The goal of this paper is to study an output stabilization problem: the gradient stabilization for linear distributed systems. Firstly, we give definitions and properties of the gradient stability. Then we characteriz...The goal of this paper is to study an output stabilization problem: the gradient stabilization for linear distributed systems. Firstly, we give definitions and properties of the gradient stability. Then we characterize controls which stabilize the gradient of the state. We also give the stabilizing control which minimizes a performance given cost. The obtained results are illustrated by simulations in the case of one-dimensional distributed systems.展开更多
This paper addresses a gradient tracking problem of a bilinear reaction–diffusion equation evolvingin a spatial domainΩ ⊂ Rn, n ≤ 3. Such an equation is excited with distributed and boundedcontrols. The problem is ...This paper addresses a gradient tracking problem of a bilinear reaction–diffusion equation evolvingin a spatial domainΩ ⊂ Rn, n ≤ 3. Such an equation is excited with distributed and boundedcontrols. The problem is formulated by the minimisation of a functional constituted of the deviationbetween the desired gradient and the current one all over a time interval and the energyterm. Then we prove the existence of an optimal control that we characterise by an optimalitysystem. Moreover, we discuss two sets of particular controls: the set of time dependent controlsand the space dependent ones. A computational approach and illustrative simulations are alsogiven.展开更多
The aim of this paper is to investigate a regional constrained optimal control problem for a class of semi[inear distributed systems, which are linear in the control but nonlinear in the state. For a quadratic cost fu...The aim of this paper is to investigate a regional constrained optimal control problem for a class of semi[inear distributed systems, which are linear in the control but nonlinear in the state. For a quadratic cost functional and a closed convex set of admissible controls, the existence of an optimal control is proven, and then this is characterized for three cases of constraints. A useful algorithm is developed, and the approach is illustrated through simulations for a heat equation.展开更多
This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output stabilisation.Also,the output sta...This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output stabilisation.Also,the output stabilisation is discussed using a minimisation problem.Examples and simulations are given.展开更多
文摘The goal of this paper is to study an output stabilization problem: the gradient stabilization for linear distributed systems. Firstly, we give definitions and properties of the gradient stability. Then we characterize controls which stabilize the gradient of the state. We also give the stabilizing control which minimizes a performance given cost. The obtained results are illustrated by simulations in the case of one-dimensional distributed systems.
文摘This paper addresses a gradient tracking problem of a bilinear reaction–diffusion equation evolvingin a spatial domainΩ ⊂ Rn, n ≤ 3. Such an equation is excited with distributed and boundedcontrols. The problem is formulated by the minimisation of a functional constituted of the deviationbetween the desired gradient and the current one all over a time interval and the energyterm. Then we prove the existence of an optimal control that we characterise by an optimalitysystem. Moreover, we discuss two sets of particular controls: the set of time dependent controlsand the space dependent ones. A computational approach and illustrative simulations are alsogiven.
文摘The aim of this paper is to investigate a regional constrained optimal control problem for a class of semi[inear distributed systems, which are linear in the control but nonlinear in the state. For a quadratic cost functional and a closed convex set of admissible controls, the existence of an optimal control is proven, and then this is characterized for three cases of constraints. A useful algorithm is developed, and the approach is illustrated through simulations for a heat equation.
基金Thiswork was supported byAcadémieHassan II des Sciences et Techniques[630/2016].
文摘This paper is concerned with the output stabilisation for a class of distributed bilinear system evolving in a spatial domain.We give sufficient conditions for strong and weak output stabilisation.Also,the output stabilisation is discussed using a minimisation problem.Examples and simulations are given.
