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Optimal control of viscous fingering

JOURNAL OF PROCESS CONTROL 2024年 135卷

作者： Petit, Nicolas PSL Univ Ctr Automat & Syst MINES Paris 60 Bd St Michel F-75272 Paris France

The paper considers the problem of optimally filling a Hele-Shaw cell. The system is subject to viscous fingering effect. It is shown that, despite the threshold terms appearing on the right-hand side of the governing equations, the dynamics can be rewritten using several prime integrals. This allows reforming optimal control problems for the Fourier modes describing the fluid interface into smooth optimization problems, in the sense of Gateaux derivative. Some numerical experiments illustrate the advantages of using the optimal solutions obtained using this reformulation instead of the currently known time-dependent injection rates.

关键词： Microfluidics Control of micro- and nano-systems Non-smooth optimal control problems Hele-Shaw cell distributed parameters systems

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Motion Planning for Viscous Fingering

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IEEE CONTROL systems LETTERS 2024年 8卷 1409-1414页

作者： Petit, Nicolas PSL Univ Ctr Automatique & Syst Mines Paris F-75272 Paris France

This letter considers the problem of controlling the shape of the moving interface between two fluids contained in a Hele-Shaw cell during its filling. This system is subject to viscous fingering. The interface shape dynamics is described using a modal decomposition where each mode is governed by a non-smooth ordinary differential equation with a random initial condition that is unknown. Once the interface is visibly non circular, a motion planning technique is employed to control the growth of the modes with the goal of approaching a shape of interest. This letter describes the dynamics at stake, studies its reachability property and proposes a constructive method to solve the motion planning problem. Some numerical experiments illustrate the presented methodology.

关键词： Shape Fluids Planning Dynamics Viscosity Mathematical models Fingers Microfluidics control of micro- and nano-systems non-smooth dynamics Hele-Shaw cell distributed parameters systems motion planning

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Optimal Energy-Efficient Control in distributed Parameter systems

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OPTOELECTRONICS INSTRUMENTATION AND DATA PROCESSING 2021年第4期57卷 345-355页

作者： Pleshivtseva, Yu E. Rapoport, E. Ya Samara State Tech Univ Samara 443100 Russia

A method for analytical construction of optimal regulators in problems of energy-efficient control of linear distributed parameters systems under conditions of a given accuracy of the uniform approximation of the terminal state of the object to the required spatial distribution of the controlled quantity is proposed. The developed approach is based on the previously designed alternance method of constructing parameterized algorithms of optimal programmed control. It is shown that the sought procedure of optimal regulator design is reduced to constructing a linear feedback control system by incomplete measurement of the state. The feedback transfer coefficients are known functions of time and finite values of the controlled quantity which are determined by preliminary calculation of the programmed control action.

关键词： distributed parameters systems minimum energy consumption programmed control alternance method optimal control design optimal regulator

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State feedback control law design for an age-dependent SIR model

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AUTOMATICA 2023年 158卷

作者： Sonveaux, Candy Winkin, Joseph J. Univ Namur Dept Math Rue Bruxelles 61 B-5000 Namur Belgium naXys Rue Bruxelles 61 B-5000 Namur Belgium

An age-dependent SIR model is considered with the aim to develop a state-feedback vaccination law in order to eradicate a disease. A dynamical analysis of the system is performed using the principle of linearized stability and shows that, if the basic reproduction number is larger than 1, the disease free equilibrium is unstable. This result justifies the development of a vaccination law. Two approaches are used. The first one is based on a discretization of the partial integro-differential equations (PIDE) model according to the age. In this case a linearizing feedback law is found using Isidori's theory. Conditions guaranteeing stability and positivity are established. The second approach yields a linearizing feedback law developed for the PIDE model. This law is deduced from the one obtained for the ODE case. Using semigroup theory, stability conditions are also obtained. Finally, numerical simulations are presented to reinforce the theoretical arguments.(c) 2023 Elsevier Ltd. All rights reserved.

关键词： Epidemiology Nonlinear system distributed parameters systems Partial integro-differential equations Dynamical analysis Semigroup Feedback law Stability

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Control systems with Tomographic Sensors-A Review

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SENSORS 2022年第8期22卷 2847页

作者： Hlava, Jaroslav Abouelazayem, Shereen Tech Univ Liberec Inst Mechatron & Comp Engn Fac Mechatron Informat & Interdisciplinary Studie Liberec 46117 Czech Republic

Industrial process tomography offers two key advantages over conventional sensing systems. Firstly, process tomography systems provide information about 2D or 3D distributions of the variables of interest. Secondly, tomography looks inside the processes without penetrating them physically, i.e., sensing is possible despite harsh process conditions, and the operation of the process is not disturbed by intrusive sensors. These advantages open new perspectives for the field of process control, and the potential of closed-loop control applications is one of the main driving forces behind the development of industrial tomography. Despite these advantages and decades of development, closed-loop control applications of tomography are still not really common. This article provides an overview of the current state-of-the-art in the field of control systems with tomographic sensors. An attempt is made to classify the different control approaches, critically assess their strengths and weak points, and outline which directions may lead to increased future utilization of industrial tomography in the closed-loop feedback control.

关键词： industrial process tomography process control control systems in process engineering distributed parameters systems

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Geometric spatial reduction for port-Hamiltonian systems

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systems & CONTROL LETTERS 2019年 125卷 1-8页

作者： Ngoc Minh Trang Vu Lefevre, Laurent Maschke, Bernhard Univ Grenoble Alpes LCIS Grenoble INP F-26000 Valence France Univ Claude Bernard Lyon 1 Lab Automat & Genie Proc Lyon France

A geometric spatial reduction method is presented in this paper. It applies to port Hamiltonian models for open systems of balance equations. It is based on projections which make use of the spatial symmetries in the model and preserve the "natural" power pairing. Reductions from 3D to 2D and 1D domains are illustrated via two examples. The first one is a vibro-acoustic system with cylindrical symmetry where 3D-2D reduction is applied. The second one is the system of two coupled parabolic equations describing the poloidal magnetic flux diffusion and heat radial transport in tokamak reactors. In this latter example the toroidal symmetry allows to perform a 3D-1D reduction. Obtained reduced models are compared with the common control models found in the literature for these two examples. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Geometric reduction distributed parameters systems Port Hamiltonian systems Tokamak plasma control Vibro-acoustic system

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A PDE approach to deployment of mobile agents under leader relative position measurements

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AUTOMATICA 2019年 106卷 47-53页

作者： Wei, Jieqiang Fridman, Emilia Johansson, Karl Henrik KTH Royal Inst Technol Sch Elect Engn & Comp Sci Dept Automat Control SE-10044 Stockholm Sweden Tel Aviv Univ Sch Elect Engn Tel Aviv Israel

We study the deployment of a first-order multi-agent system over a desired smooth curve in 2D or 3D space. We assume that the agents have access to the local information of the desired curve and their relative positions with respect to their closest neighbors, whereas in addition a leader is able to measure his relative position with respect to the desired curve. For the case of an open C-2 curve, we consider two boundary leaders that use boundary instantaneous static output-feedback controllers. For the case of a closed C-2 curve we assume that the leader transmits his measurement to other agents through a communication network. The resulting closed-loop system is modeled as a heat equation with a delayed (due to the communication) boundary state, where the state is the relative position of the agents with respect to the desired curve. By choosing appropriate controller gains (the diffusion coefficient and the gain multiplying the leader state), we can achieve any desired decay rate provided the delay is small enough. The advantage of our approach is in the simplicity of the control law and the conditions. Numerical example illustrates the efficiency of the method. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： distributed parameters systems Multi-agent systems Time delays Deployment

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A sliding mode observer for a linear reaction-convection-diffusion equation with disturbances

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systems & CONTROL LETTERS 2019年 124卷 40-48页

作者： Dimassi, Habib Winkin, Joseph J. Vande Wouwer, Alain Univ Sousse High Inst Appl Sci & Technol Sousse Sousse 4003 Tunisia Univ Namur NaXys 8 Rempart Vierge B-5000 Namur Belgium Univ Namur Dept Math 8 Rempart Vierge B-5000 Namur Belgium Univ Mons Lab Automat 31 Blvd Dolez B-7000 Mons Belgium Natl Engn Sch Monastir LA2SE Monastir Tunisia

A sliding mode observer is designed and analyzed for a linear reaction-convection-diffusion equation subject to external disturbances. Based on a discontinuous input, the proposed observer ensures both state estimation and disturbance rejection using only one boundary measurement. An appropriate Lyapunov function is used to prove the asymptotic convergence of the observation error. The performance of the proposed observer is illustrated by some numerical simulation results. (C) 2018 Elsevier B.V. All rights reserved.

关键词： distributed parameters systems Partial differential equations Sliding modes Observer design Reaction-convection-diffusion equation

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Multi-agent deployment under the leader displacement measurement: a PDE-based approach 18

Multi-agent deployment under the leader displacement measure...

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18th European Control Conference (ECC)

作者： Wei, Jieqiang Fridman, Emilia Selivanov, Anton Johansson, Karl H. KTH Royal Inst Technol Sch Elect Engn & Comp Sci Dept Automat Control SE-10044 Stockholm Sweden Tel Aviv Univ Sch Elect Engn Tel Aviv Israel

ISBN: (纸本)9783907144008

We study the deployment of a first-order multi-agent system over a desired smooth curve in 3D space. We assume that the agents have access to the local information of the desired curve and their displacements with respect to their closest neighbors, whereas in addition a leader is able to measure his absolute displacement with respect to the desired curve. In this paper we consider the case that the desired curve is a closed C-2 curve and we assume that the leader transmit his measurement to other agents through a communication network. We start the algorithm with displacement-based formation control protocol. Connections from this ODE model to a PDE model (heat equation), which can be seen as a reduced model, are then established. The resulting closed-loop system is modeled as a heat equation with delay (due to the communication). The boundary condition is periodic since the desired curve is closed. By choosing appropriate controller gains (the diffusion coefficient and the gain multiplying the leader state), we can achieve any desired decay rate provided the delay is small enough. The advantage of our approach is in the simplicity of the control law and the conditions. Numerical example illustrates the efficiency of the method.

关键词： distributed parameters systems Lyapunov method Time delays Multi-agent systems Deployment

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Discrete Controllability of distributed parameters systems using Lattice Boltzmann Models: an application to the Shallow Water Equations

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IFAC Proceedings Volumes 2011年第1期44卷 9206-9211页

作者： Diemer Anda Ondo Laurent Lefèvre Bastien Chopard LCIS 50 rue Barthélémy de Laffémas BP54 26902 VALENCE Cedex 09 France LAGEP Université Claude Bernard Lyon 1 bât 308G ESCPE-Lyon 43 bd du 11 Novembre 1918 69622 Villeurbanne Cedex France University of Geneva Batelle Building A 7 route de Drize 1227 Carouge Switzerland

Abstract The Lattice Boltzmann (cellular automata) model equivalent to the 1D shallow water equations is first introduced. Then, its state-space representation with the introduction of input-output variables is presented. Finally, the discrete controllability problem is investigated. First considerations and methods suitable for large scale discrete dynamical systems Gramian computations are presented. Then controllability analysis arguments are developed based on the obtained Gramians and on the convergence of energy properties.

关键词： Lattice Boltzmann models controllability and observability gramians Lyapunov equations distributed parameters systems Shallow water equations

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