Existence of Solutions and Approximate Controllability of Fractional Nonlocal Neutral Impulsive Stochastic Differential Equations of Order 1 &lt; <Emphasis Type="Italic">q</Emphasis> &lt; 2 with Infinite Delay and Poisson Jumps

In this paper, we study the existence of mild solutions and the approximate controllability of nonlinear fractional nonlocal neutral impulsive stochastic differential equations of order 1 < q < 2 with infinite delay and Poisson jumps in which the initial value belong to the abstract phase space C _h . The existence of mild solutions is derived with the help of Sadovskii’s fixed point theorem. The approximate controllability of the nonlinear fractional nonlocal neutral impulsive stochastic differential systems of order 1 < q < 2 with infinite delay and Poisson jumps is discussed under the assumption that the corresponding linear system is approximately controllable. Moreover, the approximate controllability of the above control system is established by using Lebesgue dominated convergence theorem. An example is provided to illustrate the theory.     

Approximate Controllability of Fractional Semilinear Stochastic System of Order <Emphasis Type="Italic">α</Emphasis>∈ (1,2]

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in L _p spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory.     

Approximate Controllability of Nonlocal Neutral Fractional Integro-Differential Equations with Finite Delay

In this paper, we obtain a set of sufficient conditions to prove the approximate controllability for a class of nonlocal neutral fractional integro-differential equations, with time varying delays, considered in a Hilbert space. We also establish the existence of a mild solution of the system. The main tools used in our analysis are the theory of analytic semigroups, the theory of fractional powers of operators, α-norm, fractional calculus, and Krasnoselskii’s fixed point theorem. An example is provided to illustrate the applicability of the main results.     

Approximate controllability of semilinear partial functional differential systems

In this paper, we study the approximate controllability of semilinear neutral functional-differential systems and impulsive functional-differential systems with finite delay. Since the considered equations admit nonlinear terms involving spatial derivatives, the fraction power theory and α-norm is used to discuss the problem so that the established results can be applied to them. An example is provided to illustrate the application of the obtained results. This work is supported by NNSF of China (No. 10671069) and Shanghai Leading Academic Discipline Project (No. B407).     

Approximate controllability for neutral impulsive differential inclusions with nonlocal conditions

In this paper, we study the approximate controllability of semilinear impulsive functional differential inclusions with nonlocal conditions. Analytic semigroup theory and α-norm arguments are employed to ensure that the obtained results can be applied to the systems involving spatial derivatives. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in literature is not required here. An example is provided to illustrate the application of the obtained results.     

Approximate Controllability for a Class of Linear Neutral Evolution Systems with Infinite Delay

This paper deals with the approximate controllability problem for a class of linear neutral evolution systems with infinite delay in Banach spaces. Since the concerned system involves additional linear terms, the fundamental solution theory is used to describe the mild solutions. Based on the spectral analysis and the adjoint system, sufficient conditions for the approximate controllability of the concerned system are established. The rank condition is also shown when the control space is finite-dimensional. A practical example is given to show the application of the obtained results.

     

Null Controllability with Constraints on the State for Stochastic Heat Equation

This paper is concerned with a null controllability problem for stochastic heat equation with finite number of constraints on the state. First, we transform the problem into a null controllability problem with constraint on the control. Then, we prove an adapted Carleman estimate. Applying this estimate, we establish a bilinear form and obtain the main result.     

Existence and Controllability for Impulsive Evolution Inclusions without Compactness

In this paper, we investigate the existence and controllability for impulsive evolution inclusions in Banach spaces. By using weak topology technique and Glicksberg-Ky Fan fixed point theorem, we obtain the existence of mild solutions and controllability outcomes, avoiding hypotheses of compactness on the semigroup generated by the linear part and any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. Finally, we show an illustration to outline the plausibility of the theoretical results.     

计及随机波动风速、风向的风电场建模方法研究

提出风电场建模方法建立风电场随机模型,对风电场运行特性进行仿真,为实现大规模风力发电的可预测、可控制目标服务。通过对风电场等值模型与详细模型的仿真比较,验证建模方法的合理性,并得出在研究风电场动态特性及其对电网影响时应考虑风速、风向的随机波动建立风电场模型。     

Mild Solution and Constrained Local Controllability of Semilinear Boundary Control Systems

The existence of mild solution and the constrained local controllability of a retarded boundary control system with nonlocal delay condition have been established. The theory of extrapolation spaces is applied to derive the mild solution. Then, the constrained local controllability is established using the generalized open mapping theorem. In the last section, application of the result is shown through examples of control systems represented by hyperbolic partial differential equations.     

动态控制锅炉低温腐蚀和节能的有效措施

从控制原理、系统设计、锅炉的可控性、暖风器的可控性等方面论述了一种动态控制锅炉低温腐蚀的有效措施及其经济性。图 1表 4参 3     

Discharge of a shock wave from an open end of a tube

IntroductionWhen a Pressure wave such as the shock waveprOPagates along a constant area straight tube andreaches at the open end, an impulsive wave is emittedOutward from the tube exit toward the surrounding areaand causes an impulsive noise laal a sonic boomproduced by a supersonic aircraft. Therefore, someauthors have investigated the discharge of a weakcompression wave from an open end in order to reducethe impulsive noise in relation to'the high speed railWaytUImel in the previous paped'…     

Deformation and tearing of clamped circular work-hardening plates under impulsive loading

An approximate theory is presented in this paper to predict the deformation and tearing of clamped circular work-hardening plates subjected to uniformly distributed impulsive loads. Based on a power law stress-strain relationship throughout, various equations are obtained and an effective strain failure criterion is suggested for the rupture of the plates. It is shown that the theoretical predictions are in good agreement with the experimental observations in terms of the maximum permanent transverse displacements and the critical input impulses which caused the tensile tearing failure of the plates under impulsive loading when material strain rate sensitivity is taken into account. It is also shown that, to a first approximation, the theory developed for circular plates is applicable to rectangular plates.     

时滞分数阶直驱风力发电机模糊混沌控制

为研究含有状态时滞的分数阶直驱风电系统（D-PMSG）混沌控制问题,提出模糊记忆状态反馈控制策略。首先,利用T-S模糊理论和分数阶微积分理论建立D-PMSG时滞系统模糊混沌模型;其次,基于并行分布补偿（PDC）控制技术,设计出模糊记忆状态反馈控制器;然后,利用Lyapunov稳定性理论和分数阶微积分性质,基于Schur补引理,以线性矩阵不等式（LMI）形式给出系统渐近稳定的充分条件;最后,利用Oustaloup滤波器逼近分数阶微积分算子,搭建仿真模型,验证该系统模型的正确性及控制方案的有效性,与无记忆状态反馈控制器相比,模糊记忆状态反馈控制器具有更好的控制性能和鲁棒性能。     

Fractional phase-lag Green–Naghdi thermoelasticity theories

The constitutive equations are given with a fractional Maxwell–Cattaneo heat conduction law using the Caputo fractional derivative and the fractional order heat transport equation is given. The uniqueness theorem is proved, the reciprocity relation is deduced and the variational characterization of solution is given. Seven thermoelasticity theories result from the given problem as special cases (Coupled, Lord–Shulman, phase-lag Green–Naghdi theories, Green–Naghdi theory without energy dissipation and the Green–Naghdi theory of type III).     

基于转速估计的PMSM分数阶积分滑模控制

针对永磁同步电机(PMSM)运行过程中内部参数变化和外部负载扰动影响控制性能的问题,采用基于分数阶滑模观测器的PMSM分数阶积分滑模控制(FOISMC)策略。基于FOISMC技术,设计基于新型趋近律的分数阶积分滑模转速调节器,给出能保证系统全局鲁棒性的全程积分滑模面设计方法。基于分数阶理论和滑模控制理论构造分数阶滑模观测器,以实现对速度和转子位置角的高精度估计。仿真实验验证了所提方法的可行性和有效性。     

Local Controllability for Linear Control Systems on Lie Groups

Abtract  In this work, we study controllability properties of linear control systems on Lie groups. Using Lie theory of semigroups, we obtain local controllability results for this type of systems. In addition, properties for the flow of the drift vector field X and for the reachable set of the system are presented. Finally, an example on the Heisenberg Lie group is considered, and its properties are proved using the theory developed. 2000 Mathematics Subject Classification. Primary 93B05; Secondary 93C25, 93B27. The authors want to thank the Fachbereich Mathematik of the Technische Universit?t Darmstadt for warm hospitality during the production of this work. The first author is pleased to thank Professor Guillermo Ferreyra and the department of mathematics at LSU for their support.     

Two temperature fractional order thermoelasticity theory in a spherical domain

This article is an application of fractional thermoelasticity in association with two-temperature theory. The fractional heat conduction model has been proposed to investigate the thermal variations within the bounded spherical region. The corresponding heat conduction equation has been derived in the context of the generalized two-temperature theory of fractional thermoelasticity. The analytical solutions of thermal variations have been obtained in the Laplace domain, which are inverted using the Gaver–Stehfest algorithm in the time domain. Kuznetsov convergence criterion has been discussed for the bounded variations and stability of the problem. The delay time translations used in the heat flux vector and the temperature gradient result in the finite speed of thermal wave propagation. As a special case of time fractional derivative, the classical and generalized thermoelasticity theories have been recovered.     

Transient response of a hygrothermoelastic cylinder based on fractional diffusion wave theory

A coupled fractional hygrothermoelasticity theory is formulated within the framework of fractional calculus. Both the classical Fourier’s and Fick’s laws are generalized to anomalous diffusion which is characterized by the time- fractional diffusion-wave equation. Based on the fractional hygrothermoelasticity theory, the transient response of an infinitely long cylinder subjected to hygrothermal loadings at the surface is analyzed. The finite Hankel integral transform method and decoupled technique are used to derive closed-form expressions for temperature, moisture, displacement, and hygrothermal stresses in the solid. The coupling effect of temperature and moisture on elastic fields is discussed. Numerical results of transient response of hygrothermoelastic fields are presented graphically for the cases of subdiffusion, normal diffusion, and superdiffusion, respectively.