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Generating a robustly stabilizable class of nonlinear systems for a converse optimality problem

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Generating a robustly stabilizable class of nonlinear system...

European control Conference (ECC)

作者： Rania Tafat Thomas Gö hrt Stefan Streif Technische Universitat Chemnitz Chemnitz Germany Automatic Control and System Dynamics Lab

ISBN: (数字)9783907144077

ISBN: (纸本)9781665497336

Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered disturbances. In this paper, the converse optimality theory is extended to the class of affine systems with disturbances in continuous time while considering norm constraints on both control inputs and disturbances. The admissibility theorem and the design of the internal dynamics model are generalized in this context. A robust stabilizability condition is added for the initial converse optimality problem using inverse optimality's tool: the robust control Lyapunov function. A design for nonlinear class of systems that are both robustly stabilizable and globally asymptotically stable in open loop is obtained. A case study illustrates the presented theory.

关键词： Robust control Optimal control Europe Nonlinear systems Lyapunov methods Context modeling

Deep Neural Network Based Optimal control of Greenhouses

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Deep Neural Network Based Optimal Control of Greenhouses

European control Conference (ECC)

作者： Kiran Kumar Sathyanarayanan Philipp Sauerteig Stefan Streif Automatic Control and System Dynamics Lab Technische Universität Chemnitz Chemnitz Germany Department of Bioresources Fraunhofer Institute for Molecular Biology and Applied Ecology Giessen Germany

ISBN: (数字)9783907144107

ISBN: (纸本)9798331540920

automatic control of greenhouse crop production is of great interest owing to the increasing energy and labor costs. In this work, we use two-level control, where the upper level generates suitable reference trajectories for states and control inputs based on day-ahead predictions. These references are tracked in the lower level using Nonlinear Model Predictive control (NMPC). In order to apply NMPC, a model of the greenhouse dynamics is essential. However, the complex nature of the underlying model including discontinuities and nonlinearities results in intractable computational complexity and long sampling times. As a remedy, we employ NMPC as a data generator to learn the tracking control policy using deep neural networks. Then, the references are tracked using the trained Deep Neural Network (DNN) to reduce the computational burden. The efficiency of our approach under real-time disturbances is demonstrated by means of a simulation study.

关键词： Power demand Computational modeling Memory management Optimal control Artificial neural networks Production Real-time systems

Some remarks on robustness of sample-and-hold stabilization

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arXiv 2025年

作者： Schmidt, Patrick Osinenko, Pavel Streif, Stefan Technische Uni-versität Chemnitz Automatic Control and System Dynamics Lab Chemnitz09126 Germany patrick.schmidt Skolkovo Institute of Science and Technology Moscow143026 Russia

This work studies robustness to system disturbance and measurement noise of some popular general practical stabilization techniques, namely, Dini aiming, optimization-based stabilization and inf-convolution stabilization. Common to all these techniques is the explicit usage of a (general nonsmooth) control Lyapunov function, thus allowing to see them as a kind of generalization to the celebrated Sontag’s formula. It turns out that certain details of the above described robustness properties have not yet received the attention in literature they deserved. We provide new remarks, formalized in mathematical propositions, on robustness of selected popular stabilization techniques along with an extensive statistical case study on a robot parking problem. © 2025, CC BY-NC-ND.

关键词： Lyapunov functions

Predictive control with Learning-Based Terminal Costs Using Approximate Value Iteration

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arXiv 2022年

作者： Moreno-Mora, Francisco Beckenbach, Lukas Streif, Stefan Technische Universität Chemnitz Chemnitz09126 Germany Automatic Control and System Dynamics Lab

Stability under model predictive control (MPC) schemes is frequently ensured by terminal ingredients. Employing a (control) Lyapunov function as the terminal cost constitutes a common choice. Learning-based methods may be used to construct the terminal cost by relating it to, for instance, an infinite-horizon optimal control problem in which the optimal cost is a Lyapunov function. Value iteration, an approximate dynamic programming (ADP) approach, refers to one particular cost approximation technique. In this work, we merge the results of terminally unconstrained predictive control and approximate value iteration to draw benefits from both fields. A prediction horizon is derived in dependence on different factors such as approximation-related errors to render the closed-loop asymptotically stable further allowing a suboptimality estimate in comparison to an infinite horizon optimal cost. The result extends recent studies on predictive control with ADP-based terminal costs, not requiring a local initial stabilizing controller. We compare this controller in simulation with other terminal cost options to show that the proposed approach leads to a shorter minimal horizon in comparison to previous *** Codes 93B45 © 2022, CC BY-NC-ND.

关键词： Model predictive control

High-gain observer for the nitrification process including sensor dynamics

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arXiv 2022年

作者： Schmidt, Patrick Hempel, Arne-Jens Streif, Stefan Technische Universität Chemnitz Chemnitz09126 Germany Automatic Control and System Dynamics Lab

Fertilization is commonly used to increase harvests. The lack of knowledge of soil properties and the excessive use of fertilizers can result in overfertilization. Current sensor technology is able to measure the concentrations of some of the involved substances only at selected locations and depths. Point measurements of adjacent sensors in coarse sensor networks can be used to infer upon the state of nitrate concentrations in the sensor surroundings. For this purpose, a high-gain observer is proposed. Models of the nitrification process as well as the measurement dynamics for the observer design are derived and discretized on a grid to obtain a system of ordinary differential equations. It is shown that the nonlinearities of the model can be bounded and how the observer gain can be computed via linear matrix inequalities. Furthermore, a model reduction is proposed, which allows the consideration of more grid points. A simulation study demonstrates the proposed approach. © 2022, CC BY-NC-ND.

关键词： Nitrates

Modeling and optimal control of growth, energy, and resource dynamics of Hermetia illucens in mass production environment

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arXiv 2022年

作者： Padmanabha, Murali Kobelski, Alexander Hempel, Arne-Jens Streif, Stefan Automatic Control and System Dynamics Lab Technische Universität Chemnitz Chemnitz09107 Germany

Mass production of Hermetia illucens insect larvae is now being adopted in many countries and is taking an industrial production approach. Despite abundant literature on factors that affect larvae growth and the optimal static parameters identified in laboratory setup, for an industrial production process it is necessary to identify the trajectories such that the growth as well as the production process is optimal. To achieve this in this work, some of the important requirements and challenges involved thereof are identified and objectives of the automation process are formulated within a model based optimal control setup. Mechanistic models necessary for the optimization framework are derived as differential equations that describe the dynamic variation of resources (feed, water, O2 etc.), energy, and larval biomass. In addition, the elevated metabolic activity of larvae corresponding to the final instar development is identified and also modelled based on the observation from experiments. The mass and energy balance approach used in modelling enables the quantification and distinction of the mass and energy flux components in various levels (e.g. larvae body, growing medium, production environment, and external environment) while holding its applicability for both open and closed/reactor based production setups. Finally, the trajectories generated using the synthesized optimal controller are tested under different scenarios showcasing significant reduction in resource consumption compared to a fixed set-point operation of the production setup. Results presented in this work not only showcase the potential of the mechanistic models and their application in identifying the relevant process parameters (e.g. reactor properties such as volume, thermal conductivity, actuator capacities), but most importantly in optimizing the process dynamically and tuning the process objectives as desired (e.g. maximize larvae mass, reduce energy). © 2022, CC BY-NC-ND.

关键词： Differential equations

Deep Neural Network Based Optimal control of Greenhouses

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arXiv 2023年

作者： Sathyanarayanan, Kiran Kumar Sauerteig, Philipp Streif, Stefan Technische Universität Chemnitz Automatic Control and System Dynamics Lab Chemnitz09126 Germany Fraunhofer Institute for Molecular Biology and Applied Ecology Department of Bioresources Giessen Germany

关键词： Deep neural networks

Quantized Deep Neural Network Based Optimal control of Greenhouses on a Microcontroller

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Quantized Deep Neural Network Based Optimal Control of Green...

European control Conference (ECC)

作者： Kiran Kumar Sathyanarayanan Philipp Sauerteig Pablo Zometa Stefan Streif Automatic Control and System Dynamics Lab Technische Universität Chemnitz Chemnitz Germany Faculty of Engineering German International University Berlin Germany Department of Bioresources Fraunhofer Institute for Molecular Biology and Applied Ecology Giessen Germany

ISBN: (数字)9783907144107

ISBN: (纸本)9798331540920

Growing crops in controlled-Environment Agriculture (CEA) farms, such as greenhouses and vertical farms, can help in meeting the demands of urban centers and achieving climate goals. Recently, many advanced control techniques like Model Predictive control (MPC) and its variants have been developed for energy-efficient operation and minimization of resource utilization. However, real-time implementation of these advanced strategies come along with certain computational hardware requirements, thus, increasing the operating costs. In this work, we propose to learn the MPC policy of a greenhouse control by means of a Deep Neural Network (DNN) in order to be implemented on a low-cost microcontroller. Additionally, we use a feedback law to reduce undesired quantization effects. The efficiency of our approach is exemplified by means of a simulation study for greenhouse control.

关键词： Quantization (signal) Microcontrollers Optimal control Greenhouses Artificial neural networks Minimization Real-time systems

Extraction of a computer-certified ODE solver

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Extraction of a computer-certified ODE solver

European control Conference (ECC)

作者： Grigory Devadze Lars Flessing Stefan Streif Automatic Control and System Dynamics Lab Technische Universitt Chemnitz Germany

Reliably determining system trajectories is essential in many analysis and control design approaches. To this end, an initial value problem has to be usually solved via numerical algorithms which rely on a certain software realization. Because software realizations can be error-prone, proof assistants may be used to verify the underlying mathematical concepts and corresponding algorithms. In this work we present a computer-certified formalization of the solution of the initial value problem of ordinary differential equations. The concepts are performed in the framework of constructive analysis and the proofs are written in the Minlog proof system. We show the extraction of a program, which solves an ODE numerically and provide some possible optimization regarding the efficiency. Finally, we provide numerical experiments to demonstrate how programs of a certain high level of abstraction can be obtained efficiently. The presented concepts may also be viewed as a part of preliminary work for the development of formalized nonlinear control theory, hence offering the possibility of computer-assisted controller design and program extraction for the controller implementation.

关键词： Asymptotic stability Software algorithms Ordinary differential equations Reliability engineering Software Stability analysis Trajectory