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High-gain observer for the nitrification process including sensor dynamics

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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Observability Analysis of PEM Fuel Cell systems with Anode Recirculation

Observability Analysis of PEM Fuel Cell Systems with Anode R...

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European control Conference (ECC)

作者： Michael Hauck Felix Petzke Rania Tafat Stefan Streif Automatic Control and System Dynamics Lab Technische Universität Chemnitz Chemnitz Germany

ISBN: (数字)9783907144107

ISBN: (纸本)9798331540920

The optimal control of gas partial pressures in fuel cell systems is a key part to increase the efficiency and the lifetime of the fuel cell. In automotive applications, the nitrogen and hydrogen gas partial pressures are not measurable with actual sensors. Therefore an observer is required to determine the gas partial pressures in the fuel cell system. In this paper we present an observability analysis for PEM fuel cell systems with anode recirculation for an automotive application. The fuel cell stack voltage and the total gas pressure in front of the fuel cell are assumed as measurable outputs. The opening of the input valve and purge valve as well as the total pressure at the cathode are inputs. The fuel cell stack current is a measurable disturbance. It is shown that the hydrogen and nitrogen partial pressures in front of the fuel cell, inside the fuel cell, and behind the fuel cell are globally differentially observable as long as the fuel cell system is not in idle mode. As a result, asymptotic and finite time observers can be used to observe the total pressures and partial hydrogen pressures in an fuel cell system with anode recirculation.

关键词： Voltage measurement Current measurement Hydrogen Automotive applications Fuel cells Observers Valves

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Formal proofs for Lyapunov stability theorems in exact real arithmetic

Formal proofs for Lyapunov stability theorems in exact real ...

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European control Conference (ECC)

作者： Grigory Devadze Stefan Streif Automatic Control and System Dynamics Lab Technische Universität Chemnitz Germany

We present computer-assisted proofs for Lyapunov stability theorems for autonomous discrete-time dynamical systems. Our approach is supported by the concrete formally-verified realization of the exact real arithmetic. The selected variants of the Lyapunov stability theorems are reproduced within the proof system Minlog. Finally, we demonstrate how the formal proofs can be reused to prove other Lyapunovrelated theorems and the soundness of discrete-time backstepping control design

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Extraction of a computer-certified SMT solver for nonlinear theories

Extraction of a computer-certified SMT solver for nonlinear ...

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European control Conference (ECC)

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

We present an effective procedure for solving of the so-called $\delta-$satisfiability modulo theory (SMT) problem over the reals. Our methods are supported by the special approach to the exact real arithmetic: constructive analysis. First, we present an alternative proof of the decidability of the bounded $\delta-$SMT problem within our framework and an efficient branch-and-bound algorithm, which is based on the rational interval arithmetic. We provide some initial experiments to demonstrate the applicability of the derived solver. Finally, we discuss potential extensions and possible optimizations of the suggested algorithm.

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Safety-Critical control for Ensemble systems

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IFAC-PapersOnLine 2023年第2期56卷 3152-3157页

作者： Yang Guo Felix Petzke Philipp Rumschinski Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Lab Hochschule Furtwangen Faculty of Mechanical and Medical Engineering

In this paper, we derive set constraints for a reduced order model and augment them into a model predictive control (MPC) scheme to ensure safe operation of the large-scale ensemble system. For the control feedback, only the aggregated information of the whole system is required. For the constraint satisfaction, we consider an adaptive tube formulation to characterize the deviation between the reduced order model and the ensemble system. Employing the robust control invariant set, we ensure recursive feasibility and initial feasibility under an easily verifiable condition.

关键词： robust control model predictive and optimization-based control constrained control linear systems feasibility ensemble systems

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A map-based model predictive control approach for train operation

A map-based model predictive control approach for train oper...

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European control Conference (ECC)

作者： Michael Hauck Patrick Schmidt Alexander Kobelski Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Lab Chemnitz Germany

Trains are a corner stone of public transport and play an important role in daily life. A challenging task in train operation is to avoid skidding and sliding, i.e. spinning or blocking of the wheels, during fast changes of traction conditions, which can, for example, occur due to changing weather conditions, crossings, tunnels or forest entries. The latter depends on local track conditions and can be recorded in a map together with other location-dependent information like speed limits and inclination. In this paper, a model predictive control (MPC) approach is developed. Thanks to the knowledge of future changes of traction conditions, the approach is able to avoid short-term skidding and sliding even under fast changes of traction conditions. In a first step, an optimal reference trajectory is determined by a multiple-shooting approach. In a second step, the reference trajectory is tracked by an MPC setup. The developed method is simulated along a track with fast-changing traction conditions for different scenarios, like changing weather conditions and unexpected delays. In all cases, skidding and sliding is avoided.

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Formal Verification of a controller Implementation in Fixed-Point Arithmetic

Formal Verification of a Controller Implementation in Fixed-...

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European control Conference (ECC)

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

For the implementations of controllers on digital processors, certain limitations, e.g. in the instruction set and register length, need to be taken into account, especially for safety-critical applications. This work aims to provide a computer-certified inductive definition for the control functions that are implemented on such processors accompanied with the fixed-point data type in a proof assistant. Using these inductive definitions we formally ensure correct realization of the controllers on a digital processor. Our results guarantee overflow-free computations of the implemented control algorithm. The method presented in this paper currently supports functions that are defined as polynomials within an arbitrary fixed-point structure. We demonstrate the verification process in the case study on an example with different scenarios of fixed-point type implementations.

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A map-based model predictive control approach for train operation

arXiv

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arXiv 2023年

作者： Hauck, Michael Schmidt, Patrick Kobelski, Alexander Streif, Stefan Technische Universität Chemnitz Chemnitz09126 Germany Automatic Control and System Dynamics Lab

关键词： Model predictive control

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Some remarks on practical stabilization via CLF-based control under measurement noise

arXiv

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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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