Lyapunov type functions for classes of autonomous parabolic feedback control problems and applications

In this note we provide sufficient conditions for the existence of a Lyapunov function for a class of parabolic feedback control problems. The results are applied to the long-time behavior of state functions for the following problems: (i) a model of combustion in porous media; (ii) a model of conduction of electrical impulses in nerve axons; and (iii) a climate energy balance model.     

The convergence guarantee of the iterative hard thresholding algorithm with suboptimal feedbacks for large systems

Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be computationally expensive and/or prohibitive. The null space tuning algorithm with hard thresholding and feedbacks (NST+HT+FB) has a mean to expedite its procedure by a suboptimal feedback, in which sub-matrix inversion is replaced by an eigenvalue-based approximation. The resulting suboptimal feedback scheme becomes exceedingly effective for large system recovery problems. An adaptive algorithm based on thresholding, suboptimal feedback and null space tuning (AdptNST+HT+subOptFB) without a prior knowledge of the sparsity level is also proposed and analyzed. Convergence analysis is the focus of this article.     

基于便携式多元反馈机制的无机化学混合式教学的实践研究

目前,基于慕课的混合式教学存在反馈手段单一,教学无法充分调动学生积极性的问题,结合多种手机APP,构建了便携式多元反馈机制,分别对课前、课中和课后及单元学习进行多元反馈。基于反馈信息优化教学设计,充分利用各种信息技术,打造讨论型课堂,进行混合式教学。这种"反馈指导教学,教学中有反馈"的教学模式有助于提高学生的学习意愿和教师的教学质量。     

Precise generation of dynamic biochemical signals by controlling the programmable pump in a Y-shaped microfluidic chip with a “christmas tree” inlet

The generation of dynamic biochemical signals in a microfluidic control system is of importance for the study of the interaction between biological cells and their niches. However, most of microfluidic control systems are not able to provide dynamic biochemical signals with high precision and stability due to inherent mechanical vibrations caused by the actuators of the programmable pumps. In this paper, we propose a novel microfluidic feedback control system integrating an external feedback control system with a Y-shaped microfluidic chip with a “Christmas tree” inlet. The Proportional Integral Derivative (PID) controller is implemented to reduce the influence of vibrations. In order to regulate the control parameters efficiently, a mathematical model is built to describe the actuator of the programmable pump, in which a fractional-order model is utilized. Both simulation and experimental studies are carried out, confirming that the microfluidic feedback control system can precisely and stably generate desired dynamic biochemical signals.     

Regular linear systems governed by neutral FDEs

The aim of this paper is to prove that a class of distributed parameter systems governed by neutral FDEs provides regular linear systems. Employing the well established theory of representation, transfer function and feedback of these later we then give new representations of the state and the output function of the neutral systems.     

Global asymptotic stability in n-species non-autonomous Lotka–Volterra competitive systems with infinite delays and feedback control

A non-autonomous Lotka–Volterra competition system with infinite delays and feedback control and without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the system. Some new results are obtained.     

Crowding effects promote coexistence in the chemostat

This paper deals with an almost-global stability result for a particular chemostat model. It deviates from the classical chemostat because crowding effects are taken into consideration. This model can be rewritten as a negative feedback interconnection of two systems which are monotone (as input/output systems). Moreover, these subsystems behave nicely when subject to constant inputs. This allows the use of a particular small-gain theorem which has recently been developed for feedback interconnections of monotone systems. Application of this theorem requires—at least approximate—knowledge of two gain functions associated to the subsystems. It turns out that for the chemostat model proposed here, these approximations can be obtained explicitly and this leads to a sufficient condition for almost-global stability. In addition, we show that coexistence occurs in this model if the crowding effects are large enough.     

模拟低频反馈系统的初步尝试

 为了提高注入束流的积累，抑制由于注入系统误差引起较大的β残余振荡是非常有必要的。较系统地介绍了利用合肥光源逐圈测量（turn by turn）系统［１］，研究束流不稳定性，并给出了抑制注入β振荡的反馈系统设计原理和线路及初步实验结果。作为原理论证和预研，使用了一个相对简单的模拟滤波移相器对Kicker过程激发的β振荡进行反馈，得到了明显的对damping时间和振荡幅度的抑制作用，为以后低频和高频逐束团（bunch by bunch） 反馈系统研制和抑制束流的横向和纵向不稳定性的研究打下了良好的基础。     

Internal stabilization of semilinear parabolic systems

This work is concerned with the internal stabilization of the steady-state solutions to semilinear parabolic systems via finite-dimensional feedback controllers. The internal controller is active on a nonempty open subset and in one equation only.     

On solutions of differential inclusions in homogeneous spaces of functions

In this paper we study the solvability of some classes of differential inclusions with multivalued linear operators in homogeneous spaces of functions. These spaces include a large number of functional spaces like periodic functions and Bohr and Stepanov almost periodic functions. As an application, we consider some existence results for feedback control systems governed by degenerate differential equations of Sobolev type in a Banach space.