A closed loop exponential feeding law: Invariance and global stability analysis

This article addresses the computation of invariant control laws [A. Fradkov, I. Miroshnik, V. Nikiforov, Nonlinear and Adaptive Control of Complex Systems, Kluwer, 1999] for fed-batch fermenters represented by two standard models. It will be shown how to derive partial state feedbacks that, assuming ideal conditions and perfect model, keep the specific growth rate μ constant provided the initial conditions are adequate. The invariant control law is the closed loop version of the exponential feeding already suggested in several references as shown later. The paper presents an analysis of invariance and a study of global stability within the framework of partial stability. That is, stability with respect to some of the state variables. This enables us to treat the case with Haldane-like or non-monotonous kinetics.     

Stabilization of uncertain boundary control systems

We consider a class of linear infinite-dimensional systems subject to boundary uncertainties, which are linear and time-invariant. Using a deterministic approach to the design of stabilizing feedback controls, uniform exponential stability of the zero state is achieved. Lyapunov techniques are combined with Datko or Ichikawa theory. Three illustrative examples are presented.     

Ce,Eu双掺BSO晶体光折变效应研究

在ＢＳＯ晶体中同时掺入Ｃｅ和Ｅｕ离子，生长了Ｃｅ：Ｅｕ：ＢＳＯ晶体，对晶体的二波耦合和四波混频性能了测试。结果表明，Ｃｅ和Ｅｕ离子对晶体的光折变效应起到了增强的作用。     

Static output feedback control via PDE boundary and ODE measurements in linear cascaded ODE–beam systems

This paper addresses the problem of feedback control design for a class of linear cascaded ordinary differential equation (ODE)–partial differential equation (PDE) systems via a boundary interconnection, where the ODE system is linear time-invariant and the PDE system is described by an Euler–Bernoulli beam (EBB) equation with variable coefficients. The objective of this paper is to design a static output feedback (SOF) controller via EBB boundary and ODE measurements such that the resulting closed-loop cascaded system is exponentially stable. The Lyapunov’s direct method is employed to derive the stabilization condition for the cascaded ODE–beam system, which is provided in terms of a set of bilinear matrix inequalities (BMIs). Furthermore, in order to compute the gain matrices of SOF controllers, a two-step procedure is presented to solve the BMI feasibility problem via the existing linear matrix inequality (LMI) optimization techniques. Finally, the numerical simulation is given to illustrate the effectiveness of the proposed design method.     

Exploring the dynamic model of the returns from value stocks and growth stocks using time series mining

This study considered that value stocks and growth stocks are 2-dimensional concepts. We defined the book-to-market ratio as the value factor and the return on equity as the growth factor. We used these 2 factors to divide stocks into 4 types: high-value, low-value, high-growth, and low-growth stocks. Furthermore, we explored the change in stock prices and stock returns for these 4 categories before and after the formation of investment portfolios. We also established a dynamic model showing the returns from value stocks and growth stocks, called the exponential decay model. Finally, we used Taiwan Stock Exchange data to examine effectiveness of the model during the period from 1995 to 2009. The results are as follows: first, high-value stocks and low-value stocks exhibit a significantly over-reacting phenomenon. Second, high-growth stocks and low-growth stocks exhibit an obviously under-reacting phenomenon. Third, in each current quarter, high-value stocks exhibit the lowest returns; however, in the subsequent quarter, they have the highest returns, and then demonstrate a slow declining trend in the following quarters. These results showed that the stock market can exhibit a dramatic response to extraordinary information and proved that the stock market requires considerable time to correct themselves from an excessive reaction, thus high-value stocks exhibited a higher return. Fourth, in each current quarter, high-growth stocks had the highest return, followed by a rapidly decreasing trend in the following quarters. The t + 3 quarter returns were lower than those of low-growth stocks. This result demonstrated that the stock market does not exhibit an adequate reaction, but still remains rather efficient for routine financial information. Finally, regardless of value stocks or growth stocks, exponential decay models could accurately match with the data.     

PARAMETER ESTIMATION IN EXPONENTIAL MODELS

Abstract. In this paper the problems of parameter estimation and order determination of an exponential (EX) model are studied in the time domain. In order to estimate the parameters, the parameter equations of an EX model are given in terms of the autocorrelation function, which is similar to the Yule-Walker equations of an autoregressive moving-average model. Estimates of parameters are obtained with the aid of the parameter equations and theorems are proved relating the convergence rate and asymptotic distribution of the estimates. We present two kinds of methods for estimating the order and prove that the estimates of the order are consistent.     

Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term

We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small.     

Maximum quasi-likelihood estimation for the near(2) model

Abstract.  Maximum quasi-likelihood estimation is investigated for the NEAR(2) model, an autoregressive time series model with marginal exponential distributions. In certain regions of the parameter space, simulations indicate that maximum quasi-likelihood estimators perform better than two-stage conditional least squares estimators in terms of the per cent of estimates falling in the parameter space. The problem of out-of-range estimates is shown to be caused by the lack of information in the data rather than the characteristics of the method of estimation.     

Stabilization of One‐Dimensional Schrödinger Equation with Variable Coefficient under Delayed Boundary Output Feedback

This article considers stabilization of a one‐dimensional Schrödinger equation with variable coefficient and boundary observation which suffers from an arbitrary given time delay. We design an observer and predictor to stabilize the system. The state is estimated in the time span where the observation is available, and also predicted in the time interval where the observation is not available. It is shown that the estimated state feedback stabilizes the system exponentially. A numerical simulation is presented to illustrate the effect of the stabilizing controller.