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Analysis of the Caratheodory's Theorem on Dynamical system Trajectories Under Numerical Uncertainty

IEEE/CAA Journal of automatica Sinica 2018年第4期5卷 787-793页

作者： Pavel Osinenko Grigory Devadze Stefan Streif Automatic Control and System Dynamics Laboratory Technische Universitat Chemnitz09107 ChemnitzGermany IEEE

The current work proposes a new and constructive proof for the Caratheodory's theorem on existence and uniqueness of trajectories of dynamical systems. The key concern is the numerical uncertainty, i.e., the discrepancy between mathematical proofs, algorithms, and their implementations, which may affect the correct functioning of a control system. Due to growing demands on security and compliance with specifications,correctness of the control system functioning is becoming ever more important. Since in both dynamical systems and many control design approaches, one of the central notions is the system trajectory, it is important to address existence and uniqueness of system trajectories in a way which incorporates numerical uncertainty. Constructive analysis is a particular approach to formalizing numerical uncertainty and is used as the basis of the current work. The major difficulties of guaranteeing existence and uniqueness of system trajectories arise in the case of systems and controllers which possess discontinuities in time,since classical solutions to initial value problems do not *** issue is addressed in Caratheodory's theorem. A particular constructive variant of the theorem is proven which covers a large class of problems found in practice.

关键词： Constructive analysis Caratheodory’s theorem dynamical systems

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Stacked adaptive dynamic programming with unknown system model

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IFAC-PapersOnLine 2017年第1期50卷 4150-4155页

作者： Osinenko P. Göhrt T. Devadze G. Streif S. Laboratory for Automatic Control and System Dynamics Technische Universität Chemnitz Chemnitz 09107 Germany

Adaptive dynamic programming is a collective term for a variety of approaches to infinite-horizon optimal control. Common to all approaches is approximation of the infinite-horizon cost function based on dynamic programming philosophy. Typically, they also require knowledge of a dynamical model of the system. In the current work, application of adaptive dynamic programming to a system whose dynamical model is unknown to the controller is addressed. In order to realize the control algorithm, a model of the system dynamics is estimated with a Kalman filter. A stacked control scheme to boost the controller performance is suggested. The functioning of the new approach was verified in simulation and compared to the baseline represented by gradient descent on the running cost. © 2017

关键词： Dynamic programming Kalman filters Optimal control

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Constructive analysis of control system stability

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IFAC-PapersOnLine 2017年第1期50卷 7467-7474页

作者： Osinenko P. Devadze G. Streif S. Laboratory for Automatic Control and System Dynamics Technische Universität Chemnitz Chemnitz 09107 Germany

Stability of control systems is one of the central subjects in control theory. The classical asymptotic stability theorem states that the norm of the residual between the state trajectory and the equilibrium is zero in the limit. Unfortunately, it does not in general allow computing a rate of convergence, whereas proving exponential stability is notoriously complicated. This work proposes to revisit the asymptotic stability theory with the aim of computing convergence rates using constructive analysis which is a mathematical tool that realizes equivalence between certain theorems and computational algorithms. The overall goal of the current study matches with the trend for introducing formal verification tools into control theory. Besides existing approaches, constructive analysis, suggested within this work, can also be considered for formal verification of control systems. A computational example is provided that demonstrates extraction of a convergence certificate for a dynamical system. © 2017

关键词： computational methods Dynamic stability formal verification

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Tube-based MPC for Two-Timescale Discrete-Time Nonlinear Processes with Robust control Contraction Metrics 63

Tube-based MPC for Two-Timescale Discrete-Time Nonlinear Pro...

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63rd IEEE Conference on Decision and control, CDC 2024

作者： Guo, Yang Sauerteig, Philipp Streif, Stefan Technische Universität Chemnitz Automatic Control and System Dynamics Laboratory Chemnitz09107 Germany

ISBN: (纸本)9798350316339

A computationally efficient model predictive control scheme is proposed for constrained nonlinear processes with inherent slow and fast dynamics. Specifically, the nonlinear process is approximated by a surrogate model, whose slow state is sampled with a larger time interval than the fast one. This reduces optimization variables and, on the other hand, introduces prediction errors and henceforth may induce constraint violation without further treatments. To mitigate these issues, we tighten constraints by leveraging Robust control Contraction Metrics. Furthermore, a back-up strategy is employed to ensure feasibility over time. The numerical efficiency of this proposed scheme is illustrated with a crops growth process, e.g., in indoor farming. © 2024 IEEE.

关键词： Robust control

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Sustainability Analysis of Interconnected Food Production systems via Theory of Barriers

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IFAC-PapersOnLine 2020年第2期53卷 15765-15770页

作者： Tim Aschenbruck Willem Esterhuizen Murali Padmanabha Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Laboratory Germany

controlled environment agriculture (CEA) is used for efficient food production. Efficiency can be increased further by interconnecting different CEA systems (e.g. plants and insect larvae or fish and larvae), using products and by-products of one system in the other. These interconnected systems define an overall system that can be described by models of interacting species. It is necessary to identify system parameters (e.g. initial species concentration, harvest rate, feed quality, etc.) such that the resources are not exhausted. For such systems with interacting species, modelled by the Lotka-Volterra equations, a set-based approach based on the recent results of the theory of barriers to exactly determine the so-called admissible set (also known as viability kernel) and the maximal robust positively invariant set is presented. Using an example of a larvae-fish based production system, steps to obtain special trajectories which are the boundaries of the admissible set are shown. This admissible set is used to prevent the under and over population of the species in the CEA. Furthermore, conditions of the system parameters are stated, such that the existence of these trajectories can be guaranteed.

关键词： Nonlinear systems Continuous time systems system analysis Constraint satisfaction problems Sets controlled environment agriculture

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A reinforcement learning method with closed-loop stability guarantee

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IFAC-PapersOnLine 2020年第2期53卷 8043-8048页

作者： Pavel Osinenko Lukas Beckenbach Thomas Göhrt Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Laboratory Germany

Reinforcement learning (RL) in the context of control systems offers wide possibilities of controller adaptation. Given an infinite-horizon cost function, the so-called critic of RL approximates it with a neural net and sends this information to the controller (called “actor”). However, the issue of closed-loop stability under an RL-method is still not fully addressed. Since the critic delivers merely an approximation to the value function of the corresponding infinite-horizon problem, no guarantee can be given in general as to whether the actor’s actions stabilize the system. Different approaches to this issue exist. The current work offers a particular one, which, starting with a (not necessarily smooth) control Lyapunov function (CLF), derives an online RL-scheme in such a way that practical semi-global stability property of the closed-loop can be established. The approach logically continues the work of the authors on parameterized controllers and Lyapunov-like constraints for RL, whereas the CLF now appears merely in one of the constraints of the control scheme. The analysis of the closed-loop behavior is done in a sample-and-hold (SH) manner thus offering a certain insight into the digital realization. The case study with a non-holonomic integrator shows the capabilities of the derived method to optimize the given cost function compared to a nominal stabilizing controller.

关键词： Reinforcement learning control Stability of nonlinear systems Lyapunov methods

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A method of online traction parameter identification and mapping

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IFAC-PapersOnLine 2020年第2期53卷 13933-13938页

作者： Alexander Kobelski Pavel Osinenko Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Laboratory Germany

Fuel consumption of heavy-duty vehicles such as tractors, bulldozers etc. is comparably high due to their scope of operation. The operation settings are usually fixed and not tuned to the environmental factors, such as ground conditions. Yet exactly the ground-to-propelling-unit properties are decisive in energy efficiency. Optimizing the latter would require a means of identifying those properties. This is the central matter of the current study. More specifically, the goal is to estimate the ground conditions from the available measurements, such as drive train signals, and to establish a map of those. The ground condition parameters are estimated using an adaptive unscented Kalman filter. A case study is provided with the actual and estimated ground condition maps. Such a mapping can be seen as a crucial milestone in optimal operation control of heavy-duty vehicles.

关键词： Traction control Identification algorithms Data storage Kalman filters Dynamic modelling Vehicle dynamics

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Optimal control of centrifugal spreader

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IFAC-PapersOnLine 2020年第2期53卷 15841-15846页

作者： Franz Rußwurm Pavel Osinenko Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Laboratory Germany

Achieving an evenly distributed fertilization spread pattern is a complex technical task. A corresponding control algorithm must account for the tractor movement, the settings of the spreader, the prescribed dosage as well as machine constraints. It dictates, in particular, the fertilization process needs be estimated ahead to achieve an optimized spread pattern. The presented work is concerned with the development of a predictive control scheme for optimized fertilizer application using modeling of the tractor moving on the field and the spread pattern in form of a crescent behind the tractor. In particular, the form of the spread pattern is modeled via four normal distributions, two for each side of the pattern. The control goal is to achieve a desired fertilizer distribution on the field. The study presents three algorithms for comparison: a one-step optimization and two approaches using model-predictive control – one with a simplified model of the spread pattern in the prediction horizon, and one with a comprehensive one model, respectively. The best results are obtained with model-predictive control using the comprehensive model.

关键词： agriculture control applications model nonlinear control systems normal distribution optimal control optimization predictive control

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Nonsmooth stabilization and its computational aspects

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IFAC-PapersOnLine 2020年第2期53卷 6370-6377页

作者： Pavel Osinenko Patrick Schmidt Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Laboratory Germany

This work has the goal of briefly surveying some key stabilization techniques for general nonlinear systems, for which, as it is well known, a smooth control Lyapunov function may fail to exist. A general overview of the situation with smooth and nonsmooth stabilization is provided, followed by a concise summary of basic tools and techniques, including general stabilization, sliding-mode control and nonsmooth backstepping. Their presentation is accompanied with examples. The survey is concluded with some remarks on computational aspects related to determination of sampling times and control actions.

关键词： Stabilization nonsmooth analysis control Lyapunov function

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On Maximal Robust Positively Invariant Sets in Constrained Nonlinear systems

arXiv

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arXiv 2019年

作者： Esterhuizen, Willem Aschenbruck, Tim Streif, Stefan Automatic Control and System Dynamics Laboratory Technische Universitat Chemnitz Germany

In this technical communiqu_e we study the maximal robust positively invariant set for state-constrained continuous-time nonlinear systems subjected to a bounded disturbance. Extending results from the theory of barriers, we show that this set is closed and that its boundary consists of two complementary parts, one of which we name the invariance barrier, which consists of trajectories that satisfy the maximum *** Codes 37B35 (Primary), 93C15 (Secondary), 34H05 © 2019, CC BY-NC-ND.

关键词： Constraint satisfaction problems

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