Ilyasse Aksikas - Academia.edu (original) (raw)
Papers by Ilyasse Aksikas
2007 European Control Conference (ECC)
A general linear controller design method for a class of hyperbolic partial differential equation... more A general linear controller design method for a class of hyperbolic partial differential equations (PDE's) systems is presented, which uses infinite-dimensional Hilbert state-space description. A state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation in the space variable. The proposed method is applied to a fixed-bed chemical reactor control problem where one elementary reaction takes place. An optimal controller is designed for the linearized fixed-bed reactor model, it is applied to the nonlinear original model and the resulting closed-loop stability is analyzed.
International Journal of Systems Science
This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combin... more This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combined with a linear-quadratic state feedback controller for a system of hyperbolic PDEs. The design is based on the duality fact between the control design and the observer design. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to a fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the temperature and the reactant concentration in a fixed-bed reactor is investigated by using the developed algorithm, which lead to express the jacket temperature (manipulated variable) as a feedback of the estimated temperature and concentration in the reactor.
Journal of Process Control
In this work, control and estimation problems have been studied for a catalytic reversal flow rea... more In this work, control and estimation problems have been studied for a catalytic reversal flow reactor (CFRR). A stabilizing compensator is developed on the basis of the infinite-dimensional state-space description of the CFRR. Linear-quadratic technique is used to design both an optimal state-feedback controller and an output injection operator. The later is developed based on the duality fact between regulation and estimation. Indeed, the output injection operator is the adjoint of the feedback control operator of the dual process. The developed compensator is tested numerically for the catalytic combustion of lean methane emissions.
2007 European Control Conference (ECC)
A general linear controller design method for a class of hyperbolic partial differential equation... more A general linear controller design method for a class of hyperbolic partial differential equations (PDE's) systems is presented, which uses infinite-dimensional Hilbert state-space description. A state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation in the space variable. The proposed method is applied to a fixed-bed chemical reactor control problem where one elementary reaction takes place. An optimal controller is designed for the linearized fixed-bed reactor model, it is applied to the nonlinear original model and the resulting closed-loop stability is analyzed.
International Journal of Systems Science
This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combin... more This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combined with a linear-quadratic state feedback controller for a system of hyperbolic PDEs. The design is based on the duality fact between the control design and the observer design. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to a fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the temperature and the reactant concentration in a fixed-bed reactor is investigated by using the developed algorithm, which lead to express the jacket temperature (manipulated variable) as a feedback of the estimated temperature and concentration in the reactor.
Journal of Process Control
In this work, control and estimation problems have been studied for a catalytic reversal flow rea... more In this work, control and estimation problems have been studied for a catalytic reversal flow reactor (CFRR). A stabilizing compensator is developed on the basis of the infinite-dimensional state-space description of the CFRR. Linear-quadratic technique is used to design both an optimal state-feedback controller and an output injection operator. The later is developed based on the duality fact between regulation and estimation. Indeed, the output injection operator is the adjoint of the feedback control operator of the dual process. The developed compensator is tested numerically for the catalytic combustion of lean methane emissions.
2020 24th International Conference on System Theory, Control and Computing (ICSTCC)
This work is devoted to the development of an optimal infinite-dimensional Luenberger observer fo... more This work is devoted to the development of an optimal infinite-dimensional Luenberger observer for a system of hyperbolic PDEs. For this purpose, the duality fact linking the control design and the observer design is used. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to the process of fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the fixed-bed reactor state is investigated by using the developed algorithm.
2009 European Control Conference (ECC), 2009
The concept of asymptotic stability is studied for a class of dissipative semi-linear infinite-di... more The concept of asymptotic stability is studied for a class of dissipative semi-linear infinite-dimensional Banach state space systems with nonlinearity defined on a convex subset of the state space. Stability criteria are established, which are based on a weaker technical condition of the m-dissipativity. These theoretical results are applied to a class of transport-reaction processes. Different types of nonlinearity are studied by adapting the criteria given in the early portions of the paper.
2020 24th International Conference on System Theory, Control and Computing (ICSTCC)
This work is devoted to the development of an optimal infinite-dimensional Luenberger observer fo... more This work is devoted to the development of an optimal infinite-dimensional Luenberger observer for a system of hyperbolic PDEs. For this purpose, the duality fact linking the control design and the observer design is used. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to the process of fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the fixed-bed reactor state is investigated by using the developed algorithm.
2017 13th IEEE International Conference on Control & Automation (ICCA), 2017
This paper is devoted to design an optimal linear quadratic controller for a time-varying system ... more This paper is devoted to design an optimal linear quadratic controller for a time-varying system of coupled parabolic and hyperbolic partial differential equations (PDEs). Infinite-dimensional state space approach is adopted to solve the control problem via the well-known operator Riccati equation. The latter is converted into a scalar partial differential equation coupled with a set of ordinary differential equations. The main algorithm to solve the Riccati equation is presented. The designed controller is tested on a model of catalytic packed-bed chemical reactor to show the performances of the developed controller.
2009 European Control Conference (ECC), 2009
The concept of asymptotic stability is studied for a class of dissipative semi-linear infinite-di... more The concept of asymptotic stability is studied for a class of dissipative semi-linear infinite-dimensional Banach state space systems with nonlinearity defined on a convex subset of the state space. Stability criteria are established, which are based on a weaker technical condition of the m-dissipativity. These theoretical results are applied to a class of transport-reaction processes. Different types of nonlinearity are studied by adapting the criteria given in the early portions of the paper.
Journal of the Franklin Institute, 2020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
2017 13th IEEE International Conference on Control & Automation (ICCA), 2017
This paper is devoted to design an optimal linear quadratic controller for a time-varying system ... more This paper is devoted to design an optimal linear quadratic controller for a time-varying system of coupled parabolic and hyperbolic partial differential equations (PDEs). Infinite-dimensional state space approach is adopted to solve the control problem via the well-known operator Riccati equation. The latter is converted into a scalar partial differential equation coupled with a set of ordinary differential equations. The main algorithm to solve the Riccati equation is presented. The designed controller is tested on a model of catalytic packed-bed chemical reactor to show the performances of the developed controller.
International Journal of Control, 2018
This paper deals with the design of a boundary optimal controller for a general model of paraboli... more This paper deals with the design of a boundary optimal controller for a general model of parabolichyperbolic PDEs coupled with an ODE. The augmented infinite-dimensional state-space representation has been used in order to solve the optimal state-feedback control problem. By using the perturbation theorem, it has been shown that the system generates a C 0-semigroup on the augmented state space. Also, the dynamical properties of both the original and the augmented systems have been studied. Under some technical conditions, it has been shown that the augmented system generates an exponentially stabilisable and detectable C 0-semigroups. The linear-quadratic control problem has been solved for the augmented system. A decoupling technique has been implemented to decouple and solve the corresponding Riccati equation. Monolithic catalyst reactor model has been used to test the performances of the developed controller through numerical simulations.
Journal of the Franklin Institute, 2020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
International Journal of Systems Science, 2018
This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller fo... more This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolicassociated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.
International Journal of Control, 2018
This paper deals with the design of a boundary optimal controller for a general model of paraboli... more This paper deals with the design of a boundary optimal controller for a general model of parabolichyperbolic PDEs coupled with an ODE. The augmented infinite-dimensional state-space representation has been used in order to solve the optimal state-feedback control problem. By using the perturbation theorem, it has been shown that the system generates a C 0-semigroup on the augmented state space. Also, the dynamical properties of both the original and the augmented systems have been studied. Under some technical conditions, it has been shown that the augmented system generates an exponentially stabilisable and detectable C 0-semigroups. The linear-quadratic control problem has been solved for the augmented system. A decoupling technique has been implemented to decouple and solve the corresponding Riccati equation. Monolithic catalyst reactor model has been used to test the performances of the developed controller through numerical simulations.
International Journal of Control, 2018
The present work proposes an extension of single-step formulation of full-state feedback control ... more 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.
2007 European Control Conference (ECC)
A general linear controller design method for a class of hyperbolic partial differential equation... more A general linear controller design method for a class of hyperbolic partial differential equations (PDE's) systems is presented, which uses infinite-dimensional Hilbert state-space description. A state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation in the space variable. The proposed method is applied to a fixed-bed chemical reactor control problem where one elementary reaction takes place. An optimal controller is designed for the linearized fixed-bed reactor model, it is applied to the nonlinear original model and the resulting closed-loop stability is analyzed.
International Journal of Systems Science
This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combin... more This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combined with a linear-quadratic state feedback controller for a system of hyperbolic PDEs. The design is based on the duality fact between the control design and the observer design. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to a fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the temperature and the reactant concentration in a fixed-bed reactor is investigated by using the developed algorithm, which lead to express the jacket temperature (manipulated variable) as a feedback of the estimated temperature and concentration in the reactor.
Journal of Process Control
In this work, control and estimation problems have been studied for a catalytic reversal flow rea... more In this work, control and estimation problems have been studied for a catalytic reversal flow reactor (CFRR). A stabilizing compensator is developed on the basis of the infinite-dimensional state-space description of the CFRR. Linear-quadratic technique is used to design both an optimal state-feedback controller and an output injection operator. The later is developed based on the duality fact between regulation and estimation. Indeed, the output injection operator is the adjoint of the feedback control operator of the dual process. The developed compensator is tested numerically for the catalytic combustion of lean methane emissions.
2007 European Control Conference (ECC)
A general linear controller design method for a class of hyperbolic partial differential equation... more A general linear controller design method for a class of hyperbolic partial differential equations (PDE's) systems is presented, which uses infinite-dimensional Hilbert state-space description. A state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation in the space variable. The proposed method is applied to a fixed-bed chemical reactor control problem where one elementary reaction takes place. An optimal controller is designed for the linearized fixed-bed reactor model, it is applied to the nonlinear original model and the resulting closed-loop stability is analyzed.
International Journal of Systems Science
This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combin... more This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combined with a linear-quadratic state feedback controller for a system of hyperbolic PDEs. The design is based on the duality fact between the control design and the observer design. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to a fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the temperature and the reactant concentration in a fixed-bed reactor is investigated by using the developed algorithm, which lead to express the jacket temperature (manipulated variable) as a feedback of the estimated temperature and concentration in the reactor.
Journal of Process Control
In this work, control and estimation problems have been studied for a catalytic reversal flow rea... more In this work, control and estimation problems have been studied for a catalytic reversal flow reactor (CFRR). A stabilizing compensator is developed on the basis of the infinite-dimensional state-space description of the CFRR. Linear-quadratic technique is used to design both an optimal state-feedback controller and an output injection operator. The later is developed based on the duality fact between regulation and estimation. Indeed, the output injection operator is the adjoint of the feedback control operator of the dual process. The developed compensator is tested numerically for the catalytic combustion of lean methane emissions.
2020 24th International Conference on System Theory, Control and Computing (ICSTCC)
This work is devoted to the development of an optimal infinite-dimensional Luenberger observer fo... more This work is devoted to the development of an optimal infinite-dimensional Luenberger observer for a system of hyperbolic PDEs. For this purpose, the duality fact linking the control design and the observer design is used. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to the process of fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the fixed-bed reactor state is investigated by using the developed algorithm.
2009 European Control Conference (ECC), 2009
The concept of asymptotic stability is studied for a class of dissipative semi-linear infinite-di... more The concept of asymptotic stability is studied for a class of dissipative semi-linear infinite-dimensional Banach state space systems with nonlinearity defined on a convex subset of the state space. Stability criteria are established, which are based on a weaker technical condition of the m-dissipativity. These theoretical results are applied to a class of transport-reaction processes. Different types of nonlinearity are studied by adapting the criteria given in the early portions of the paper.
2020 24th International Conference on System Theory, Control and Computing (ICSTCC)
This work is devoted to the development of an optimal infinite-dimensional Luenberger observer fo... more This work is devoted to the development of an optimal infinite-dimensional Luenberger observer for a system of hyperbolic PDEs. For this purpose, the duality fact linking the control design and the observer design is used. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to the process of fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the fixed-bed reactor state is investigated by using the developed algorithm.
2017 13th IEEE International Conference on Control & Automation (ICCA), 2017
This paper is devoted to design an optimal linear quadratic controller for a time-varying system ... more This paper is devoted to design an optimal linear quadratic controller for a time-varying system of coupled parabolic and hyperbolic partial differential equations (PDEs). Infinite-dimensional state space approach is adopted to solve the control problem via the well-known operator Riccati equation. The latter is converted into a scalar partial differential equation coupled with a set of ordinary differential equations. The main algorithm to solve the Riccati equation is presented. The designed controller is tested on a model of catalytic packed-bed chemical reactor to show the performances of the developed controller.
2009 European Control Conference (ECC), 2009
The concept of asymptotic stability is studied for a class of dissipative semi-linear infinite-di... more The concept of asymptotic stability is studied for a class of dissipative semi-linear infinite-dimensional Banach state space systems with nonlinearity defined on a convex subset of the state space. Stability criteria are established, which are based on a weaker technical condition of the m-dissipativity. These theoretical results are applied to a class of transport-reaction processes. Different types of nonlinearity are studied by adapting the criteria given in the early portions of the paper.
Journal of the Franklin Institute, 2020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
2017 13th IEEE International Conference on Control & Automation (ICCA), 2017
This paper is devoted to design an optimal linear quadratic controller for a time-varying system ... more This paper is devoted to design an optimal linear quadratic controller for a time-varying system of coupled parabolic and hyperbolic partial differential equations (PDEs). Infinite-dimensional state space approach is adopted to solve the control problem via the well-known operator Riccati equation. The latter is converted into a scalar partial differential equation coupled with a set of ordinary differential equations. The main algorithm to solve the Riccati equation is presented. The designed controller is tested on a model of catalytic packed-bed chemical reactor to show the performances of the developed controller.
International Journal of Control, 2018
This paper deals with the design of a boundary optimal controller for a general model of paraboli... more This paper deals with the design of a boundary optimal controller for a general model of parabolichyperbolic PDEs coupled with an ODE. The augmented infinite-dimensional state-space representation has been used in order to solve the optimal state-feedback control problem. By using the perturbation theorem, it has been shown that the system generates a C 0-semigroup on the augmented state space. Also, the dynamical properties of both the original and the augmented systems have been studied. Under some technical conditions, it has been shown that the augmented system generates an exponentially stabilisable and detectable C 0-semigroups. The linear-quadratic control problem has been solved for the augmented system. A decoupling technique has been implemented to decouple and solve the corresponding Riccati equation. Monolithic catalyst reactor model has been used to test the performances of the developed controller through numerical simulations.
Journal of the Franklin Institute, 2020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
International Journal of Systems Science, 2018
This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller fo... more This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolicassociated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.
International Journal of Control, 2018
This paper deals with the design of a boundary optimal controller for a general model of paraboli... more This paper deals with the design of a boundary optimal controller for a general model of parabolichyperbolic PDEs coupled with an ODE. The augmented infinite-dimensional state-space representation has been used in order to solve the optimal state-feedback control problem. By using the perturbation theorem, it has been shown that the system generates a C 0-semigroup on the augmented state space. Also, the dynamical properties of both the original and the augmented systems have been studied. Under some technical conditions, it has been shown that the augmented system generates an exponentially stabilisable and detectable C 0-semigroups. The linear-quadratic control problem has been solved for the augmented system. A decoupling technique has been implemented to decouple and solve the corresponding Riccati equation. Monolithic catalyst reactor model has been used to test the performances of the developed controller through numerical simulations.
International Journal of Control, 2018
The present work proposes an extension of single-step formulation of full-state feedback control ... more 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.