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Synthesis of Lyapunov functions using formal verification

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arXiv 2021年

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

Recent employments of SMT solvers within the Lyapunov function synthesis provided effective tools for automated construction of Lyapunov functions alongside with sound computer-assisted certificates. The main benefit of the suggested approach is the formal correctness and elimination of the numerical uncertainty. In the present work we extend the SMT-based synthesis approach for wider classes of continuous and discrete-time systems. Additionally, we address constructions of Lyapunov functions for state-dependent switching systems. We illustrate our approach by means of various examples from the control systems literature. © 2021, CC BY-NC-ND.

关键词： Lyapunov functions

Synthesis of interconnected control systems under reachability specifications

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Synthesis of interconnected control systems under reachabili...

IEEE Conference on Decision and control

作者： Mohammad Al Khatib Stefan Streif Automatic Control and System Dynamics Lab Technische Universität Chemnitz Chemnitz Germany

ISBN: (纸本)9781665436601

In this work we synthesize constrained control laws in a compositional way to enforce a reachability specification for an interconnected control system. We first synthesize for each system a controller enforcing a local reachability specification using linear feasibility programs. Then within the framework of parametric assume-guarantee contracts, which encode the behavior of a control system in a parametric domain, we establish a small gain theorem guaranteeing the overall specification after interconnecting the systems together. The resulting controller could then be implemented in a decentralized, distributed, or mixed setup. We also show the effectiveness of our approach with a room temperature control example.

关键词： Heating systems Conferences Production Interconnected systems Predictive models Aerospace electronics control systems

Formal verification of a controller implementation in fixed-point arithmetic

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arXiv 2021年

作者： Flessing, Lars Devadze, Grigory Streif, Stefan The 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. © 2021, CC BY-NC-ND.

关键词： controllers

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

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

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

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arXiv 2021年

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

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. © 2021, CC BY-NC-ND.

关键词： Robust control

Global Observability Analysis of a Growth Model for Insects Farming

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Global Observability Analysis of a Growth Model for Insects ...

European control Conference (ECC)

作者： Rania Tafat Jaime A. Moreno Stefan Streif Technische Universität Chemnitz Chemnitz Germany Automatic Control and System Dynamics Lab Eléctrica y Computación Instituto de Ingeniería-UNAM Universidad Nacional Autónoma de México Department of Bioresources Fraunhofer Institute for Molecular Biology and Applied Ecology Giessen Germany

ISBN: (数字)9783907144107

ISBN: (纸本)9798331540920

The Hermetia illucens insects or the black soldier fly has been attracting a growing interest in the food and feed industry. For its high nutritional value on the one hand, and because it is an adequate species for insects in controlled environmental agriculture systems, on the other. Therefore, several models describing this larvae's behaviour have been developed in the literature. Due to the complex nature of living organisms, systems of controlled environment agriculture are characterised by their strong nonlinearities. In this paper, we present a three dimensional nonlinear model describing the black soldier fly dry biomass weight dynamic changes due to the temperature's influence. In practice, this biomass weight is not measured in real time. This becomes problematic for applying feedback control strategies that assume full information of the states. Thus, this work investigates the observability of the dry biomass of a Hermetia illucens farming batch. The instantaneous and global observability of the aforementioned model is proven by constructing an injective transformation between the state space and a higher dimensional space where the transformed states are observable.

关键词： Temperature measurement Weight measurement Analytical models Biological system modeling Insects Observers Time measurement

Global observability analysis of a growth model for insects farming

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arXiv 2024年

作者： Tafat, Rania Moreno, Jaime A. Streif, Stefan The Technische Universität Chemnitz Chemnitz09126 Germany Automatic Control and System Dynamics Lab The Eléctrica y Computación Instituto de Ingeniería UNAM Universidad Nacional Autónoma de México Mexico The Fraunhofer Institute for Molecular Biology and Applied Ecology Department of Bioresources Giessen Germany

The Hermetia illucens insects or the black soldier fly has been attracting a growing interest in the food and feed industry. For its high nutritional value on the one hand, and because it is an adequate species for insects in controlled environmental agriculture systems, on the other. Therefore, several models describing this larvae’s behaviour have been developed in the literature. Due to the complex nature of living organisms, systems of controlled environment agriculture are characterised by their strong nonlinearities. In this paper, we present a three dimensional nonlinear model describing the black soldier fly dry biomass weight dynamic changes due to the temperature’s influence. In practice, this biomass weight is not measured in real time. This becomes problematic for applying feedback control strategies that assume full information of the states. Thus, this work investigates the observability of the dry biomass of a Hermetia illucens farming batch. The instantaneous and global observability of the aforementioned model is proven by constructing an injective transformation between the state space and a higher dimensional space where the transformed states are observable. Copyright © 2024, The Authors. All rights reserved.

关键词： Invertebrates

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