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A mixed-integer framework for analyzing neural network-based controllers for piecewise affine systems with bounded disturbances

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arXiv 2025年

作者： Teichrib, Dieter Darup, Moritz Schulze Control and Cyber-physical Systems Group Faculty of Mechanical Engineering TU Dortmund University Germany

We present a method for representing the closed-loop dynamics of piecewise affine (PWA) systems with bounded additive disturbances and neural network-based controllers as mixed-integer (MI) linear constraints. We show that such representations enable the computation of robustly positively invariant (RPI) sets for the specified system class by solving MI linear programs. These RPI sets can subsequently be used to certify stability and constraint satisfaction. Furthermore, the approach allows to handle nonlinear systems based on suitable PWA approximations and corresponding error bounds, which can be interpreted as the bounded disturbances from above. © 2025, CC BY-NC-ND.

关键词： Mixed-integer linear programming

Architecture of Digital Twin for Automating Waste and Recycling Material Sorting Process

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Architecture of Digital Twin for Automating Waste and Recycl...

International Conference on Emerging Technologies and Factory Automation (ETFA)

作者： Shreyas Parbat Imam Iqbal Isabell Viedt Leon Urbas Chair of Process Control Systems & Process Systems Engineering Group Technische Universität Dresden Dresden Germany

ISBN: (数字)9798350361230

ISBN: (纸本)9798350361247

Waste and recycling material sorting is crucial for reducing environmental impact and promoting resource recovery. However, its complexity poses significant challenges, necessitating the development of effective sorting processes. Manual operation of these plants can be less efficient than automated systems. The first step toward automation is utilizing a Digital Twin, which combines fundamental principles and data-driven insights into the waste sorting process. To achieve this, the equipment involved in waste sorting plants can be analyzed in detail, focusing on operational settings and their impact on overall efficiency. Initially, a steady-state model of the plant is developed, followed by the implementation of advanced strategies like model predictive control. The model can be rigorously tested and refined using a case study on German post-consumer waste. The architecture of the Digital Twin, comprising various building blocks such as the modeling and simulation block, is being developed to transition away from manual operations. This Digital Twin aims to enhance sorting efficiency through offline and online optimization of operational set points, leading to a more sustainable and resource-efficient future. Through simulations and real-time data integration, a Digital Twin for the waste and recycling material process can aid with process design, fine-tuning, and plant automation.

关键词： Process design Predictive models Real-time systems Digital twins Recycling Steady-state Optimization Manufacturing automation Sorting Predictive control

Towards a unifying framework for data-driven predictive control with quadratic regularization

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arXiv 2024年

作者： Klädtke, Manuel Darup, Moritz Schulze The Control and Cyberphysical Systems Group Faculty of Mechanical Engineering TU Dortmund University Germany

Data-driven predictive control (DPC) has recently gained popularity as an alternative to model predictive control (MPC). Amidst the surge in proposed DPC frameworks, upon closer inspection, many of these frameworks are more closely related (or perhaps even equivalent) to each other than it may first appear. We argue for a more formal characterization of these relationships so that results can be freely transferred from one framework to another, rather than being uniquely attributed to a particular framework. We demonstrate this idea by examining the connection between γ-DDPC and the original DeePC formulation. © 2024, CC BY-NC-ND.

关键词： Model predictive control

Predictable Interval MDPs through Entropy Regularization

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arXiv 2024年

作者： van Zutphen, Menno Delimpaltadakis, Giannis Heemels, Maurice Antunes, Duarte Control Systems Technology Group Department of Mechanical Engineering Eindhoven University of Technology Netherlands

Regularization of control policies using entropy can be instrumental in adjusting predictability of real-world systems. Applications benefiting from such approaches range from, e.g., cybersecurity, which aims at maximal unpredictability, to human-robot interaction, where predictable behavior is highly desirable. In this paper, we consider entropy regularization for interval Markov decision processes (IMDPs). IMDPs are uncertain MDPs, where transition probabilities are only known to belong to intervals. Lately, IMDPs have gained significant popularity in the context of abstracting stochastic systems for control design. In this work, we address robust minimization of the linear combination of entropy and a standard cumulative cost in IMDPs, thereby establishing a trade-off between optimality and predictability. We show that optimal deterministic policies exist, and devise a value-iteration algorithm to compute them. The algorithm solves a number of convex programs at each step. Finally, through an illustrative example we show the benefits of penalizing entropy in IMDPs. © 2024, CC BY-NC-ND.

关键词： Stochastic systems

MPC using mixed-integer programming for aquifer thermal energy storages

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arXiv 2024年

作者： van Randenborgh, Johannes Darup, Moritz Schulze Control and Cyberphysical Systems Group Faculty of Mechanical Engineering TU Dortmund University Germany

Aquifer thermal energy storages (ATES) are used to temporally store thermal energy in groundwater saturated aquifers. Typically, two storages are combined, one for heat and one for cold, to support heating and cooling of buildings. This way, the use of classical fossil fuel-based heating, ventilation, and air conditioning can be significantly reduced. Exploiting the benefits of ATES beyond "seasonal" heating in winter and cooling in summer as well as meeting legislative restrictions requires sophisticated control. We propose a tailored model predictive control (MPC) scheme for the sustainable operation of ATES systems, which mainly builds on a novel model and objective function. The new approach leads to a mixed-integer quadratic program. Its performance is evaluated on real data from an ATES system in Belgium. © 2024, CC BY-NC-ND.

关键词： Predictive control systems

Reachability analysis for piecewise affine systems with neural network-based controllers

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Reachability analysis for piecewise affine systems with neur...

IEEE Conference on Decision and control

作者： Dieter Teichrib Moritz Schulze Darup Department of Mechanical Engineering Control and Cyberphysical Systems Group TU Dortmund University Germany

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

Neural networks (NN) have been successfully applied to approximate various types of complex control laws, resulting in low-complexity NN -based controllers that are fast to evaluate. However, when approximating control laws using NN, performance and stability guarantees of the original controller may not be preserved. Recently, it has been shown that it is possible to provide such guarantees for linear systems with NNbased controllers by analyzing the approximation error with respect to a stabilizing base-line controller or by computing reachable sets of the closed-loop system. The latter has the advantage of not requiring a base-line controller. In this paper, we show that similar ideas can be used to analyze the closed-loop behavior of piecewise affine (PWA) systems with an NNbased controller. Our approach builds on computing overapproximations of reachable sets using mixed-integer linear programming, which allows to certify that the closed-loop system converges to a small set containing the origin while satisfying input and state constraints. We also show how to modify a given NN-based controller to ensure asymptotic stability for the controlled PWA system.

关键词： Linear systems Asymptotic stability Costs Computational modeling Artificial neural networks Predictive models Stability analysis Mixed integer linear programming Closed loop systems Reachability analysis

Predictable Interval MDPs through Entropy Regularization

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Predictable Interval MDPs through Entropy Regularization

IEEE Conference on Decision and control

作者： M.J.T.C. van Zutphen G. Delimpaltadakis W.P.M.H. Heemels D.J. Antunes Department of Mechanical Engineering Control Systems Technology Group Eindhoven University of Technology The Netherlands

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

Regularization of control policies using entropy can be instrumental in adjusting predictability levels of real-world systems. Applications benefiting from such approaches range from cybersecurity, which aims at maximal unpredictability, to human-robot interaction, where predictable behavior is highly desirable. In this paper, we consider entropy regularization for interval Markov decision processes (IMDPs), which are uncertain MDPs where transition probabilities are only known to belong to specified intervals. Lately, IMDPs have gained significant popularity in the context of abstracting stochastic systems for control design. In this work, we address robust minimization of the linear combination of entropy and a standard cumulative cost in IMDPs, thereby establishing a trade-off between optimality and predictability. We show that optimal deterministic policies exist, and devise a value-iteration algorithm to compute them. The algorithm solves a number of convex programs at each step. Finally, through an illustrative example we show the benefits of penalizing entropy in IMDPs.

关键词： Costs control design Stochastic systems Markov decision processes Instruments Human-robot interaction Prediction algorithms Minimization Entropy Standards

LEROjD: Lidar Extended Radar-Only Object Detection

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arXiv 2024年

作者： Palmer, Patrick Krüger, Martin Schütte, Stefan Altendorfer, Richard Adam, Ganesh Bertram, Torsten Institute of Control Theory and Systems Engineering TU Dortmund University Germany ZF Group

Accurate 3D object detection is vital for automated driving. While lidar sensors are well suited for this task, they are expensive and have limitations in adverse weather conditions. 3+1D imaging radar sensors offer a cost-effective, robust alternative but face challenges due to their low resolution and high measurement noise. Existing 3+1D imaging radar datasets include radar and lidar data, enabling cross-modal model improvements. Although lidar should not be used during inference, it can aid the training of radar-only object detectors. We explore two strategies to transfer knowledge from the lidar to the radar domain and radar-only object detectors: 1. multi-stage training with sequential lidar point cloud thin-out, and 2. cross-modal knowledge distillation. In the multistage process, three thin-out methods are examined. Our results show significant performance gains of up to 4.2 percentage points in mean Average Precision with multi-stage training and up to 3.9 percentage points with knowledge distillation by initializing the student with the teacher’s weights. The main benefit of these approaches is their applicability to other 3D object detection networks without altering their architecture, as we show by analyzing it on two different object detectors. Our code is available at https://***/rst-tu-dortmund/lerojd. Copyright © 2024, The Authors. All rights reserved.

关键词： Radar imaging

SRG Analysis of Lur’e systems and the Generalized Circle Criterion

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arXiv 2024年

作者： Krebbekx, Julius P.J. Tóth, Roland Das, Amritam Control Systems Group Department of Electrical Engineering Eindhoven University of Technology Netherlands Systems and Control Lab HUN-REN Institute for Computer Science and Control Budapest Hungary

Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. However, we show that the current SRG analysis suffers from some pitfalls that limit its applicability in analysing practical nonlinear systems. We overcome these pitfalls by modifying the SRG of a linear time invariant operator, combining the SRG with the Nyquist criterion, and apply our result to Lur’e systems. We thereby obtain a generalization of the celebrated circle criterion, which deals with broader class of nonlinearities, and provides (incremental) L2-gain performance bounds. We illustrate the power of the new approach on the analysis of the controlled Duffing oscillator. © 2024, CC BY.

关键词： Frequency domain analysis