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Papers by SOUFIANE YAHYAOUI

In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equa... more In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equation. We first study the problem of optimal control in a finite-time interval and then focus on the case of the infinite time horizon. We further show that the obtained optimal control guarantees the strong stability of the system at hand. An illustrating numerical example is given.

International Journal of Control, May 25, 2022

In this work, we will investigate the question of optimal control for bilinear systems with const... more In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former. Then a class of bilinear systems for which the optimal control can be expressed as a time-varying feedback law will be identified. Finally, applications to parabolic and hyperbolic partial differential equations are provided.

Research Square (Research Square), Oct 17, 2022

In this paper, we will investigate the optimal control problem for unbounded bilinear systems, wi... more In this paper, we will investigate the optimal control problem for unbounded bilinear systems, with (p, q)-admissible control operators. We will first study the case of finite time-horizon with unconstrained or constrained endpoint. This result is further applied to build the optimal control for infinite time horizon. Finally, we solve the bilinear optimal control for the transport equation. Then we consider the fractional diffusion equation, for which we prove the strong stabilisation by an optimal time-varying feedback control.

Lecture notes in networks and systems, Nov 14, 2020

In this work, we consider a stabilization problem of a class of distributed bilinear systems defi... more In this work, we consider a stabilization problem of a class of distributed bilinear systems defined on a Hilbert state space. Then we give an explicit stabilizing control that minimizes an appropriate quadratic cost. The approach is based on Lyapunov function techniques and on a spectral decomposed method. Applications and simulations for parabolic and hyperbolic systems are developed.

In this paper, we will investigate the optimal control problem for unbounded bilinear systems, wi... more In this paper, we will investigate the optimal control problem for unbounded bilinear systems, with (p, q)-admissible control operators. We will first study the case of finite time-horizon with unconstrained or constrained endpoint. This result is further applied to build the optimal control for infinite time horizon. Finally, we solve the bilinear optimal control for the transport equation. Then we consider the fractional diffusion equation, for which we prove the strong stabilisation by an optimal time-varying feedback control.

In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equa... more In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equation. We first study the problem of optimal control in a finite-time interval and then focus on the case of the infinite time horizon. We further show that the obtained optimal control guarantees the strong stability of the system at hand. An illustrating numerical example is given.

In this work, we will investigate the question of optimal control for bilinear systems with const... more In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former. Then a class of bilinear systems for which the optimal control can be expressed as a time-varying feedback law will be identified. Finally, applications to parabolic and hyperbolic partial differential equations are provided.

In this work, we consider a stabilization problem of a class of distributed bilinear systems defi... more In this work, we consider a stabilization problem of a class of distributed bilinear systems defined on a Hilbert state space. Then we give an explicit stabilizing control that minimizes an appropriate quadratic cost. The approach is based on Lyapunov function techniques and on a spectral decomposed method. Applications and simulations for parabolic and hyperbolic systems are developed.

Optimal Control Applications and Methods

In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equa... more In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equation. We first study the problem of optimal control in a finite-time interval and then focus on the case of the infinite time horizon. We further show that the obtained optimal control guarantees the strong stability of the system at hand. An illustrating numerical example is given.

International Journal of Control, May 25, 2022

In this work, we will investigate the question of optimal control for bilinear systems with const... more In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former. Then a class of bilinear systems for which the optimal control can be expressed as a time-varying feedback law will be identified. Finally, applications to parabolic and hyperbolic partial differential equations are provided.

Research Square (Research Square), Oct 17, 2022

In this paper, we will investigate the optimal control problem for unbounded bilinear systems, wi... more In this paper, we will investigate the optimal control problem for unbounded bilinear systems, with (p, q)-admissible control operators. We will first study the case of finite time-horizon with unconstrained or constrained endpoint. This result is further applied to build the optimal control for infinite time horizon. Finally, we solve the bilinear optimal control for the transport equation. Then we consider the fractional diffusion equation, for which we prove the strong stabilisation by an optimal time-varying feedback control.

Lecture notes in networks and systems, Nov 14, 2020

In this work, we consider a stabilization problem of a class of distributed bilinear systems defi... more In this work, we consider a stabilization problem of a class of distributed bilinear systems defined on a Hilbert state space. Then we give an explicit stabilizing control that minimizes an appropriate quadratic cost. The approach is based on Lyapunov function techniques and on a spectral decomposed method. Applications and simulations for parabolic and hyperbolic systems are developed.

In this paper, we will investigate the optimal control problem for unbounded bilinear systems, wi... more In this paper, we will investigate the optimal control problem for unbounded bilinear systems, with (p, q)-admissible control operators. We will first study the case of finite time-horizon with unconstrained or constrained endpoint. This result is further applied to build the optimal control for infinite time horizon. Finally, we solve the bilinear optimal control for the transport equation. Then we consider the fractional diffusion equation, for which we prove the strong stabilisation by an optimal time-varying feedback control.

In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equa... more In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equation. We first study the problem of optimal control in a finite-time interval and then focus on the case of the infinite time horizon. We further show that the obtained optimal control guarantees the strong stability of the system at hand. An illustrating numerical example is given.

In this work, we will investigate the question of optimal control for bilinear systems with const... more In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former. Then a class of bilinear systems for which the optimal control can be expressed as a time-varying feedback law will be identified. Finally, applications to parabolic and hyperbolic partial differential equations are provided.

In this work, we consider a stabilization problem of a class of distributed bilinear systems defi... more In this work, we consider a stabilization problem of a class of distributed bilinear systems defined on a Hilbert state space. Then we give an explicit stabilizing control that minimizes an appropriate quadratic cost. The approach is based on Lyapunov function techniques and on a spectral decomposed method. Applications and simulations for parabolic and hyperbolic systems are developed.

Optimal Control Applications and Methods