In this paper, we develop a global computational approach to a classof optimal control problems governed by impulsive dynamical systemsand subject to continuous state inequality constraint. We show thatthis problem is equivalent to an optimal control problem governed byordinary differential equations with periodic boundary conditionsand subject to a set of the continuous state inequality constraints.For this equivalent optimal control problem, a constrainttranscription method is used in conjunction with a penalty functionto construct an appended new cost functional. This leads to asequence of approximate optimal control problems only subject toperiodic boundary conditions. Each of these approximate problems canbe solved as an optimization problem using gradient-basedoptimization techniques. However, these techniques are designed onlyto find local optimal solutions. Thus, a filled function method isintroduced to supplement the gradient-based optimization method.This leads to a combined method for finding a global optimalsolution. A numerical example is solved using the proposed approach.
Due to the structural coupling of a space shuttle vehicle, the selection of a suitable controller gain has been a difficult task. However, this task is very critical as it will affect the performance of the controller. In this brief, a band-stop filter is constructed by using a combined network of a low-pass filter and a high-pass filter. On this basis, digital processing is carried out using bilinear transformation and predistorted processing. To solve the parameters of the filter, a frequency-domain method and an optimization method are applied. The designed filter can effectively reduce the structural coupling, as well as broaden the margin for the regulation of the control law.
The discrete-time envelope constrained (EC) filtering problem can be formulated as a quadratic programming (QP) problem with linear inequality constraints. In this paper, the QP problem is approximated by an unconstrained minimization problem with two parameters. These parameters can be selected so that given an acceptable deviation from the norm of the optimal EC filter, the solution to the unconstrained problem satisfies both the deviation and envelope constraints. Newton's method with line search is applied to solve the unconstrained problem iteratively.
Multirate signal processing is important in a wide range of signal processing applications. Drawbacks when using multirate processing are mainly related to aliasing, reconstruction effects and the delays. In this paper, the authors investigate the design of uniform DFT filter bank with finite precision prototype filters and a minimum total number of power-of-two for the coefficients. The design problem is formulated as a mixed integer optimization problem. This problem can then be solved by using e.g. the mean field annealing algorithm. Design examples show that the filter bank can be designed with less total number of power-of-two than the quantized filter bank while achieving approximately the same performance
In this article, a class of nonconvex unconstrained optimization problems is considered. As the Armijo line search is less costing in finding a steplength, a new Armijo-type line search (called WALS) with desirable features of the Wolfe condition is employed in the proposed modified BFGS method. A new updating formula incorporated with WALS is constructed and generates approximate Hessian matrices which are positive definite. On this basis, a class of well-defined modified BFGS algorithms is developed. It shows that under some suitable conditions, the modified BFGS algorithm is globally convergent. Numerical experiments are carried out on 20 benchmark test problems and the obtained results clearly indicate the effectiveness of the developed algorithm over two most popular BFGS-type algorithms available in the literature.
The aim of the study is to derive deeper insights into the control of the spread of COVID-19 during the second half of 2021, from seven countries that are among the earliest to have accelerated the deployment of COVID-19 vaccines. Methodology. This study used data from the Global COVID-19 Index and Google COVID-19 Community Mobility Reports. Data was extracted on the 5th of each month from July to December 2021. Seven countries were selected-United Kingdom, United States of America, Israel, Canada, France, Italy, and Austria. The sample comprised number of new cases, hospitalisations, ICU admissions and deaths due to COVID-19, government stringency measures, partial and full vaccination coverage, and changes in human mobility. Principal component analysis was conducted, and the results were interpreted and visualized through 2-dimensional and 3-dimensional plots to reveal the systematic patterns of the data.The first three principal components captured around 77.3% of variance in the data. The first component was driven by the spread of COVID-19 (31.6%), the second by mobility activities (transit, retail, and recreational) (24.3%), whereas the third by vaccination coverage, workplace-related mobility, and government stringency measures (21.4%). Visualizations showed lower or moderate levels of severity in COVID-19 during this period for most countries. By contrast, the surge in the USA was more severe especially in September 2021. Human mobility activities peaked in September for most countries and then receded in the following months as more stringent government measures were imposed, and countries began to grapple with a surge in COVID-19 cases.This study delineated the spread of COVID-19, human mobility patterns, widespread vaccination coverage, and government stringency measures on the overall control of COVID-19. While at least moderate levels of stringency measures are needed, high vaccine coverage is particularly important in curbing the spread of this disease.
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