Boundary controllability for the quasi-linear wave equations coupled in parallel

We study the boundary exact controllability for a system of two quasi-linear wave equations coupled in parallel with springs and viscous terms. We prove the locally exact controllability around superposition equilibria under some checkable geometrical conditions. We then establish the globally exact controllability in such a way that the state of the coupled quasi-linear system moves from a superposition equilibrium in one location to a superposition equilibrium in another location. Our results show that exact controllability is geometrical characters of a Riemannian metric, given by the coefficients and superposition equilibria of the system.     

Energy decay for the linear Klein–Gordon equation and boundary control

In this work we study the asymptotic behavior of the solutions of the linear Klein–Gordon equation in R^N${\mathbb{R}}^N$, N?1$N?1$. We prove that local energy of solutions to the Cauchy problem decays polynomially. Afterwards, we use the local decay of energy to study exact boundary controllability for the linear Klein–Gordon equation in general bounded domains of R^N${\mathbb{R}}^N$, N?1$N?1$.     

Global Exact Boundary Controllability for General First-Order Quasilinear Hyperbolic Systems

For general first-order quasilinear hyperbolic systems, based on the analysis of simple wave solutions along characteristic trajectories, the global two-sided exact boundary controllability is achieved in a relatively short controlling time.     

Controllability of Hilfer Fractional Differential Systems with Non-Dense Domain

In this paper, some exact controllability results are investigated for an integral solution of a non-densely defined abstract fractional differential system involving Hilfer fractional derivative. We tend to implement semigroup theory, fractional calculus, and measure of noncompactness to obtain the main results by fixed point technique. Finally, an application is given to illustrate the obtained results.     

光学镜面离子束加工去除函数工艺可控性分析

实验分析了离子束加工去除函数的工艺可控性问题并进行了初步修形实验。从工艺实现的角度分析光学镜面离子束加工技术对去除函数的要求,以去除函数环半峰全宽、体积去除率和峰值去除率为评价指标研究去除函数的长时稳定性、线性性、小扰动鲁棒性以及大参数调节变化等特征,以此分析结果为依据,对Φ100mm K4平面样件进行了修形,经过三次迭代面形RMS误差从0.149λ收敛到0.013λ。实验结果表明:离子束加工中的去除函数具有较长时稳定性,去除量对时间具有线性关系,对工艺参数小扰动的鲁棒性,可以通过调节离子源电源参数优化选取去除函数的宽度和幅值;利用离子束可以对镜面进行高效地修形。     

Generalized airy functions with complex variables

In the present paper,we have made a detailed study of the generalized Airy functions,which have found wide applications in the field of wave propagation and hydrodynamicstability.A series of tables and graphs are provided for the above functions with complexvariables.The results are proved satisfactory.     

Controllability of nonlinear Hilfer fractional Langevin dynamical system

The main objective of this article is to prove the controllability result of a nonlinear Hilfer fractional Langevin dynamical system in an abstract-weighted space. This paper initiates with the persistence of the control formula for the Hilfer fractional Langevin dynamical system. Furthermore, As ensue is extended to the controllability result of Hilfer fractional Langevin dynamical system by the use of Krasnoselskii fixed point theorem. Ultimately, an example is furnished to demonstrate our outcomes.     

Asymptotical feedback controllability of continuous-time probabilistic logic control networks

In this article, we study the controllability of continuous-time probabilistic logic control networks (CT-PLCNs) under sampled-data feedback controls (SDFCs). First, we demonstrate that the concept of finite-time controllability with probability one for discrete-time probabilistic logic control networks cannot be generalized to CT-PLCNs. Then, we propose the concepts of asymptotical feedback reachability and asymptotical feedback controllability for CT-PLCNs. Based on the invariant subsets, we prove that a target state is asymptotically feedback reachable if and only if the target state is a control equilibrium point and any initial state has an admissible path to the target state. Moreover, we introduce the concept of reachability matrix and propose an easily verifiable criterion for asymptotical feedback reachability expressed in terms of the reachability matrix. Based on these, we prove that a CT-PLCN is asymptotically feedback controllable if and only if every state is a control equilibrium point and there is an admissible path between any pair of initial and target states. The relation between controllability and stabilizability is also discussed. We prove that a CT-PLCN is asymptotically feedback controllable if and only if every state is asymptotically feedback stabilizable. For a controllable CT-PLCN, we propose an algorithm of designing a stabilizing SDFC for any given target state. Additionally, we discuss the asymptotical feedback controllability of CT-PLCNs under time-varying nonuniform SDFCs. Finally, an illustrative example is presented to explain the proposed methods and verify the controllability criteria.