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Input-to-state stability of coupled hyperbolic PDE-ODE systems via boundary feedback control

Liguo Zhang, Jianru Hao, Junfei Qiao
2019 Science China Information Sciences  
Using the strict Lyapunov function, some sufficient conditions in terms of matrix inequalities are obtained for the boundary ISS of the closed-loop hyperbolic PDE-ODE systems.  ...  We herein investigate the boundary input-to-state stability (ISS) of a class of coupled hyperbolic partial differential equation-ordinary differential equation (PDE-ODE) systems with respect to the presence  ...  In [1] , an observer was designed for a class of hyperbolic PDE-ODE cascade systems with the boundary measurement.  ... 
doi:10.1007/s11432-018-9437-x fatcat:2wzbba5j65hitgcdihtbv7gikm

Control-oriented model reduction for a class of hyperbolic systems with application to managed pressure drilling

T.C.P.F. Leenen, S. Naderi Lordejani, B. Besselink, W.H.A. Schilders, N. van de Wouw
2020 IFAC-PapersOnLine  
This paper presents a model reduction approach for systems of hyperbolic partial differential equations (PDEs) with nonlinear boundary conditions.  ...  We show that the linear PDE subsystem can effectively be approximated by a cascaded structure of systems of continuous time difference equations (CTDEs) and ordinary differential equations (ODEs), where  ...  For many drilling scenarios, a drilling system with MPD can be described by a linear system of PDEs of the form (1) and boundary conditions of the form (2).  ... 
doi:10.1016/j.ifacol.2020.12.1514 fatcat:gblxecdmzff2fjf7ytlkdaah6e

Non-asymptotic State Estimation of Linear Reaction Diffusion Equation using Modulating Functions

Lilia Ghaffour, Matti Noack, Johann Reger, Taous-Meriem Laleg-Kirati
2020 IFAC-PapersOnLine  
This results in a signal model control problem for a system of auxiliary PDEs in order to determine the modulation kernels.  ...  In this paper, we propose a non-asymptotic state estimation method for the linear reaction diffusion equation with general boundary conditions.  ...  More recently, a boundary observer has been designed by Hasan et al. (2016) , for a coupled system of hyperbolic dynamical cascade systems with measurements at the boundary to estimate the states of the  ... 
doi:10.1016/j.ifacol.2020.12.2570 fatcat:xcqhqo6rjjfclisrvd32he4d2i

Backstepping stabilization of 2×2 linear hyperbolic PDEs coupled with potentially unstable actuator and load dynamics

David Bou Saba, Federico Bribiesca-Argomedo, Michael Di Loreto, Damien Eberard
2017 2017 IEEE 56th Annual Conference on Decision and Control (CDC)  
We consider the problem of full-state feedback stabilization of a (possibly unstable) system of hyperbolic partial differential equations (PDEs).  ...  This structure can arise when considering linear (or linearized) systems of balance laws with finite-dimensional actuator and load dynamics.  ...  Future work will be focused on designing the observer for the ODE-PDE-ODE system and avoiding the use of the timederivatives in the control.  ... 
doi:10.1109/cdc.2017.8264016 dblp:conf/cdc/SabaALE17 fatcat:4jyyrgyt2neotcvzcpf7dpxrdu

Observer Design for a Coupled ODE-PDE System from a Wellbore Reservoir Drilling Model

Leobardo Camacho-Solorio, Naveen Velmurugan, Florent Di Meglio, Miroslav Krstic
2019 2019 IEEE 58th Conference on Decision and Control (CDC)  
The problem of state estimation for a coupled ODE-PDE system is addressed here by means of the backstepping method for PDEs.  ...  The estimate is defined as the state of an observer; constructed as a copy of the coupled system ODE-PDE with output error feedback.  ...  CONCLUSION We have derived an observer for coupled ODE-PDE system with bidirectional coupling.  ... 
doi:10.1109/cdc40024.2019.9029250 dblp:conf/cdc/Camacho-Solorio19 fatcat:rilu4hbbmnb7zetkpvx3oaddxu

Observer design for a class of nonlinear system in cascade with counter-convecting transport dynamics

Xiushan Cai, Linling Liao, Junfeng Zhang, Wei Zhang
2016 Kybernetika (Praha)  
Stabilization of a system of n + 1 coupled first-order hyperbolic linear PDEs with a single boundary input was dealt with in [16] .  ...  Observer design for ODE-PDE cascades is motivated by problems faced in the oil and gas industry.  ... 
doi:10.14736/kyb-2016-1-0076 fatcat:ujmz7x7hgbajrltxf2js3bbrq4

Delay-robust stabilization of an n+m hyperbolic PDE-ODE system

Jean Auriol, Federico Bribiesca-Argomedo
2019 2019 IEEE 58th Conference on Decision and Control (CDC)  
In this paper, we study the problem of stabilizing a linear ordinary differential equation through a system of an n + m (hetero-directional) coupled hyperbolic equations in the actuating path.  ...  the ODE.  ...  two linear PDEs coupled with an ODE.  ... 
doi:10.1109/cdc40024.2019.9029421 dblp:conf/cdc/AuriolA19 fatcat:fi6dhru7cjcgzlkwf5firzmkie

Backstepping boundary control for first order hyperbolic PDEs and application to systems with actuator and sensor delays

Miroslav Krstic, Andrey Smyshlyaev
2007 2007 46th IEEE Conference on Decision and Control  
We also show that the proposed method can be used for the boundary control of a Korteweg-de Vries-like third-order PDE. The designs are illustrated with simulations. (M.  ...  We design controllers using a backstepping method, which has been recently developed for parabolic PDEs.  ...  We combine the backstepping design for hyperbolic PDEs with the backstepping design for linear ODEs [15] to recover classical results for linear systems with actuator and sensor delay [25, 21, 23, 2  ... 
doi:10.1109/cdc.2007.4434474 dblp:conf/cdc/KrsticS07 fatcat:og2zx5gnk5f6zcv4vmj5ob2b6a

Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays

Miroslav Krstic, Andrey Smyshlyaev
2008 Systems & control letters (Print)  
We also show that the proposed method can be used for the boundary control of a Korteweg-de Vries-like third-order PDE. The designs are illustrated with simulations. (M.  ...  We design controllers using a backstepping method, which has been recently developed for parabolic PDEs.  ...  We combine the backstepping design for hyperbolic PDEs with the backstepping design for linear ODEs [15] to recover classical results for linear systems with actuator and sensor delay [25, 21, 23, 2  ... 
doi:10.1016/j.sysconle.2008.02.005 fatcat:ma7nomh7urgz3hu24grifjxsxe

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

Joachim Deutscher, Nicole Gehring, Richard Kern
2017 arXiv   pre-print
This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients.  ...  In order to implement the state feedback controller, the design of observers for the ODE-PDE systems in question is considered, whereby anticollocated measurements are assumed.  ...  Nevertheless, an alternative method for the backstepping stabilization of coupled linear heterodirectional hyperbolic PDE-ODE systems is proposed in this paper.  ... 
arXiv:1711.00700v1 fatcat:q6djdhm3vrajjcgho7djipgnay

Output Feedback Control of Coupled Linear Parabolic ODE-PDE-ODE Systems [article]

Joachim Deutscher, Nicole Gehring
2020 arXiv   pre-print
This paper deals with the backstepping design of observer-based compensators for parabolic ODE-PDE-ODE systems.  ...  The results of the paper are illustrated by the output feedback control of an unstable ODE-PDE-ODE system with two coupled parabolic PDEs.  ...  Remark 9: Similar to the observer design for hyperbolic ODE-PDE-ODE systems in [6] , the proposed observer (47) requires a time derivative of the output.  ... 
arXiv:2008.11784v1 fatcat:4rgogn6kwjbcjpeh7u2bhzzimy

LQ control of coupled hyperbolic PDEs and ODEs: Application to a CSTR-PFR system

Amir Alizadeh Moghadam, Ilyasse Aksikas, Stevan Dubljevic, J. Fraser Forbes
2010 IFAC Proceedings Volumes  
In this paper an infinite-dimensional LQR control-based design for a system containing linear hyperbolic partial differential equations coupled with linear ordinary differential equations is presented.  ...  The design is based on an infinite-dimensional Hilbert state-space representation of the coupled system.  ...  In section 2, general formulation for a system containing a set of coupled linear first-order hyperbolic PDEs and linear ODEs is described.  ... 
doi:10.3182/20100705-3-be-2011.00119 fatcat:qx7v56siincndasjrbi4thi4xi

Robust characteristic-based MPC of a fixed-bed reactor

L Mohammadi, S Dubljevic, J F Forbes
2010 Proceedings of the 2010 American Control Conference  
In this work a model predictive control methodology is applied to a set of hyperbolic partial differential equations (PDEs) which models a chemical fixed-bed reactor.  ...  Initially, the model of the fixed-bed reactor is linearized and by the method of characteristics is transformed into the set of ODEs which is explored within the model predictive controller synthesis.  ...  Then the controller design can be performed on ODEs instead of PDEs without approximation. Unfortunately, the constrained model predictive control for hyperbolic systems has not been done.  ... 
doi:10.1109/acc.2010.5531050 fatcat:nbspmuqui5dxldai6kizjzu5ci

Delay-robust stabilization of a hyperbolic PDE–ODE system

Jean Auriol, Federico Bribiesca-Argomedo, David Bou Saba, Michael Di Loreto, Florent Di Meglio
2018 Automatica  
the stabilization problem of the PDE-ODE system to that of a time-delay system for which a predictor can be constructed.  ...  We detail in this article the development of a delay-robust stabilizing feedback control law for a linear ordinary differential equation coupled with two linear first order hyperbolic equations in the  ...  The control of systems of coupled ODEs and hyperbolic PDEs is a very active research topic, see for instance [5, 7, 11, 22] .  ... 
doi:10.1016/j.automatica.2018.06.033 fatcat:vjsy2ouf5jbo5dlq3flfpm6oji

Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions

André F. Caldeira, Christophe Prieur, Daniel Coutinho, Valter J.S. Leite
2018 European Journal of Control  
Regional stability and stabilization of a class of linear hyperbolic systems with nonlinear quadratic dynamic boundary conditions.  ...  More precisely, sufficient stability conditions are derived to guarantee the exponential stability of a linear hyperbolic differential equation system subject to nonlinear quadratic dynamic boundary conditions  ...  for the boundary control of hyperbolic and time-delayed systems was considered in [28] , the dynamic boundary stabilization of linear parameter-varying (LPV) hyperbolic systems using the LMI framework  ... 
doi:10.1016/j.ejcon.2018.05.003 fatcat:w57josj5ozdapjfy32stzfeulm
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