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arXiv 2025年

作者： Schmidt, Patrick Osinenko, Pavel Streif, Stefan Technische Universität Chemnitz Automatic Control and System Dynamics Lab Chemnitz09126 Germany Skolkovo Institute of Science and Technology Moscow143026 Russia

Practical stabilization of input-affine systems in the presence of measurement errors and input constraints is considered in this brief note. Assuming that a Lyapunov function and a stabilizing control exist for an input-affine system, the required measurement accuracy at each point of the state space is computed. This is done via the Lyapunov function-based decay condition, which describes along with the input constraints a set of admissible controls. Afterwards, the measurement time points are computed based on the system dynamics. It is shown that between these self-triggered measurement time points, the system evolves and converges into the so-called target ball, i.e. a vicinity of the origin, where it remains. Furthermore, it is shown that the approach ensures the existence of a control law, which is admissible for all possible states and it introduces a connection between measurement time points, measurement accuracy, target ball, and decay. The results of the approach are shown in three examples. © 2025, CC BY-NC-ND.

关键词： Lyapunov functions

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Some remarks on robustness of sample-and-hold stabilization

arXiv

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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

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Addressing infinite-horizon optimization in MPC via Q-learning

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IFAC-PapersOnLine 2018年第20期51卷 60-65页

作者： Beckenbach, Lukas Osinenko, Pavel Streif, Stefan Technische Universität Chemnitz Automatic Control and System Dynamics Lab Chemnitz09111 Germany

Model predictive control (MPC) is the standard approach to infinite-horizon optimal control which usually optimizes a finite initial fragment of the cost function so as to make the problem computationally tractable. Globally optimal controllers are usually found by Dynamic Programming (DP). The computations involved in DP are notoriously hard to perform, especially in online control. Therefore, different approximation schemes of DP, the so-called “critics”, were suggested for infinite-horizon cost functions. This work proposes to incorporate such a critic into dual-mode MPC as a particular means of addressing infinite-horizon optimal control. The proposed critic is based on Q-learning and is used for online approximation of the infinite-horizon cost. Stability of the new approach is analyzed and certain sufficient stabilizing constraints on the critic are derived. A case study demonstrates the applicability. © 2018

关键词： Dynamic programming

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Hierarchical control with Guaranteed Fault Diagnosability

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IFAC-PapersOnLine 2018年第24期51卷 1105-1110页

作者： Stoican, Florin Petzke, Felix Prodan, Ionela Streif, Stefan University POLITEHNICA of Bucharest Automatic Control and Systems Engineering Department 313 Splaiul Independentei Bucharest Romania Technische Universität Chemnitz Automatic Control and System Dynamics Lab Chemnitz09107 Germany GrenobleINP France

A multiple time-scale hierarchical control approach with guarantees for active fault diagnosability (detection and isolation) is presented. Robust positive invariance notions are used to provide a set-membership test for FDI validation at the low level and sufficient constraints for guaranteeing FDI at the high level. Due to the computational burden of the involved bilinear optimization problem, the high-level reference governor operates at a slower sampling time than the controller of the low-level system. Therefore, corner cutting avoidance constraints are imposed such that the faster-sampled lower level is still guaranteed to function properly. A case study illustrates the presented theoretical notions. © 2018

关键词： Fault detection Edge detection Bilinear optimizations Computational burden Corner cutting Fault diagnosability Hierarchical control isolation Positive invariance Reference governors

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Prototypical Description and controller Design for a Set of systems Using ν-gap Based Clustering

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IFAC-PapersOnLine 2020年第2期53卷 4623-4628页

作者： Lukas Munser Arne-Jens Hempel Grigory Devadze Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Lab Germany

We present an approach to design stabilizing controllers for a set of linear systems without restrictions regarding their modeling order. To this end, the systems are treated as abstract objects in the space of the ν-gap metric. Via a cluster analysis the set of systems is split into ν-gap similar clusters which are treated separately. For this purpose we provide an algorithm that constructs an explicit prototype system by generalizing the information of a given set of systems. Applying this algorithm to each cluster a set of prototype systems is obtained. Given these prototypes we design controllers in such a way that all systems assigned to a cluster will be stabilized by a corresponding controller. The approach is demonstrated for a set of 80 linear systems.

关键词： Robust control Classification Model-based control Distance transformation Stabilizing controllers

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A reinforcement learning method with closed-loop stability guarantee for systems with unknown parameters

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IFAC-PapersOnLine 2020年第2期53卷 8157-8162页

作者： Thomas Göhrt Fritjof Griesing-Scheiwe Pavel Osinenko Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Lab 09107 Chemnitz Germany

This work is concerned with the application of reinforcement learning (RL) techniques to adaptive dynamic programming (ADP) for systems with partly unknown models. In ADP, one seeks to approximate an optimal infinite horizon cost function, the value function. Such an approximation, i.e., critic, does not in general yield a stabilizing control policies, i.e., stabilizing actors. Guaranteeing stability of nonlinear systems under RL/ADP is still an open issue. In this work, it is suggested to use a stability constraint directly in the actor-critic structure. The system model considered in this work is assumed to be only partially known, specifically, it contains an unknown parameter vector. A suitable stabilizability assumption for such systems is an adaptive Lyapunov function, which is commonly assumed in adaptive control. The current approach formulates a stability constraint based on an adaptive Lyapunov function to ensure closed-loop stability. Convergence of the actor and critic parameters in a suitable sense is shown. A case study demonstrates how the suggested algorithm preserves closed-loop stability, while at the same time improving an infinite-horizon performance.

关键词： Consensus Reinforcement learning control Nonlinear adaptive control

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High-gain observer for the nitrification process including sensor dynamics

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IFAC-PapersOnLine 2023年第2期56卷 1633-1640页

作者： Patrick Schmidt Arne-Jens Hempel Stefan Streif Technische Universität Chemnitz 09126 Chemnitz 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.

关键词： high-gain observer nitrate monitoring model reduction

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

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IFAC-PapersOnLine 2023年第2期56卷 3874-3879页

作者： Francisco Moreno-Mora Lukas Beckenbach Stefan Streif Technische Universität Chemnitz Chemnitz 09126 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 results.

关键词： model predictive control reinforcement learning learning-based control

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Extraction of a computer-certified ODE solver

Extraction of a computer-certified ODE solver

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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

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Extraction of a computer-certified ODE solver

arXiv

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arXiv 2021年

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

关键词： Extraction

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