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Single-step full-state feedback control design for nonlinear hyperbolic PDEs

INTERNATIONAL JOURNAL OF CONTROL 2019年第11期92卷 2484-2498页

作者： Xu, Qingqing Aksikas, Ilyasse Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB Canada Qatar Univ Dept Math Doha Qatar

The present work proposes an extension of single-step formulation of full-state feedback control design to the class of distributed parameter system described by nonlinear hyperbolic partial differential equations (PDEs). Under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear state feedback law, both feedback control and stabilisation design objectives given as target stable dynamics are accomplished in one step. In particular, the mathematical formulation of the problem is realised via a system of first-order quasi-linear singular PDEs. By using Lyapunov's auxiliary theorem for singular PDEs, the necessary and sufficient conditions for solvability are utilised. The solution to the singular PDEs is locally analytic, which enables development of a PDE series solution. Finally, the theory is successfully applied to an exothermic plug-flow reactor system and a damped second-order hyperbolic PDE system demonstrating ability of in-domain nonlinear control law to achieve stabilisation.

关键词： Lyapunov's auxiliary theorem single-step full-state feedback design distributed-parameter systems exothermic plug-flow reactor damped wave equation

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Robust distributed control of quasilinear reaction-diffusion equations via infinite-dimensional sliding modes

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AUTOMATICA 2019年 104卷 165-172页

作者： Cristofaro, Andrea Univ Oslo Fac Math & Nat Sci Dept Technol Syst N-2007 Kjeller Norway Univ Camerino Math Div Sch Sci & Technol I-62032 Camerino Italy

This paper investigates the problem of robust tracking control for quasilinear reaction-diffusion partial differential equations subject to external unknown perturbations. The considered class of equations is quite general, and includes classical equations such as the heat equation or the Fisher-KPP equation as special cases. Global practical stabilization of the tracking error system is established under mild conditions on the disturbance term using a regularized infinite-dimensional sliding-mode controller. Extensive simulations support and validate the theoretical results. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Reaction-diffusion equations Sliding-mode control

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Observer and filter design for linear transport-reaction systems

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EUROPEAN JOURNAL OF CONTROL 2019年 49卷 26-43页

作者： Xie, Junyao Xu, Qingqing Ni, Dong Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 1H9 Canada China Univ Petr Dept Mech & Transportat Engn Beijing 102249 Peoples R China Zhejiang Univ Coll Control Sci & Engn Hangzhou 310007 Zhejiang Peoples R China

The present work extends known finite dimensional Luenberger observer and Kalman filter designs to the realm of linear transport-reaction systems frequently present in chemical engineering practice. A unified modelling framework for distributed parameter systems (DPS) which does not account for any type of spatial approximation or order reduction is developed. The Cayley-Tustin transformation of continuous linear distributed parameter system yields structure and properties preserving discrete distributed parameter models, amenable to observer and filter design developments. Designs presented here explore well known state reconstruction methodologies starting from least square estimation, continuous and discrete Luenberger observers and one-step predictor Kalman filter realization. Simple implementation and realization account for the appealing nature of the discrete system observers and filter designs for linear transport-reaction systems. The simulation scenarios cover the majority of representative examples found in the common engineering process control practice. (C) 2019 European Control Association. Published by Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Transport-reaction systems Cayley-Tustin discretization Observer Kalman filter

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Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

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INTERNATIONAL JOURNAL OF CONTROL 2019年第10期92卷 2274-2290页

作者： Deutscher, J. Gehring, N. Kern, R. Univ Erlangen Nurnberg Lehrstuhl Regelungstech Erlangen Germany Univ Linz Inst Regelungstech & Prozessautomatisierung Linz Austria Tech Univ Munich Lehrstuhl Regelungstech Garching Germany

This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially varying coefficients. Thereby, the ODE is coupled to the PDE in-domain and at the uncontrolled boundary, whereas the ODE is coupled with the latter boundary. For the state feedback design, a two-step backstepping approach is developed, which yields the conventional kernel equations and additional decoupling equations of simple form. In order to implement the state feedback controller, the design of observers for the PDE-ODE systems in question is considered, whereby anti-collocated measurements are assumed. Exponential stability with a prescribed convergence rate is verified for the closed-system pointwise in space. The resulting compensator design is illustrated for a 4 x 4 heterodirectional hyperbolic system coupled with a third-order ODE modelling a dynamic boundary condition.

关键词： distributed-parameter systems hyperbolic systems backstepping boundary control observers coupled PDE-ODE systems

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Adaptive set-point regulation of linear n+1 hyperbolic systems with uncertain affine boundary condition using collocated sensing and control

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systems & CONTROL LETTERS 2020年 145卷 104777-104777页

作者： Holta, Haavard Aamo, Ole Morten Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway

We solve an adaptive control problem for n + 1 hyperbolic systems using collocated sensing and control, extending recent results for adaptive control of 2 x 2 systems and systems with non-collocated sensing and control. The boundary condition has an affine form with both unknown reflective and additive parameters and can be used to model well-reservoir interactions in oil and gas drilling where properties of the reservoir are unknown. Boundedness of the system states in the L-2-norm, and convergence to a steady state profile satisfying a control objective relevant to the drilling application, are proved. The state estimation error is shown to converge to zero in the L-2-norm and one of the boundary parameter estimates (modelling the reservoir pressure in the drilling application) is shown to converge to the true parameter value. The design is illustrated in a simulation example. (C) 2020 The Author(s). Published by Elsevier B.V.

关键词： distributed-parameter systems Adaptive control parameter estimation

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Output feedback boundary control of heterodirectional semilinear hyperbolic systems

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AUTOMATICA 2020年 117卷 108990-108990页

作者： Strecker, Timm Aamo, Ole Morten Cantoni, Michael Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3010 Australia Norwegian Univ Sci & Technol NTNU Dept Engn Cybernet N-7491 Trondheim Norway

We solve the problem of stabilizing a general class of 1-d semilinear hyperbolic systems with an arbitrary number of states convecting in each direction and with the actuation and sensing restricted to one boundary. The control design is based on the dynamics on the characteristic lines along which the inputs propagate through the domain and the predictability of states in the interior of the domain up to the time they are affected by the inputs. In the context of broad solutions, the state-feedback controller drives systems with globally Lipschitz nonlinearities from an arbitrary initial condition to the origin in minimum time. Alternatively, it is possible to satisfy a tracking objective at the uncontrolled boundary or, for systems with C-1-coefficients and initial conditions, to design the control inputs to obtain classical C-1-solutions that also reach the origin in finite time. Further, we design an observer that estimates the distributed state from boundary measurements only. The observer combined with the state-feedback controller solves the output-feedback control problem. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Hyperbolic partial differential equations distributed-parameter systems Boundary control Stabilization Estimation

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Social Organisation of Mobile Sensors for Wildfire Spread Estimation

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IFAC-PapersOnLine 2020年第2期53卷 3596-3601页

作者： T. Plenet C. Raïevsky L. Lefèvre S. El Yacoubi IMAGES - UMR eSPACe-DeV University of Perpignan Via Domitia Univ. Grenoble Alpes Grenoble INP LCIS 26000 Valence France

In this paper, we focus on social organisation of mobile sensor network for the observation of distributed parameter systems. We built a framework that allows us to compare different social organisation in terms of observation performance. First, we studied the topology of generic social organisation with graph theory criteria. Then, we benchmarked some of these organisations when we applied them to mobile sensor network for the observation of a cellular-automaton simulated wildfire.

关键词： Forest Fire Spread Dynamics Mobile Sensors Multi-agent systems Cellular Automaton distributed-parameter systems Observers

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Control of the Vertical Gradient Freeze crystal growth process via backstepping

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IFAC-PapersOnLine 2020年第2期53卷 7758-7764页

作者： Stefan Ecklebe Frank Woittennek Jan Winkler

This contribution presents a backstepping-based state feedback design for the tracking control of a two-phase Stefan problem which is encountered in the Vertical Gradient Freeze crystal growth process. A two-phase Stefan problem consists of two coupled free boundary problems and is a vital part of many crystal growth processes due to the time-varying extent of crystal and melt during growth. In addition, a different approach for the numerical approximation of the backstepping transformations kernel is presented.

关键词： Vertical Gradient Freeze two-phase Stefan problem distributed-parameter systems backstepping tracking control numerical methods

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Boundary observer design for cascaded ODE - Hyperbolic PDE systems: A matrix inequalities approach

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AUTOMATICA 2020年 119卷 109027-109027页

作者： Ferrante, Francesco Cristofaro, Andrea Prieur, Christophe Univ Grenoble Alpes GIPSA Lab Grenoble INP CNRS F-38000 Grenoble France Sapienza Univ Rome Dept Comp Control & Management Engn I-00185 Rome Italy

Boundary observer design for a system of ODEs in cascade with hyperbolic PDEs is studied. An infinite dimensional observer is used to solve the state estimation problem. The interconnection of the observer and the system is written in estimation error coordinates and analyzed as an abstract dynamical system. The design of the observer is performed to achieve global exponential stability of the estimation error with respect to a suitable norm and with a tunable convergence rate. Sufficient conditions in the form matrix inequalities are given for the design of the observer. The effectiveness of the approach is shown in a numerical example. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Observers Convex optimization Lyapunov methods Computer-aided design

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Closed-form H-infinity optimal control for a class of infinite-dimensional systems

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AUTOMATICA 2020年 117卷 108916-108916页

作者： Bergeling, Carolina Morris, Kirsten A. Rantzer, Anders Lund Univ Dept Automat Control Box 118 SE-22100 Lund Sweden Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada

H infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose algorithms for H-infinity synthesis. The results also apply to finite-dimensional systems. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： H-infinity control Linear systems distributed-parameter systems Optimal control Optimal estimation

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