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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

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

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arXiv 2020年

作者： Munser, Lukas Hempel, Arne-Jens Devadze, Grigory Streif, Stefan 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. Copyright © 2020, The Authors. All rights reserved.

关键词： Linear systems

A comprehensive dynamic growth and development model of Hermetia illucens larvae

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arXiv 2020年

作者： Padmanabha, Murali Kobelski, Alexander Hempel, Arne-Jens Streif, Stefan Automatic Control and System Dynamics Lab Technische Universitt Chemnitz Chemnitz09107 Germany

Larvae of Hermetia illucens, also commonly known as black soldier fly (BSF) have gained significant importance in the feed industry, primarily used as feed for aquaculture and other livestock farming. Mathematical model such as Von Bertalanffy growth model and dynamic energy budget models are available for modelling the growth of various organisms but have their demerits for their application to the growth and development of BSF. Also, such dynamic models were not yet applied to the growth of the BSF larvae despite models proven to be useful for automation of industrial production process (e.g. feeding, heating/cooling, ventilation, harvesting, etc.). This work primarily focuses on developing a model based on the principles of the afore mentioned models from literature that can provide accurate mathematical description of the dry mass changes throughout the life cycle and the transition of development phases of the larvae. To further improve the accuracy of these models, various factors affecting the growth and development such as temperature, feed quality, feeding rate, moisture content in feed, and airflow rate are developed and integrated into the dynamic growth model. An extensive set of data were aggregated from various literature and used for the model development, parameter estimation and validation. Models describing the environmental factors were individually validated based on the data sets collected. In addition, the dynamic growth model was also validated for dry mass evolution and development stage transition of larvae reared on different substrate feeding rates. The developed models with the estimated parameters performed well highlighting its application in decision-support systems and automation for large scale production. Copyright © 2020, The Authors. All rights reserved.

关键词： Decision support systems

On inf-convolution-based robust practical stabilization under computational uncertainty

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arXiv 2021年

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

This work is concerned with practical stabilization of nonlinear systems by means of inf-convolution-based sample-and-hold control. It is a fairly general stabilization technique based on a generic non-smooth control Lyapunov function (CLF) and robust to actuator uncertainty, measurement noise, etc. The stabilization technique itself involves computation of descent directions of the CLF. It turns out that non-exact realization of this computation leads not just to a quantitative, but also qualitative obstruction in the sense that the result of the computation might fail to be a descent direction altogether and there is also no straightforward way to relate it to a descent direction. Disturbance, primarily measurement noise, complicate the described issue even more. This work suggests a modified inf-convolution-based control that is robust w. r. t. system and measurement noise, as well as computational uncertainty. The assumptions on the CLF are mild, as, e. g., any piece-wise smooth function, which often results from a numerical LF/CLF construction, satisfies them. A computational study with a three-wheel robot with dynamical steering and throttle under various tolerances w. r. t. computational uncertainty demonstrates the relevance of the addressed issue and the necessity of modifying the used stabilization technique. Similar analyses may be extended to other methods which involve optimization, such as Dini aiming or steepest descent. © 2021, CC BY-NC-ND.

关键词： Nonlinear systems

A Hierarchical MPC Scheme for Ensembles of Hammerstein systems

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IFAC-PapersOnLine 2020年第2期53卷 6951-6956页

作者： Felix Petzke Marcello Farina Stefan Streif Technische Universität Chemnitz Automatic Control & System Dynamics Lab Chemnitz Germany Dipartimento di Elettronica Informazione e Bioingegneria Politecnico di Milano Milan Italy

Hierarchical control approaches have been one of the elective methods for the optimal control of large-scale systems in the last decades. In (Petzke et al., 2018) we presented a multirate hierarchical MPC scheme for linear systems, with remarkable flexibility and scalability properties. In this paper we extend the former approach to ensembles of Hammerstein systems and we complement the method by proposing a suitable high-level optimizer. The theoretical properties are discussed in the light of the theoretical properties of the former method. Lastly, an example case study is presented to show the effectiveness of the proposed method.

关键词： Hierarchical control model predictive control Hammerstein systems

PoCET: a Polynomial Chaos Expansion Toolbox for Matlab

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IFAC-PapersOnLine 2020年第2期53卷 7256-7261页

作者： Felix Petzke Ali Mesbah Stefan Streif Automatic Control & System Dynamics Lab at Technische Universität Chemnitz Faculty for Electrical Engineering and Information Technology Chemnitz Germany Department of Chemical and Biomolecular Engineering University of California Berkeley CA USA

We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic parameters or initial conditions, as well as several simulation tools. It offers a built-in handling of Gaussian, uniform, and beta probability density functions, projection and collocation-based calculation of PCE coefficients, and the calculation of stochastic moments from a PCE. Efficient algorithms for the calculation of the involved integrals have been designed in order to increase its applicability. PoCET comes with a variety of introductory and instructive examples. Throughout the paper we show how to perform a polynomial chaos expansion on a simple ordinary differential equation using PoCET, as well as how it can be used to solve the more complex task of optimal experimental design.

关键词： polynomial chaos simulation tools optimal experiment design optimal control

Reserve Balancing in a Microgrid system for Safety Analysis ⁎

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IFAC-PapersOnLine 2020年第2期53卷 13581-13586页

作者： Clemens Kiebler Ionela Prodan Felix Petzke Stefan Streif Technische Universität Chemnitz Automatic Control and System Dynamics Lab Univ. Grenoble Alpes Grenoble INP Institute of Engineering Univ. Grenoble Alpes. LCIS F-26000 Valence

This work presents a robust MPC (Model Predictive control) approach for reserve balancing in DC microgrid systems under uncertainties like wind power and energy price variations and different types of fault events. The robust MPC algorithm considers a variable-length prediction horizon which accounts for forecasts in energy price and renewable power over one day. Furthermore, a storage system is used to increase the utility of the demands and minimize the energy costs. The algorithm is tested for multiple fault types which affect the system (line and loss of power faults).

关键词： Energy management systems DC microgrid Fault events Distributed energy resources Robust MPC (Model Predictive control)

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

COMPUTER-ASSISTED PROOFS FOR LYAPUNOV STABILITY VIA SUMS OF SQUARES CERTIFICATES AND CONSTRUCTIVE ANALYSIS

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arXiv 2020年

作者： Devadze, Grigory Magron, Victor Streif, Stefan Technische Universität Chemnitz Automatic Control and System Dynamics Lab Chemnitz09107 Germany LAAS 7 avenue du Colonel Roche Toulouse31077 Cedex 4 France

We provide a computer-assisted approach to ensure that a given discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analysis together with formally certified sums of squares Lyapunov functions. The crucial steps are formalized within the proof assistant Minlog. We illustrate our approach with various examples issued from the control system literature. Copyright © 2020, The Authors. All rights reserved.

关键词： Lyapunov functions