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
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
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
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.
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)
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.
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.
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.