacity. Our theoretical results will be substantiated by simulation studies and practical experiments with AUVs and UAVs.
      81
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    Grid- and transformation-free model order reduction for linear parameter varying systemsGrid- and transformation-free model order reduction for linear parameter varying systems
    This project considers model order reduction for linear parameter varying (LPV) systems. LPV systems are dynamic systems where the state space matrices are functions of a time-varying parameter vector which is not known in advance but measurable at each time instant. The main advantage of the LPV framework is that it allows to extend linear controller design techniques to nonlinear and time-varying systems, such that analysis and synthesis problems are being solved by solving linear matrix inequalities (LMIs). The computational complexity solving LMIs grows however rapidly with increasing state and parameter dimensions, and model approximation is required when dealing with large scale systems.In this project balanced truncation for LPV models is addressed, and three open problems arising in existing approaches will be solved:- The need of solving LMI conditions on a grid in parameter space will be avoided by developing a grid-free reduction method based on the full-block S-procedure.- The need of parameter-dependent transformations of the model will be avoided by representing the reduction problem as an equivalent fixed-structure controller synthesis problem, leading to a transformation free-reduction procedure. - The open and practically important problem of modal decomposition of LPV models will be addressed by combining the fixed-structure approach above with existing modal matching results.
      80
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      97
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      82
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    Event Triggered Control
    Kooperationen: University of Georgia, Athens, Georgia, USA
      73
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    SPP 1914: Cyber-Physical Networking: Analysis and synthesis of combined cooperative control and topology control over wireless network models
    In this project we consider cooperative control of mobile agents or nodes that interact over a wireless network. The network is set up by the nodes, i.e. no external communication infrastructure is assumed. Cooperative control of multi-agent systems, as well as topology control in communication networks, have been studied extensively, but separately. Research on cooperative control of multi-agent systems usually assumes the interaction topology to be given (possibly uncertain). Research on topology control usually aims at improving the network in the sense of communication properties. However, as the interaction topology in a network of mobile agents has a considerable effect on the achievable cooperative control performance, a control scheme that combines dynamic control of the agents motion with adapting the interaction structure to the time-varying conditions of the communication network is expected to significantly improve the achievable performance. To the best of the applicants knowledge, to date such a combined control scheme has not been reported in the literature. The objectives of the proposed research project can be summarised as follows:1. Local topology control will maintain the highest level of algebraic connectivity (aiming at high performance and robustness) while taking into account SINR constraints. This will be achieved by control of the wireless network graph and the interaction graph. Methods of investigation are graph spanners, backbones, and node relocation.2. A distributed cooperative control scheme will be developed for LPV agent models and gain-scheduled local feedback controllers; this will allow to consider mobile robots and vehicles subject to nonholonomic constraints. Analysis and synthesis conditions will be derived that guarantee stability and performance in the sense of the L2 -norm, with a complexity independent of the number of agents while taking constraints on communication resources into account.3. Local information about network properties will be gathered and used for topology control as well as for cooperative control to adapt interconnection weights. Our focus is on distributed and local solutions with the goal to support any system scale.4. Proof of concept will be given by simulation studies based on source-seeking scenarios, which will be selected to highlight the various features of the proposed integrated collaborative control and topology control scheme.
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