Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous sta...Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.展开更多
The paper gives two examples of larger construction projects with typical stability problems. The first example is from Sakhalin Island in the Russian Far East. It is connected with a construction of oil and gas pipel...The paper gives two examples of larger construction projects with typical stability problems. The first example is from Sakhalin Island in the Russian Far East. It is connected with a construction of oil and gas pipelines through the mountainous terrain in Makarov region. The region has an active geotectonic history and is highly affected by uncontrolled erosion and extensive landslips. Basic principles of landslide hazard mitigation are presented. The second example is from a motorway construction in Azerbaijan. This motorway leads from Baku to Russia through a seismo-tectonically active area at the toe of Caucasian mountains and in some places is situated in deep cuts at the toe of high slopes. This unsuitable routing, together with seismic activity, led to a slope stability failure of a slope affected by recent tectonic movements near the village of Devechi. Stability conditions and designed remedy measures are presented.展开更多
For stabilized saddle-point problems, we apply the two iteration parameters idea for regularized Hermitian and skew-Hermitian splitting (RHSS) method and establish accelerated RHSS (ARHSS) iteration method. Theoretica...For stabilized saddle-point problems, we apply the two iteration parameters idea for regularized Hermitian and skew-Hermitian splitting (RHSS) method and establish accelerated RHSS (ARHSS) iteration method. Theoretical analysis shows that the ARHSS method converges unconditionally to the unique solution of the saddle point problem. Finally, we use a numerical example to confirm the effectiveness of the method.展开更多
This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incr...This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.展开更多
The solution of a slope stability problem can be approached by its least upper-bound and maximum lower-bound with high accuracy. The limit equilibrium methods that employ vertical slices imply a lower bound of the fac...The solution of a slope stability problem can be approached by its least upper-bound and maximum lower-bound with high accuracy. The limit equilibrium methods that employ vertical slices imply a lower bound of the factor of safety. It has been successfully extended to the area of active earth pressure analysis that accounts for different input of locations of earth pressure applications. Those methods that employ slices with inclined interfaces give an upper-bound approach to the stability analysis. It enjoys a sound mechanical background and is able to provide accurate solutions of soil plasticity. It has been successfully extended to the area of bearing capacity analysis in which various empirical coefficients are no longer necessary. The 3D upper- and lower-bound methods under this framework have been made possible and show great potential for solving various engineering problems.展开更多
In terms of Hadamard product, a new model is proposed for the control of connection coefficients of the state variables of the systems. The control law to stabilize the systems via the regulations of connection coeffi...In terms of Hadamard product, a new model is proposed for the control of connection coefficients of the state variables of the systems. The control law to stabilize the systems via the regulations of connection coefficients is obtained via a Hadamard product involved bilinear matrix inequalities. This new control model may be of significant applications in many fields, especially may be of some special sense in the emergency control such as isolation and obstruction control.展开更多
The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading ...The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.展开更多
In this paper. we discuss the existence and stability of solution for two semi-homogeneous boundary value problems. The relative theorems in [1.2] are extended. Meanwhile. we obtain some new results.
We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved ...We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging.展开更多
In this paper, we discuss the problem of stability of Volterra integrodifferential equationwith the decompositionwhere andin which is an matrix of functionB continuous forin which is an matrix of functionscontinuous f...In this paper, we discuss the problem of stability of Volterra integrodifferential equationwith the decompositionwhere andin which is an matrix of functionB continuous forin which is an matrix of functionscontinuous for 0≤S≤ t<∞.According to the decomposition theory of large scale system and with the help of Liapunovfunctional, we give a criterion for concluding that the zero solution of (2) (i.e. large scale system(1)) is uniformly asymptotically stable.We also discuss the large scale system with the decompositionand give a criterion for determining that the solutions of (4) (i.e. large scale system (3)) areuniformly bounded and uniformly ultimately bounded.Those criteria are of simple forms, easily checked and applied.展开更多
We discuss a filtration problem in a bounded one-dimensional porous medium. Suppose that the.volumetric moisture content at the surface is constant, and the bottom is impermeable. We prove thatthe solution will tend u...We discuss a filtration problem in a bounded one-dimensional porous medium. Suppose that the.volumetric moisture content at the surface is constant, and the bottom is impermeable. We prove thatthe solution will tend uniformly to a stable solution of the filtration equation as time tends to infinity.An explicit expression of the limiting profile is given.展开更多
基金supported by the National Natural Science Foundation of China(62403393,12202058,62103118)the China Postdoctoral Science Foundation(2021T140160,2023 T160051)the Natural Science Foundation of Chongqing(CSTB 2023NSCQ-MSX0152)
文摘Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.
文摘The paper gives two examples of larger construction projects with typical stability problems. The first example is from Sakhalin Island in the Russian Far East. It is connected with a construction of oil and gas pipelines through the mountainous terrain in Makarov region. The region has an active geotectonic history and is highly affected by uncontrolled erosion and extensive landslips. Basic principles of landslide hazard mitigation are presented. The second example is from a motorway construction in Azerbaijan. This motorway leads from Baku to Russia through a seismo-tectonically active area at the toe of Caucasian mountains and in some places is situated in deep cuts at the toe of high slopes. This unsuitable routing, together with seismic activity, led to a slope stability failure of a slope affected by recent tectonic movements near the village of Devechi. Stability conditions and designed remedy measures are presented.
文摘For stabilized saddle-point problems, we apply the two iteration parameters idea for regularized Hermitian and skew-Hermitian splitting (RHSS) method and establish accelerated RHSS (ARHSS) iteration method. Theoretical analysis shows that the ARHSS method converges unconditionally to the unique solution of the saddle point problem. Finally, we use a numerical example to confirm the effectiveness of the method.
文摘This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.
基金Project (Nos. 50539100,50679035 and 50509027) supported by the National Natural ScienceFoundation of China
文摘The solution of a slope stability problem can be approached by its least upper-bound and maximum lower-bound with high accuracy. The limit equilibrium methods that employ vertical slices imply a lower bound of the factor of safety. It has been successfully extended to the area of active earth pressure analysis that accounts for different input of locations of earth pressure applications. Those methods that employ slices with inclined interfaces give an upper-bound approach to the stability analysis. It enjoys a sound mechanical background and is able to provide accurate solutions of soil plasticity. It has been successfully extended to the area of bearing capacity analysis in which various empirical coefficients are no longer necessary. The 3D upper- and lower-bound methods under this framework have been made possible and show great potential for solving various engineering problems.
基金supported by the National Natural Science Foundation of China (No.60874007)the Research Fund for the Doctoral Program of Higher Education (No.200802550024)
文摘In terms of Hadamard product, a new model is proposed for the control of connection coefficients of the state variables of the systems. The control law to stabilize the systems via the regulations of connection coefficients is obtained via a Hadamard product involved bilinear matrix inequalities. This new control model may be of significant applications in many fields, especially may be of some special sense in the emergency control such as isolation and obstruction control.
基金Project supported by the Natural Science and Engineering Research Council (NSERC) of Canada (No.NSERC-RGPIN204992)
文摘The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.
文摘In this paper. we discuss the existence and stability of solution for two semi-homogeneous boundary value problems. The relative theorems in [1.2] are extended. Meanwhile. we obtain some new results.
文摘We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging.
基金This project is supported by the National Natural Science Foundation of China
文摘In this paper, we discuss the problem of stability of Volterra integrodifferential equationwith the decompositionwhere andin which is an matrix of functionB continuous forin which is an matrix of functionscontinuous for 0≤S≤ t<∞.According to the decomposition theory of large scale system and with the help of Liapunovfunctional, we give a criterion for concluding that the zero solution of (2) (i.e. large scale system(1)) is uniformly asymptotically stable.We also discuss the large scale system with the decompositionand give a criterion for determining that the solutions of (4) (i.e. large scale system (3)) areuniformly bounded and uniformly ultimately bounded.Those criteria are of simple forms, easily checked and applied.
文摘We discuss a filtration problem in a bounded one-dimensional porous medium. Suppose that the.volumetric moisture content at the surface is constant, and the bottom is impermeable. We prove thatthe solution will tend uniformly to a stable solution of the filtration equation as time tends to infinity.An explicit expression of the limiting profile is given.
