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IFAC-PapersOnLine 2022年第7期55卷 174-180页

作者： Sebastián Espinel-Ríos Bruno Morabito Johannes Pohlodek Katja Bettenbrock Steffen Klamt Rolf Findeisen Analysis and Redesign of Biological Networks Max Planck Institute for Dynamics of Complex Technical Systems Germany Laboratory for System Theory and Automatic Control Otto von Guericke University Magdeburg Germany Control and Cyber-Physical Systems Laboratory TU Darmstadt Germany

Competitive biotechnological processes need to operate over various conditions and adapt to changing economic contexts. Dynamic ATP turnover allows trading off declines in biomass formation and volumetric productivity for enhancements of product yields in fermentations where the product pathway is linked to ATP synthesis. To facilitate its practical implementation, we propose to dynamically manipulate the cellular ATP turnover by putting the ATPase enzyme, which hydrolyzes ATP into ADP, under the control of an optogenetic gene expression system. This allows achieving dynamic control of the ATP wasting online via a tunable external input. While light as control input is promising because it is easily tunable, generally non-invasive/non-toxic, and more affordable than classical chemical inducers, it makes the overall control task challenging. Thus, we derive an expanded version of dynamic enzyme-cost flux balance analysis that takes into account the dynamics of the optogenetic actuator. We then formulate a suitable optimal control problem to find optimal inputs for achieving the desired process performance. We test our approach in simulations using the batch anaerobic lactate fermentation of glucose by Escherichia coli as a case study.

关键词： ATP wasting ATPase optimal control gene expression optogenetics batch fermentation

The Fréchet derivative of the tensor t-function

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arXiv 2023年

作者： Lund, Kathryn Schweitzer, Marcel Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany School of Mathematics and Natural Sciences Bergische Universität Wuppertal Wuppertal42097 Germany

The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in [K. Lund, The tensor t-function: a definition for functions of third-order tensors, Numer. Linear Algebra Appl. 27 (3), e2288]. In this work, we investigate properties of the Fréchet derivative of the tensor t-function and derive algorithms for its efficient numerical computation. Applications in condition number estimation and nuclear norm minimization are explored. Numerical experiments implemented by the t-Frechet toolbox hosted at https://***/katlund/t-frechet illustrate properties of the t-function Fréchet derivative, as well as the efficiency and accuracy of the proposed *** Codes 15A69, 65F60, 65F35 Copyright © 2023, The Authors. All rights reserved.

关键词： Tensors

Efficient and Simple Gaussian Process Supported Stochastic Model Predictive control for Bioreactors using HILO-MPC

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IFAC-PapersOnLine 2022年第7期55卷 922-927页

作者： Bruno Morabito Johannes Pohlodek Lena Kranert Sebastián Espinel-Ríos Rolf Findeisen Laboratory for System Theory and Automatic Control Otto von Guericke University Magdeburg Germany Analysis and Redesign of Biological Networks Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Control and Cyber-Physical Systems Laboratory TU Darmstadt Germany

Model-based control of biotechnological processes is, in general, challenging. Often the processes are complex, nonlinear, and uncertain. Hence modeling tends to be complex and is often inaccurate. For this reason, non-model-based control strategies developed via fask, bench-scale, or pilot plant experiments are often applied in the biotechnology industry. Model-based control and optimization techniques can increase processes’ performance and automation level, thereby decreasing costs and guaranteeing the desired specifications. These rely on a model of the process to make predictions and optimize the inputs to the plant. To improve the quality of the models, it is often helpful to use combined first principle and data-driven models together in a hybrid modeling approach which increases the model prediction capabilities. The residual uncertainty of the hybrid model should be taken into account in the control level to satisfy the process specifications and constraints. This paper proposes to use a stochastic model predictive control scheme that exploits a hybrid, Gaussian processes-based model. We outline the effectiveness of the stochastic model-based approach in combination with a suitable Kalman filter for state estimation considering an example biotechnological process. Furthermore, we underline that appropriate tools exist that allow the simple application of such methods even for the novice user. To do so, we use an open-source Python package — HILO-MPC, which allows the simple yet efficient formulation and solution of machine learning-supported optimal control and estimation problems.

关键词： Predictive control toolbox machine learning Gaussian process uncertain process biotechnology stochastic model predictive control HILO-MPC

On Search for All Roots of a System of Quadratic Equations 12th

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On Search for All Roots of a System of Quadratic Equations

12th International Conference on Optimization and Applications, OPTIMA 2021

作者： Gruzdeva, Tatiana V. Khamisov, Oleg V. Matrosov Institute for System Dynamics and Control Theory of SB RAS 134 Lermontov Street Irkutsk664033 Russia Melentiev Energy Systems Institute of SB RAS 130 Lermontov Street Irkutsk664033 Russia

ISBN: (纸本)9783030910587

We propose an approach to finding the roots of systems of quadratic equations in a box. This approach is based on a reduction to an auxiliary optimization problem. The auxiliary problem turns out to be, in general, a nonconvex optimization problem, with the objective function and inequality constraints given by d.c. functions. We use the linearization technique with respect to the basic nonconvexity and box partition procedure to try to find all solutions of the system or proof that there are no solutions in the box. The results of the computational simulation are given. © 2021, Springer Nature Switzerland AG.

关键词： Quadratic programming

Low-rank-modified Galerkin methods for the Lyapunov equation

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arXiv 2023年

作者： Lund, Kathryn Palitta, Davide Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany Dipartimento di Matematica Piazza di Porta S. Donato 5 Bologna40126 Italy

Of all the possible projection methods for solving large-scale Lyapunov matrix equations, Galerkin approaches remain much more popular than minimal-residual ones. This is mainly due to the different nature of the projected problems stemming from these two families of methods. While a Galerkin approach leads to the solution of a low-dimensional matrix equation per iteration, a matrix least-squares problem needs to be solved per iteration in a minimal-residual setting. The significant computational cost of these least-squares problems has steered researchers towards Galerkin methods in spite of the appealing properties of minimal-residual schemes. In this paper we introduce a framework that allows for modifying the Galerkin approach by low-rank, additive corrections to the projected matrix equation problem with the two-fold goal of attaining monotonic convergence rates similar to those of minimal-residual schemes while maintaining essentially the same computational cost of the original Galerkin method. We analyze the well-posedness of our framework and determine possible scenarios where we expect the residual norm attained by two low-rank-modified variants to behave similarly to the one computed by a minimal-residual technique. A panel of diverse numerical examples shows the behavior and potential of our new *** Codes 65F45, 65F50, 65F10, 65N22, 65J10 Copyright © 2023, The Authors. All rights reserved.

关键词： Galerkin methods

Optimization in a traffic flow model as an inverse problem in the Wasserstein space

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IFAC-PapersOnLine 2022年第16期55卷 32-37页

作者： Roman Chertovskih Fernando Lobo Pereira Nikolay Pogodaev Maxim Staritsyn Research Center for Systems and Technologies (SYSTEC) Faculdade de Engenharia Universidade do Porto Portugal Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences Irkutsk Russia

We address an inverse problem for a dynamical system in the space of probability measures, namely, the problem of restoration of the time-evolution of a probability distribution from certain given statistical information. The dynamics of the distribution is described by a nonlocal continuity equation in the Wasserstein space of probability measures. For the simplest version of this problem, associated with a toy one-dimensional model of traffic flow, we derive a necessary optimality condition and design, on its base, a numerical algorithm of the type of gradient descent. We also discuss some technical aspects of the realization of the elaborated algorithm, and present the results of computational experiments implementing an eloquent numeric scenario.

关键词： Nonlocal continuity equation Wasserstein space inverse problems traffic flow models gradient descent pseudospectral methods

Optimization of the composition of the structure of heat sources as applied to the problems of the development of heating systems 2

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Optimization of the composition of the structure of heat sou...

2nd International Scientific Conference on Sustainable and Efficient Use of Energy, Water and Natural Resources, SEWAN 2019

作者： Stennikov, V.A. Edeleva, O.A. Fereferov, E.S. Melentiev Energy Systems Institute of SB RAS Russia Matrosov Institute for System Dynamics and Control Theory of SB RAS Russia

The study outlines the concept of the structure of heat sources of developing heating systems and states the problem of searching through structures of heat sources of maximum redundancy for the optimal one. As one of the techniques of solving this problem, the authors propose to split the process of designing heating systems into multiple stages. Within the scope of the above-stated problem, the difficult part is the need to create an automated system to solve the entirety of problems arising at these stages and to reconcile them with each other. We provide a brief overview of the the available software package that we propose to integrate into the process of solving and we underline the complex nature of the interaction of individual software components between each other. The authors propose an approach in the form of the computational experiment setup that enables to consistently coordinate computational procedures with each other. The approach is based on the concept of the energy hub as its theoretical backbone, while in terms of the software implementation it is an instance of an automated information system. © 2020 IOP Publishing Ltd.

关键词： Heating equipment

DC-DC Converters Optimization in Case of Large Variation in the Load

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arXiv 2024年

作者： Domyshev, Alexander Chistyakova, Elena Dreglea, Aliona Sidorov, Denis Liu, Fang Melentiev Energy Systems Institute Siberian Branch Russian Academy Sciences Irkutsk Russia Harbin Institute of Technology Harbin China Irkutsk National Research Technical University Irkutsk Russia Institute for System Dynamics and Control Theory Siberian Branch Russian Academy Sciences Irkutsk Russia Department of Automation Central South University Changsha China

The method for controlling a DC-DC converter is proposed to ensures the high quality control at large fluctuations in load currents by using differential gain control coefficients and second derivative control. Various implementations of balancing the currents of a multiphase DC-DC converter are discussed, with a focus on achieving accurate current regulation without introducing additional delay in the control system. Stochastic particle swarm optimization method is used to find optimal values of the PID controller parameters. An automatic constraint-handling in optimization are also discussed as relevant techniques in the *** Codes 34H05 34A09 © 2024, CC BY.

关键词： Stochastic systems

Explosive synchronization in multiplex neuron-glial networks

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arXiv 2023年

作者： Laptyeva, Tetyana Jalan, Sarika Ivanchenko, Mikhail Department of Control Theory and Systems Dynamics Lobachevsky State University of Nizhny Novgorod Nizhny Novgorod Russia Complex Systems Lab Department of Physics Indian Institute of Technology Indore Indore Simrol452020 India Department of Applied Mathematics Laboratory of Systems Medicine of Healthy Aging Lobachevsky State University of Nizhny Novgorod Nizhny Novgorod Russia

Explosive synchronization refers to an abrupt (first order) transition to non-zero phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this phenomenon might be no less general then the celebrated Kuramoto scenario that belongs to the second order universality class. Importantly, the recent examples demonstrate that explosive synchronization can occur for certain network topologies and coupling types, like the global higher-order coupling, without specific requirements on the individial oscillator dynamics or dynamics-network correlations. Here we demonstrate a rich picture of explosive synchronization and desynchronization transitions in multiplex networks, where it is sufficient to have a single random sparsly connected layer with higher-order coupling terms (and not necessarily in the synchronization regime on its own), the other layer being a regular lattice without own phase transitions at all. Moreover, explosive synchronization emerges even when the random layer has only low-order pairwise coupling, althoug the hysteresis interval becomes narrow and explosive desynchronization is no longer observed. The relevance to the normal and pathological dynamics of neural-glial networks is pointed out. © 2023, CC BY.

关键词： Synchronization

INTERPOLATORY H2-OPTIMALITY CONDITIONS FOR STRUCTURED LINEAR TIME-INVARIANT systems

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arXiv 2023年

作者： Mlinarić, Petar Benner, Peter Gugercin, Serkan Department of Mathematics Virginia Tech BlacksburgVA24061 United States Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

Interpolatory necessary optimality conditions for H2-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on L2-optimal reduced-order modeling of stationary parametric problems, in this paper we develop and investigate optimality conditions for H2-optimal reduced-order modeling of structured LTI systems, in particular, for second-order, port-Hamiltonian, and time-delay systems. Under certain diagonalizability assumptions, we show that across all these different structured settings, bitangential Hermite interpolation is the common form for optimality, thus proving a unifying optimality framework for structured reduced-order modeling. Copyright © 2023, The Authors. All rights reserved.

关键词： Linear time-invariant system