An adaptive POD approximation method for the control of advection-diffusion equations

We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic Programming approximation scheme for the corresponding evolutive Hamilton-Jacobi equation. We discuss several features regarding the adaptivity of the method, the role of error estimate indicators to choose a time subdivision of the problem and the computation of the basis functions. Some test problems are presented to illustrate the method.Comment: 17 pages, 18 figure

An Iterative Model Reduction Scheme for Quadratic-Bilinear Descriptor Systems with an Application to Navier-Stokes Equations

We discuss model reduction for a particular class of quadratic-bilinear (QB) descriptor systems. The main goal of this article is to extend the recently studied interpolation-based optimal model reduction framework for QBODEs [Benner et al. '16] to a class of descriptor systems in an efficient and reliable way. Recently, it has been shown in the case of linear or bilinear systems that a direct extension of interpolation-based model reduction techniques to descriptor systems, without any modifications, may lead to poor reduced-order systems. Therefore, for the analysis, we aim at transforming the considered QB descriptor system into an equivalent QBODE system by means of projectors for which standard model reduction techniques for QBODEs can be employed, including aforementioned interpolation scheme. Subsequently, we discuss related computational issues, thus resulting in a modified algorithm that allows us to construct \emph{near}--optimal reduced-order systems without explicitly computing the projectors used in the analysis. The efficiency of the proposed algorithm is illustrated by means of a numerical example, obtained via semi-discretization of the Navier-Stokes equations

Stabilizability for nonautonomous linear parabolic equations with actuators as distributions

The stabilizability of a general class of abstract parabolic-like equations is investigated, with a finite number of actuators. This class includes the case of actuators given as delta distributions located at given points in the spatial domain of concrete parabolic equations. A stabilizing feedback control operator is constructed and given in explicit form. Then, an associated optimal control is considered and the corresponding Riccati feedback is investigated. Results of simulations are presented showing the stabilizing performance of both explicit and Riccati feedbacks.Comment: 7 figure

Ensemble Feedback Stabilization of Linear Systems

Stabilization of linear control systems with parameter-dependent system matrices is investigated. A Riccati based feedback mechanism is proposed and analyzed. It is constructed by means of an ensemble of parameters from a training set. This single feedback stabilizes all systems of the training set and also systems in its vicinity. Moreover its suboptimality with respect to optimal feedback for each single parameter from the training set can be quantified

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

Spatially dispersed corporate headquarters: a historical analysis of their prevalence, antecedents, and consequences

Our study, which complements recent works challenging the traditional conceptualization of the CHQ as a single organizational unit, has a dual purpose. First, in descriptive terms, we set out to explore the prevalence of spatially dispersed CHQs in a historical context. Second, we aim to shed additional light on the CHQ’s spatial design by exploring internal antecedents and potential consequences. Building on arguments from information-processing theory, we propose that the strategic complexity facing the CHQ (affecting its information-processing demands) is associated with the likelihood of a spatially dispersed CHQ (affecting its information-processing capacity). In line with our dual purpose, we conduct a historical study drawing on survey and archival data covering 156 public firms domiciled in four countries (Germany, the Netherlands, the UK, and the US) in the late 1990s. Our results provide empirical support for the hypothesized associations between strategic complexity and the CHQ’s spatial design. Moreover, although we find no empirical support for the expected contingency effects, the results suggest that a spatially dispersed CHQ can have negative effects on CHQ and firm performance. Overall, our theoretical arguments and empirical results advance our knowledge about complex CHQ configurations

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

Using review articles to address societal grand challenges

We introduce a special issue of International Journal of Management Reviews that demonstrates how to use review articles to address societal grand challenges—complex, large-scale issues facing humankind, such as climate change, inequality and poverty. First, we argue that review articles possess unique features that make them particularly useful for addressing societal grand challenges. Second, we discuss three distinct but related roles of review articles in addressing societal grand challenges: (1) advancing theoretical knowledge; (2) advancing methodological knowledge; and (3) advancing practical knowledge. We conclude by providing future directions to enhance contributions of review articles for addressing societal grand challenges further by: (a) spanning disciplinary boundaries; (b) engaging practitioners; and (c) using alternative review approaches

Why do firms launch corporate change programs? A contingency perspective on strategic change

We study strategic change as a visible and substantive action by examining the circumstances under which firms launch corporate change programs. Drawing on prior literature and corroborated by insights from interviews with executives, we propose a contingency perspective on the launch of corporate change programs (i.e. that different types of programs are launched under different circumstances). To do so, we combine arguments for three general motives for launching a corporate change program with two distinct types of corporate change programs. More specifically, we argue that firms are more likely to launch growth-oriented programs when the market situation is buoyant, when they have prior experience, and when they are underperforming. Furthermore, we argue that firms are more likely to launch efficiency-oriented programs when there is a new CEO, when they are underperforming, and when they are facing high levels of organizational complexity. To test our hypotheses regarding the motives for launching programs, we conducted a large-scale empirical study. Using hand-collected data for the European financial services and insurance industry over a ten-year period, we found support for our predictions. We discuss the implications of these findings for strategic change research

Temperature effects on zoeal morphometric traits and intraspecific variability in the hairy crab Cancer setosus across latitude

International audiencePhenotypic plasticity is an important but often ignored ability that enables organisms, within species-specific physiological limits, to respond to gradual or sudden extrinsic changes in their environment. In the marine realm, the early ontogeny of decapod crustaceans is among the best known examples to demonstrate a temperature-dependent phenotypic response. Here, we present morphometric results of larvae of the hairy crab , the embryonic development of which took place at different temperatures at two different sites (Antofagasta, 23°45′ S; Puerto Montt, 41°44′ S) along the Chilean Coast. Zoea I larvae from Puerto Montt were significantly larger than those from Antofagasta, when considering embryonic development at the same temperature. Larvae from Puerto Montt reared at 12 and 16°C did not differ morphometrically, but sizes of larvae from Antofagasta kept at 16 and 20°C did, being larger at the colder temperature. Zoea II larvae reared in Antofagasta at three temperatures (16, 20, and 24°C) showed the same pattern, with larger larvae at colder temperatures. Furthermore, larvae reared at 24°C, showed deformations, suggesting that 24°C, which coincides with temperatures found during strong EL Niño events, is indicative of the upper larval thermal tolerance limit.   is exposed to a wide temperature range across its distribution range of about 40° of latitude. Phenotypic plasticity in larval offspring does furthermore enable this species to locally respond to the inter-decadal warming induced by El Niño. Morphological plasticity in this species does support previously reported energetic trade-offs with temperature throughout early ontogeny of this species, indicating that plasticity may be a key to a species' success to occupy a wide distribution range and/or to thrive under highly variable habitat conditions