In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonloc...In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is also provided to show an application of the obtained result.展开更多
The aim of this work is to improve the minimum time of null controllability of the 1D heat equation by using the notion of strategic zone actuators. In fact, motivated by the work of Khodja on the null controllability...The aim of this work is to improve the minimum time of null controllability of the 1D heat equation by using the notion of strategic zone actuators. In fact, motivated by the work of Khodja on the null controllability of the heat equation and of El Jai on the controllability by the use of strategic zone actuators, we managed, in this work, to improve the minimal time of null controllability to the 1D heat equation. However, the restrictions and difficulties to establish the inequality of coercivity of the parabolic operator, require to seek other methods of internal control. Thus in this paper, a mixed method combining the method of moments and the notion of strategic profile was used to find a better minimal time of null controllability of the 1D heat equation.展开更多
This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a suffi...This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.展开更多
In this paper, we establish a bang-bang principle of time optimal controls for a controlled parabolic equation of fractional order evolved in a bounded domain Ω of R^n, with a controller w to be any given nonempty op...In this paper, we establish a bang-bang principle of time optimal controls for a controlled parabolic equation of fractional order evolved in a bounded domain Ω of R^n, with a controller w to be any given nonempty open subset of Ω. The problem is reduced to a new controllability property for this equation, i.e. the null controllability of the system at any given time T 〉 0 when the control is restricted to be active in ω× E, where E is any given subset of [0, T] with positive （Legesgue） measure. The desired controllability result is established by means of a sharp observability estimate on the eigenfunctions of the Dirichlet Laplacian due to Lebeau and Robbiano, and a delicate result in the measure theory due to Lions.展开更多
In this paper,we are dealing with the null controllability of fractional stochastic differential system with fractional Brownian motion.The null controllability for Sobolev-type Hilfer fractional stochastic differenti...In this paper,we are dealing with the null controllability of fractional stochastic differential system with fractional Brownian motion.The null controllability for Sobolev-type Hilfer fractional stochastic differential system with fractional Brownian motion of Clarke’s subdifferential type is studied.The sufficient conditions for null controllability of fractional stochastic differential system with fractional Brownian motion and control on the boundary are established.Finally,an example is given to illustrate the obtained results.展开更多
In this article, the authors establish the local null controllability property for semilinear parabolic systems in a domain whose boundary moves in time by a single control force acting on a prescribed subdomain. The ...In this article, the authors establish the local null controllability property for semilinear parabolic systems in a domain whose boundary moves in time by a single control force acting on a prescribed subdomain. The proof is based on Kakutani＇s fixed point theorem combined with observability estimates for the associated lineaxized system.展开更多
This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes th...This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathematiques Pures et Appliquees, 2016.] for a class of strictly hyperbolic systems of conservation laws.展开更多
Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability e...Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.展开更多
In the paper, the null interior controllability for a fourth order parabolic equation is obtained. The method is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of ...In the paper, the null interior controllability for a fourth order parabolic equation is obtained. The method is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of eigenfunctions of the Laplacian.展开更多
This paper deals with the problem of internal controllability of a system of heat equations posed on a bounded domain with Dirichlet boundary conditions and perturbed with analytic non-local coupling terms. Each compo...This paper deals with the problem of internal controllability of a system of heat equations posed on a bounded domain with Dirichlet boundary conditions and perturbed with analytic non-local coupling terms. Each component of the system may be controlled in a different subdomain. Assuming that the unperturbed system is controUable--a property that has been recently characterized in terms of a Kalman-like rank condition--the authors give a necessary and sufficient condition for the controllability of the coupled system under the form of a unique continuation property for the corresponding elliptic eigenvalue system. The proof relies on a compactness-uniqueness argument, which is quite unusual in the context of parabolic systems, previously developed for scalar parabolic equations. The general result is illustrated by two simple examples.展开更多
This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal Lp norm and L∞ norm of a control needed to control the system approximat...This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal Lp norm and L∞ norm of a control needed to control the system approximately or a control needed to steer the state of the system to zero. The methods we use combine observability inequalities, energy estimates for heat equations and the dual theory.展开更多
The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T ...The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T 〉 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.展开更多
In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced couple...In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced coupled system, under certain conditions of compatibility, the exact synchronization, the exact synchronization by groups, and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.展开更多
This manuscript is mainly focusing on the approximate controllability and the null controllability for fractional neutral stochastic partial differential equations with delay driven by Rosenblatt pro-cess.We discuss t...This manuscript is mainly focusing on the approximate controllability and the null controllability for fractional neutral stochastic partial differential equations with delay driven by Rosenblatt pro-cess.We discuss the sufficient conditions for approximate controllability and null controllability for Hilfer fractional neutral stochastic partial differential equations driven by Rosenblatt process.Finally,we provide two examples to verify the obtained results.展开更多
This paper discusses the null boundary controllability of two PDE's,modeling a compositesolid with different physical properties in each layer.Interface conditions are imposed.
The global stabilization of asymptotically null controllable linear systems by bounded control is considered. A nested type saturation control law is proposed which is a generalization of the existing results reported...The global stabilization of asymptotically null controllable linear systems by bounded control is considered. A nested type saturation control law is proposed which is a generalization of the existing results reported in the literature. The primary characteristic of this modified control law is that more design parameters, which are the closed-loop eigenvalues when the system is operating in linear form, are introduced and which can be well designed to achieve better system performance. Using this law, the pole locations of the closed-loop systems depending on a linear trans- formation can be placed arbitrarily within certain areas. Numerical example shows that the performance of the closed-loop system under this control law can be significantly improved if the free parameters are properly chosen.展开更多
基金supported by NSF of China (11171110)Shanghai Leading Academic Discipline Project (B407)
文摘In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is also provided to show an application of the obtained result.
文摘The aim of this work is to improve the minimum time of null controllability of the 1D heat equation by using the notion of strategic zone actuators. In fact, motivated by the work of Khodja on the null controllability of the heat equation and of El Jai on the controllability by the use of strategic zone actuators, we managed, in this work, to improve the minimal time of null controllability to the 1D heat equation. However, the restrictions and difficulties to establish the inequality of coercivity of the parabolic operator, require to seek other methods of internal control. Thus in this paper, a mixed method combining the method of moments and the notion of strategic profile was used to find a better minimal time of null controllability of the 1D heat equation.
基金supported by the National Natural Science Foundation of China under Grants 61821004,62250056,62350710214,U23A20325,62350055the Natural Science Foundation of Shandong Province,China(ZR2021ZD14,ZR2021JQ24)+2 种基金High-level Talent Team Project of Qingdao West Coast New Area,China(RCTD-JC-2019-05)Key Research and Development Program of Shandong Province,China(2020CXGC01208)Science and Technology Project of Qingdao West Coast New Area,China(2019-32,2020-20,2020-1-4).
文摘This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.
基金Partially supported by National Natural Science Foundation of China (Grant No. 10525105)the NCET of China (Grant No. 04-0882)
文摘In this paper, we establish a bang-bang principle of time optimal controls for a controlled parabolic equation of fractional order evolved in a bounded domain Ω of R^n, with a controller w to be any given nonempty open subset of Ω. The problem is reduced to a new controllability property for this equation, i.e. the null controllability of the system at any given time T 〉 0 when the control is restricted to be active in ω× E, where E is any given subset of [0, T] with positive （Legesgue） measure. The desired controllability result is established by means of a sharp observability estimate on the eigenfunctions of the Dirichlet Laplacian due to Lebeau and Robbiano, and a delicate result in the measure theory due to Lions.
文摘In this paper,we are dealing with the null controllability of fractional stochastic differential system with fractional Brownian motion.The null controllability for Sobolev-type Hilfer fractional stochastic differential system with fractional Brownian motion of Clarke’s subdifferential type is studied.The sufficient conditions for null controllability of fractional stochastic differential system with fractional Brownian motion and control on the boundary are established.Finally,an example is given to illustrate the obtained results.
文摘In this article, the authors establish the local null controllability property for semilinear parabolic systems in a domain whose boundary moves in time by a single control force acting on a prescribed subdomain. The proof is based on Kakutani＇s fixed point theorem combined with observability estimates for the associated lineaxized system.
基金supported by the National Natural Science Foundation of China(No.11501122)
文摘This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathematiques Pures et Appliquees, 2016.] for a class of strictly hyperbolic systems of conservation laws.
基金Project supported by the National Natural Science Foundation of China(No.11101070)the Grant MTM2011-29306-C02-00 of the MICINN,Spain+4 种基金the Project PI2010-04 of the Basque Governmentthe ERC Advanced Grant FP7-246775 NUMERIWAVESthe ESF Research Networking Programme OPT-PDEScientific Research Fund of Sichuan Provincial Education Department of China(No.10ZC110) the project Z1062 of Leshan Normal University of China
文摘Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10671040, 10831007, 10801041)the National Excellent Doctoral Dissertation of China (Grant No. 200522)the New Century Excellent Talents in University (Grant No. 06-0359)
文摘In the paper, the null interior controllability for a fourth order parabolic equation is obtained. The method is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of eigenfunctions of the Laplacian.
文摘This paper deals with the problem of internal controllability of a system of heat equations posed on a bounded domain with Dirichlet boundary conditions and perturbed with analytic non-local coupling terms. Each component of the system may be controlled in a different subdomain. Assuming that the unperturbed system is controUable--a property that has been recently characterized in terms of a Kalman-like rank condition--the authors give a necessary and sufficient condition for the controllability of the coupled system under the form of a unique continuation property for the corresponding elliptic eigenvalue system. The proof relies on a compactness-uniqueness argument, which is quite unusual in the context of parabolic systems, previously developed for scalar parabolic equations. The general result is illustrated by two simple examples.
基金Supported by Key Project of Chinese Ministry of Education (No. i08046)National Natural Science Foundation of China (Nos. 10601010,10471021)Grant NENU-STC07007
文摘This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal Lp norm and L∞ norm of a control needed to control the system approximately or a control needed to steer the state of the system to zero. The methods we use combine observability inequalities, energy estimates for heat equations and the dual theory.
基金supported by the National Natural Science Foundation of China (No. 10671040)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200522) the Program for the New Century Excellent Talents in University of China (No. 06-0359)
文摘The paper deals with the controllability of a heat equation. It is well-known that the heat equation yt - △y = uxE in （0, T） × Ω with homogeneous Dirichlet boundary conditions is null controllable for any T 〉 0 and any open nonempty subset E of Ω. In this note, the author studies the case that E is an arbitrary measurable set with positive measure.
文摘In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced coupled system, under certain conditions of compatibility, the exact synchronization, the exact synchronization by groups, and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.
文摘This manuscript is mainly focusing on the approximate controllability and the null controllability for fractional neutral stochastic partial differential equations with delay driven by Rosenblatt pro-cess.We discuss the sufficient conditions for approximate controllability and null controllability for Hilfer fractional neutral stochastic partial differential equations driven by Rosenblatt process.Finally,we provide two examples to verify the obtained results.
文摘This paper discusses the null boundary controllability of two PDE's,modeling a compositesolid with different physical properties in each layer.Interface conditions are imposed.
基金Supported partially by the Major Program of the National Natural Science Foundation of China (Grant No. 60710002) and the Program for Changjiang Scholars and Innovative Research Team in University
文摘The global stabilization of asymptotically null controllable linear systems by bounded control is considered. A nested type saturation control law is proposed which is a generalization of the existing results reported in the literature. The primary characteristic of this modified control law is that more design parameters, which are the closed-loop eigenvalues when the system is operating in linear form, are introduced and which can be well designed to achieve better system performance. Using this law, the pole locations of the closed-loop systems depending on a linear trans- formation can be placed arbitrarily within certain areas. Numerical example shows that the performance of the closed-loop system under this control law can be significantly improved if the free parameters are properly chosen.
