航天飞机雷达测图计划大块区域无效数据填补方法

在总结国内外对SRTM无效数据填补方法的基础上,针对直接用低精度的GTOPO30数据进行镶嵌填充SRTM无效数据会产生边界不光滑,细节表现不好的问题,采用Laplacian迭代修复算法。该算法是经典的基于偏微分方程(PDE)的图像修复算法。实例对比验证表明,该方法在对SRTM大块无效数据填补效果上明显好于用GTOPO30数据直接填补的效果,是获取完整SRTM数据的有效方法之一。     

基于耦合偏微分方程的图像去噪方法

本文基于Perona-Malik模型和四阶偏微分方程提出了耦合偏微分方程的平滑方法。实验表明,该方法能很好兼顾图像噪声消除和边缘保持,避免了二阶偏微分方程处理图像常出现的块效应,使图像平滑自然。     

基于PDE方法的遥感图像处理

前期处理后的遥感图像中主要剩有高斯白噪声和椒盐噪声,传统平滑滤波技术很难同时兼顾除噪和保持边缘的要求;所改进的偏微分方程（PDE）滤波算法能很好地适应遥感图像噪声特征,在消除噪声的同时能很好的保留边缘和纹理细节;仿真实验验证了算法的正确性及有效性;研究了算法关键参数的选择范围和处理效果,为实际应用提供指导。     

Adaptive control design for a nonlinear parabolic PDE: Application to water coning

Water coning is usually responsible for the production of undesirable water from oil wells. This phenomenon may cause a decrease in oil production rate, increase in water cut production, and costs, which subsequently leads to early shutdown of the well. Although the boundary control of the production rate was suggested for managing the problem, due to the uncertainty associated with the physical nature of petroleum reservoirs, it failed to be implemented in practice. To overcome this issue, the paper employs the adaptive control approach for the distributed parameter system, which is modelled using a nonlinear partial differential equation (PDE). For this purpose, an adaptive control law and an update law for estimating the uncertain parameter are developed using the direct Lyapunov method. Next, the global stability of the closed‐loop system with the abovementioned laws is proven. Finally, the effectiveness and performance of the proposed idea is demonstrated by numerical simulations. The results show that the thickness of an oil column tends to zero as time tends to infinity for the whole spatial domain. In other words, as time elapses, the whole oil column will be depleted before the cone breakthrough. The numerical simulation demonstrates that though water cone breakthrough is inevitable in the conventional way of production, the adaptive control approach successfully controls the cone growth up, even with no knowledge of reservoir permeability. The results of this study can be applied to any type of reservoir subjected to water coning.

     

Pricing the financial Heston–Hull–White model with arbitrary correlation factors via an adaptive FDM

This paper is concerned with the pricing procedure of one of the most challenging models known as the Heston–Hull–White partial differential equation (PDE) in option pricing, at which the model is a time-dependent 3D linear PDE including three mixed derivative terms. The model comes from the fact that the price, the volatility and the interest rate are assumed to be stochastic processes. To contribute and avoid huge discretized systems, an adaptive distribution of the nodes (viz, nonuniform nodes) is taken into account with emphasis on the hot area of the solution curve. New adaptive finite difference (FD) formulas of higher orders are constructed on these meshes. Then, a set of semi-discretized equations is attained which is tackled by a time-stepping method. Several financial tests are discussed in detail to reveal the superiority of the proposed approach.     

Boundary Control for A Flexible Inverted Pendulum System Based on A Pde Model

A partial differential equation (PDE) model for a flexible inverted pendulum system (FIPS) is derived by the use of the Hamilton principle. To solve the coupling system model, a singular perturbation method was adopted. The PDE model was divided into a fast subsystem and a slow subsystem using the singular perturbation method. To stabilize the fast subsystem, a boundary control force was applied at the free end of the beam. It then was proven that the closed‐loop subsystem is appropriate and exponentially stable. For the slow subsystem, a sliding mode control method was employed to design a controller and the Linear Matrix Inequality (LMI) method was used to design the sliding surface. It then was shown that the slow subsystem is exponentially stable.     

Modeling and vibration control for a flexible pendulum inverted system based on a PDE observer

This study addresses the problem of trajectory control of a flexible pendulum inverted system on the basis of the partial differential equation (PDE) and ordinary differential equation (ODE) dynamic model. One of the key contributions of this study is that a new model is proposed to simplify the complex system. In addition, this study proposed a nonlinear PDE observer to estimate distributed positions and velocities along flexible pendulum. Singular perturbation method is proposed to solve the coupling system of nonlinear PDE observer. The nonlinear PDE observer is divided into a fast subsystem and a slow subsystem by the use of the singular perturbation method. To stabilise this fast subsystem, a boundary controller is proposed at the free end of the beam. The sliding-mode control method is proposed to design controller for slow subsystems. The asymptotic stability of both the proposed nonlinear PDE observer and controller is validated by theoretical analysis. The results are illustrated by simulation.     

Partial differential equation boundary control of a flexible manipulator with input saturation

In this study, we consider the boundary control problem of a flexible manipulator in the presence of input saturation and input disturbances. The dynamics of the flexible system are represented by partial differential equations (PDEs). Based on disturbance observers, a boundary control scheme is designed to regulate angular position and suppress elastic vibration simultaneously. The proposed control scheme allows the application of smooth hyperbolic functions, which satisfy physical conditions and input restrictions, easily be realised. It is proved that the proposed control scheme can be guaranteed in handling input saturation and external disturbances. The stability is achieved through rigorous analysis without any simplification of the dynamics. Numerical simulations demonstrate the effectiveness of the proposed scheme.