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Formal Verification of a controller Implementation in Fixed-Point Arithmetic

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

European control Conference (ECC)

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

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Tracking of stabilizing, optimal control in fixed-time based on time-varying objective function

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Tracking of stabilizing, optimal control in fixed-time based...

IEEE Conference on Decision and control

作者： Patrick Schmidt Thomas Göhrt Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Lab Chemnitz Germany

ISBN: (纸本)9781665436601

The controller of an input-affine system is determined through minimizing a time-varying objective function, where stabilization is ensured via a Lyapunov function decay condition as constraint. This constraint is incorporated into the objective function via a barrier function. The time-varying minimum of the resulting relaxed cost function is determined by a tracking system. This system is constructed using derivatives up to second order of the relaxed cost function and improves the existing approaches in time-varying optimization. Under some mild assumptions, the tracking system yields a solution which is feasible for all times, and it converges to the optimal solution of the relaxed objective function in a user-defined fixed-time. The effectiveness of these results in comparison to exponential convergence is demonstrated in a case study.

关键词： Conferences Optimal control Linear programming Cost function Time-varying systems Lyapunov methods Convergence

Observability Analysis of PEM Fuel Cell systems with Anode Recirculation

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

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

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

A map-based model predictive control approach for train operation

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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

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. © 2023, 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

Analysis of extremum value theorems for function spaces in optimal control under numerical uncertainty

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arXiv 2017年

作者： Osinenko, Pavel Streif, Stefan Automatic Control and System Dynamics Lab Technische Universität Chemnitz Chemnitz09107 Germany

The extremum value theorem for function spaces plays the central role in optimal control. It is known that computation of optimal control actions and policies is often prone to numerical errors which may be related to computability issues. The current work addresses a version of the extremum value theorem for function spaces under explicit consideration of numerical uncertainties. It is shown that certain function spaces are bounded in a suitable sense, i. e., they admit finite approximations up to an arbitrary precision. The proof of this fact is constructive in the sense that it explicitly builds the approximating functions. Consequently, existence of approximate extremal functions is shown. Applicability of the theorem is investigated for finite-horizon optimal control, dynamic programming and adaptive dynamic programming. Some possible computability issues of the extremum value theorem in optimal control are shown on counterexamples. Copyright © 2017, The Authors. All rights reserved.

关键词： Dynamic programming

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

Tracking of stabilizing, optimal control in fixed-time based on time-varying objective function

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arXiv 2021年

作者： Schmidt, Patrick Göhrt, Thomas Streif, Stefan Technische Universität Chemnitz Automatic Control and System Dynamics Lab Chemnitz09126 Germany

关键词： Cost functions