Model order reduction approaches for infinite horizon optimal control problems via the HJB equation

We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this report we focus on the infinite horizon optimal control problem with quadratic cost functionals. We compare several model reduction methods such as Proper Orthogonal Decomposition, Balanced Truncation and a new algebraic Riccati equation based approach. Finally, we present numerical examples and discuss several features of the different methods analyzing advantages and disadvantages of the reduction methods

The ACS Exams Institute Undergraduate Chemistry Anchoring Concepts Content Map I: General Chemistry

To provide tools for programmatic assessment related to the use of ACS Exams in undergraduate chemistry courses, the ACS Exams Institute has built a content map that applies to the entire undergraduate curriculum. At the top two levels, the grain size of the content classification is large and spans the entire undergraduate curriculum. At the bottom two levels, the grain size of the content is more fine and tuned to specific course levels of the curriculum. This paper presents all four levels of the map as identified for first-year general chemistry

Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

Enhanced antiviral function of magnesium chloride-modified Heparin on a broad spectrum of viruses

Previous studies reported on the broad-spectrum antiviral function of heparin. Here we investigated the antiviral function of magnesium-modified heparin and found that modified heparin displayed a significantly enhanced antiviral function against human adenovirus (HAdV) in immortalized and primary cells. Nuclear magnetic resonance analyses revealed a conformational change of heparin when complexed with magnesium. To broadly explore this discovery, we tested the antiviral function of modified heparin against herpes simplex virus type 1 (HSV-1) and found that the replication of HSV-1 was even further decreased compared to aciclovir. Moreover, we investigated the antiviral effect against the new severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) and measured a 55-fold decreased viral load in the supernatant of infected cells associated with a 38-fold decrease in virus growth. The advantage of our modified heparin is an increased antiviral effect compared to regular heparin

Sexual harassment and abuse in sport: The research context

This special issue of the Journal of Sexual Aggression draws on the contributions to a Symposium on ‘Sexual Harassment in Sport – Challenges for Sport Psychology in the New Millennium’, held at the Xth Congress of the International Society for Sport Psychology, Skiathos, Greece from May 28th to June 2nd 2001. The symposium, which was organised by the authors of this editorial, was intended to move forward the international research agenda on sexual harassment and abuse in sport and to examine professional practice issues for sport psychologists. It was clear from the attendance of over 60 delegates at that symposium that international interest in this subject is growing. Further evidence of this came from the attendance of 26 members states – from Azerbaijan to Sweden - at a Council of Europe seminar on The Protection of Children, Young People and Women in Sport, held in Helsinki in September 2001

Energy Dissipating Devices in Falling Rock Protection Barriers

Rockfall is a phenomenon which, when uncontrolled, may cause extensive material damage and personal injury. One of the structures used to avoid accidents caused by debris flows or rockfalls is flexible barriers. The energy dissipating devices which absorb the energy generated by rock impact and reduce the mechanical stresses in the rest of the elements of the structure are an essential part of these kinds of structures. This document proposes an overview of the performance of energy dissipating devices, as well as of the role that they fulfil in the barrier. Furthermore, a compilation and a description of the dissipating elements found in the literature are proposed. Additionally, an analysis has been performed of the aspects taken into account in the design, such as experimental (quasi-static and dynamic) tests observing the variation of the behaviour curve depending on the test speed and numerical simulations by means of several finite element software packages

A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L? constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first - and second-order optimality analysis. We prove the existence of local optimal solutions and of a Lagrange multiplier associated with the inequality constraints. Furthermore, we prove a sufficient second-order optimality condition and present some numerical results underlining the good properties of the numerical scheme. Dupire equation ; parameter identification ; optimal control ; optimality conditions ; SQP method ; primal-dual active set strateg