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Filtering Discrete-Time systems With Multiplicative Noise in L2 Spaces With Applications

IEEE CONTROL systems LETTERS 2022年 6卷 734-739页

作者： Cacace, Filippo d'Angelo, Massimiliano De Iuliis, Vittorio Germani, Alfredo Univ Campus Biomed Roma CIR I-00144 Rome Italy Univ Milano Bicocca Dept Biotechnol & Biosci I-20126 Milan Italy Univ Aquila Dipartimento Ingn & Sci Informaz & Matemat I-67100 Laquila Italy

In this work we adopt a novel formulation of the distributed parameters recursive filter for discrete-time systems evolving in L-2 spaces to widen the class of systems that can be processed by a state estimation algorithm. Starting from a rigorous definition of Kronecker algebra on L-2 spaces that involves both elements and bounded operators of L-2, we provide a computationally efficient solution in the case of linear systems with multiplicative noises. We illustrate the potential application of the approach by developing a case-study concerning the conceptual design of a distributed thermo-couple in the presence of the Nyquist-Johnson noise.

关键词： distributed parameter systems filtering discrete-time systems

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Model-Based Feedforward Control of an Intra- and Interspecific Competitive Population System

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IEEE CONTROL systems LETTERS 2022年 6卷 3397-3402页

作者： Kurth, Anna-Carina Veil, Carina Sawodny, Oliver Univ Stuttgart Inst Syst Dynam D-70563 Stuttgart Germany

Intra- and interspecific competitive population systems are relevant for a variety of applications, such as bioreactors or wastewater treatment plants. These systems are described by coupled hyperbolic semilinear integro partial differential equations with non-local integral boundary conditions. This type of population system has not been considered in the context of control theory in the literature to date. It is assumed that it is possible to measure both species separately, but only one control input is available, namely the dilution rate. A system analysis allows for the determination of infinitely many, but uniquely determined steady-states that are used to derive nonlinear input-output dynamics via the relation of hyperbolic partial differential equations to integral delay equations. A model inversion yields a feedforward control to control the two different outputs, which are a weighted integral over the population density. This results in a restriction in the choice of reference trajectories due to the undercount of inputs. Simulations show the great potential that can be achieved with model-based feedforward control in the context of population systems.

关键词： Statistics Sociology Steady-state Predator prey systems Biological system modeling Organisms Mathematical models Biological systems distributed parameter systems

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Estimating Space-Dependent Coefficients for 1D Transport Using Gaussian Processes as State Estimator in the Frequency Domain

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IEEE CONTROL systems LETTERS 2022年 7卷 247-252页

作者： van Kampen, Ricky J. R. van Berkel, Matthijs Zwart, Hans DIFFER Dutch Inst Fundamental Energy Res Energy Syst & Control Grp NL-5612 AJ Eindhoven Netherlands Eindhoven Univ Technol Dept Mech Engn NL-5600 MB Eindhoven Netherlands Univ Twente Fac Elect Engn Math & Comp Sci NL-7500 AE Enschede Netherlands

This letter presents a method to estimate the space-dependent transport coefficients (diffusion, convection, reaction, and source/sink) for a generic scalar transport model, e.g., heat or mass. As the problem is solved in the frequency domain, the complex valued state as a function of the spatial variable is estimated using Gaussian process regression. The resulting probability density function of the state, together with a semi-discretization of the model, and a linear parameterization of the coefficients are used to determine the maximum likelihood solution for these space-dependent coefficients. The proposed method is illustrated by simulations.

关键词： Measurement uncertainty Gaussian processes Standards Mathematical models Kernel Uncertainty State estimation Gaussian processes grey-box modeling distributed parameter systems identification inverse problems

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Neural ODE Control for Trajectory Approximation of Continuity Equation

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IEEE CONTROL systems LETTERS 2022年 6卷 3152-3157页

作者： Elamvazhuthi, Karthik Gharesifard, Bahman Bertozzi, Andrea L. Osher, Stanley Univ Calif Riverside Dept Mech Engn Riverside CA 92521 USA Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA

We consider the controllability problem for the continuity equation, corresponding to neural ordinary differential equations (ODEs), which describes how a probability measure is pushedforward by the flow. We show that the controlled continuity equation has very strong controllability properties. Particularly, a given solution of the continuity equation corresponding to a bounded Lipschitz vector field defines a trajectory on the set of probability measures. For this trajectory, we show that there exist piecewise constant training weights for a neural ODE such that the solution of the continuity equation corresponding to the neural ODE is arbitrarily close to it. As a corollary to this result, we establish that the continuity equation of the neural ODE is approximately controllable on the set of compactly supported probability measures that are absolutely continuous with respect to the Lebesgue measure.

关键词： Neural networks Controllability Trajectory Training Topology Particle measurements Estimation distributed parameter systems machine learning neural networks

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Optimization based Feedforward mitigation of Elastic Flexure of distributed parameter System due to Reference Tracking

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IFAC-PapersOnLine 2022年第27期55卷 50-55页

作者： André Heining Oliver Sawodny

If a large scale structure performs a rigid body motion, this motion is superposed by an elastic flexure due to its inherent elasticity. In order to mitigate the elastic motion feedforward and feedback laws can be applied. By minimizing the L 2 -norm of the elastic flexure subject to a reference trajectory and the elastic system description we derive a feedforward signal that attenuates elastic motions of the structure. A comparison to simplified solution approaches shows a major improvement for reference signals in the range of the system's natural frequencies.

关键词： Vibration modal analysis Linear systems Feedforward control distributed parameter systems Input excitation design

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On Solvability of Dissipative Partial Differential-Algeraic Equations

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IEEE CONTROL systems LETTERS 2022年 6卷 3188-3193页

作者： Jacob, Birgit Morris, Kirsten Univ Wuppertal Dept Math D-42119 Wuppertal Germany Univ Waterloo Dept Appl Math KM Waterloo ON N2L 3G1 Canada

We investigate the solvability of infinite-dimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the state-space that leads to an extension of the Hille-Yosida Theorem on reflexive Banach spaces is described. For dissipative partial differential equations the Lumer-Phillips generation theorem characterizes solvability and also boundedness of the associated semigroup. An extension of the Lumer-Phillips generation theorem to dissipative differential-algebraic equations is given. The results are illustrated by coupled systems and the Dzektser equation.

关键词： Differential-algebraic systems distributed parameter systems linear systems stability of linear systems

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Robust Control of Continuous Casting Process for Various Technological Conditions 23

Robust Control of Continuous Casting Process for Various Tec...

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23rd International Carpathian Control Conference (ICCC)

作者： Zarghoon, Sohaibullah Bartalsky, Lukas Belavy, Cyril Slovak Univ Technol Bratislava Fac Mech Engn Inst Automat Measurement & Appl Informat Bratislava Slovakia

ISBN: (纸本)9781665466363

The process of continuous steel casting, specifically the part of secondary cooling, is a typical representative of a system with distributed parameters. The paper deal with the synthesis and simulation of robust control of continuous steel casting in the secondary cooling zone. During steel production, there is a smooth change between the types of steel produced (or steel grades), to which the control system must react flexibly. Therefore, a robust approach based on simple PID controllers will be chosen for control synthesis. Based on the model obtained from the ProCast software, the uncertainty limits for the simulation model will be determined. Robust control simulations will be performed on a time-space circuit, within the simulations a possible machine failure will be tested, thus a change in cooling power in individual zones. The results will be presented as temperature fields, representing the system with distributed parameters, taking into account the time and space distribution of the controlled temerature.

关键词： distributed parameter systems uncertainty robust PID control temperature field continuous casting

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Vibration Control of a High-Rise Building Structure:Theory and Experiment

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IEEE/CAA Journal of Automatica Sinica 2021年第4期8卷 866-875页

作者： Yuhua Song Wei He Xiuyu He Zhiji Han Institute of Artificial Intelligence University of Science and Technology Beijingand also with the School of Automation and Electrical EngineeringUniversity of Science and Technology BeijingBeijing 100083China Shunde Graduate School University of Scienceand Technology BeijingFoshan 528399China

In this study,an innovative solution is developed for vibration suppression of the high-rise *** infinite dimensional system model has been presented for describing high-rise building structures which have a large inertial load with the help of the Hamilton’s *** the basis of this system model and with the use of the Lyapunov’s direct method,a boundary controller is proposed and the closed-loop system is uniformly bounded in the time ***,by using the Smart Structure laboratory platform which is produced by Quancer,we conduct a set of experiments and find that the designed method is resultful.

关键词： Boundary control distributed parameter systems high-rise building structure vibration control

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Fault Isolation of a Class of Uncertain Nonlinear Parabolic PDE systems 2nd

Fault Isolation of a Class of Uncertain Nonlinear Parabolic ...

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2nd Modeling, Estimation and Control Conference (MECC)

作者： Zhang, Jingting Yuan, Chengzhi Stegagno, Paolo Zeng, Wei Univ Rhode Isl Dept Mech Ind & Syst Engn Kingston RI 02881 USA Univ Rhode Isl Dept Elect Comp & Biomed Engn Kingston RI 02881 USA Longyan Univ Sch Mech & Elect Engn Longyan 364012 Peoples R China

This paper proposes a novel fault isolation (FI) scheme for distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with nonlinear uncertain dynamics. A key feature of the proposed FI scheme is its capability of dealing with the effects of system uncertainties for accurate FI. Specifically, an approximate ordinary differential equation (ODE) system is first derived to capture the dominant dynamics of the original PDE system. An adaptive dynamics identification approach using radial basis function neural network is then proposed based on this ODE system, to achieve locally-accurate identification of the uncertain system dynamics under faulty modes. A bank of FI estimators with associated adaptive thresholds are finally designed for real-time FI decision making. Rigorous analysis on the fault isolatability is provided. Simulation study on a representative transport-reaction process is conducted to demonstrate the effectiveness of the proposed approach. Copyright (c) 2022 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0)

关键词： Partial differential equations fault isolation adaptive dynamics identification neural network distributed parameter systems

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Using mobile sensor density to approximate state feedback controllers for a class of PDEs 4th

Using mobile sensor density to approximate state feedback co...

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4th IFAC Workshop on Control of systems Governed by Partial Differential Equations (CPDE)

作者： Demetriou, Michael A. Hu, Weiwei WPI Aerosp Engn Dept Worcester MA 01609 USA Univ Georgia Dept Math Athens GA 30602 USA

This work is concerned with the use of mobile sensors to approximate and replace the full state feedback controller by static output feedback controllers for a class of PDEs. Assuming the feedback operator associated with the full-state feedback controller admits a kernel representation, the proposed optimization aims to approximate the inner product of the kernel and the full state by a finite sum of weighted scalar outputs provided by the mobile sensors. When the full state feedback operator is time-dependent thus rendering its associated kernel time-varying, the approximation results in moving sensors with time-varying static gains. To calculate the velocity of the mobile sensors within the spatial domain, the time-varying kernel is set equal to the sensor density and thus the solution to an associated advection PDE reveals the velocity field of the sensor network. To obtain the speed of the finite number of sensors, a domain decomposition based on a modification of the Centroidal Voronoi Tessellations (mu-CVT) is used to decompose the kernel into a finite number of cells, each of which contains a single sensor. A subsequent application of the mu-CVT on the velocity field provides the individual sensor speeds. The nature of this mu-CVT ensures collision avoidance by the very structure of the kernel decomposition into non-intersecting cells. Numerical simulations are provided to highlight the proposed sensor guidance. Copyright (C) 2022 The Authors.

关键词： distributed parameter systems sensor selection sensor guidance sensor density static output feedback control approximation kernel approximation computational geometry

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