The linear regulator problem for parabolic systems

An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems

Optimal control of semilinear elliptic equations in measure spaces

Optimal control problems in measure spaces governed by semilinear elliptic equations are considered. First order optimality conditions are derived and structural properties of their solutions, in particular sparsity, are discussed. Necessary and sufficient second order optimality conditions are obtained as well. On the basis of the sufficient conditions, stability of the solutions is analyzed. Highly nonlinear terms can be incorporated by utilizing an L∞(Ω) regularity result for solutions of the first order necessary optimality conditions.This author’s research was supported by Spanish Ministerio de Economía y Competitividad under project MTM2011-22711

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

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

Model Order Reduction for Rotating Electrical Machines

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that contain non-symmetric components. These are usually introduced during the mass production process and are modeled by small perturbations in the geometry (e.g., eccentricity) or the material parameters. While model order reduction for symmetric machines is clear and does not need special treatment, the non-symmetric setting adds additional challenges. An adaptive strategy based on proper orthogonal decomposition is developed to overcome these difficulties. Equipped with an a posteriori error estimator the obtained solution is certified. Numerical examples are presented to demonstrate the effectiveness of the proposed method

Greedy optimal control for elliptic problems and its application to turnpike problems

This is a post-peer-review, pre-copyedit version of an article published in Numerische Mathematik. The final authenticated version is available online at: https://doi.org/10.1007/s00211-018-1005-zWe adapt and apply greedy methods to approximate in an efficient way the optimal controls for parameterized elliptic control problems. Our results yield an optimal approximation procedure that, in particular, performs better than simply sampling the parameter-space to compute controls for each parameter value. The same method can be adapted for parabolic control problems, but this leads to greedy selections of the realizations of the parameters that depend on the initial datum under consideration. The turnpike property (which ensures that parabolic optimal control problems behave nearly in a static manner when the control horizon is long enough) allows using the elliptic greedy choice of the parameters in the parabolic setting too. We present various numerical experiments and an extensive discussion of the efficiency of our methodology for parabolic control and indicate a number of open problems arising when analyzing the convergence of the proposed algorithmsThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694126-DyCon). Part of this research was done while the second author visited DeustoTech and Univesity of Deusto with the support of the DyCon project. The second author was also partially supported by Croatian Science Foundation under ConDyS Project, IP-2016-06-2468. The work of the third author was partially supported by the Grants MTM2014-52347, MTM2017-92996 of MINECO (Spain) and ICON of the French AN

A Survey of Air-to-Ground Propagation Channel Modeling for Unmanned Aerial Vehicles

In recent years, there has been a dramatic increase in the use of unmanned aerial vehicles (UAVs), particularly for small UAVs, due to their affordable prices, ease of availability, and ease of operability. Existing and future applications of UAVs include remote surveillance and monitoring, relief operations, package delivery, and communication backhaul infrastructure. Additionally, UAVs are envisioned as an important component of 5G wireless technology and beyond. The unique application scenarios for UAVs necessitate accurate air-to-ground (AG) propagation channel models for designing and evaluating UAV communication links for control/non-payload as well as payload data transmissions. These AG propagation models have not been investigated in detail when compared to terrestrial propagation models. In this paper, a comprehensive survey is provided on available AG channel measurement campaigns, large and small scale fading channel models, their limitations, and future research directions for UAV communication scenarios

Identification of Achaete-scute complex-like 1 (ASCL1) target genes and evaluation of DKK1 and TPH1 expression in pancreatic endocrine tumours

<p>Abstract</p> <p>Background</p> <p><it>ASCL1 </it>role in pancreatic endocrine tumourigenesis has not been established. Recently it was suggested that ASCL1 negatively controls expression of the Wnt signalling antagonist <it>DKK1</it>. Notch signalling regulates expression of TPH1, the rate limiting enzyme in the biosyntesis of serotonin. Understanding the development and proliferation of pancreatic endocrine tumours (PETs) is essential for the development of new therapies.</p> <p>Methods</p> <p><it>ASCL1 </it>target genes in the pancreatic endocrine tumour cell line BON1 were identified by RNA interference and microarray expression analysis. Protein expressions of selected target genes in PETs were evaluated by immunohistochemistry.</p> <p>Results</p> <p>158 annotated <it>ASCL1 </it>target genes were identified in BON1 cells, among them DKK1 and TPH1 that were negatively regulated by ASCL1. An inverse relation of ASCL1 to DKK1 protein expression was observed for 15 out of 22 tumours (68%). Nine tumours displayed low ASCL1/high DKK1 and six tumours high ASCL1/low DKK1 expression. Remaining PETs showed high ASCL1/high DKK1 (n = 4) or low ASCL1/low DKK1 (n = 3) expression. Nine of twelve analysed PETs (75%) showed TPH1 expression with no relation to ASCL1.</p> <p>Conclusion</p> <p>A number of genes with potential importance for PET tumourigenesis have been identified. <it>ASCL1 </it>negatively regulated the Wnt signalling antagonist <it>DKK1</it>, and <it>TPH1 </it>expression in BON1 cells. In concordance with these findings DKK1 showed an inverse relation to ASCL1 expression in a subset of PETs, which may affect growth control by the Wnt signalling pathway.</p

Prostaglandin E2 Synthesizing Enzymes in Rheumatoid Arthritis B Cells and the Effects of B Cell Depleting Therapy on Enzyme Expression

Introduction: B cells may play an important role in promoting immune activation in the rheumatoid synovium and can produce prostaglandin E-2 (PGE(2)) when activated. In its turn, PGE(2) formed by cyclooxygenase (COX) and microsomal prostaglandin E-2 synthase 1 (MPGES1) contributes to the rheumatoid arthritis (RA) pathological process. Therapeutic depletion of B cells results in important improvement in controlling disease activity in rheumatoid patients. Therefore we investigated the expression of PGE(2) pathway enzymes in RA B cells and evaluated the effects of B cell depleting therapy on their expression in RA tissue. Methods: B cells expressing MPGES1 and COX-2 were identified by flow cytometry in in vitro stimulated and control mononuclear cells isolated from synovial fluid and peripheral blood of RA patients. Synovial biopsies were obtained from 24 RA patients before and at two consecutive time points after rituximab therapy. Expression of MPGES1, COX-1 and COX-2, as well as interleukin (IL)-1 beta and IL-6, known inducers of MPGES1, was quantified in immunostained biopsy sections using computerized image analysis. Results: Expression of MPGES1 or COX-2 was significantly upregulated upon stimulation of B cells from blood and synovial fluid while control cells displayed no detectable enzymes. In synovial biopsy sections, the expression of MPGES1, COX-1 or COX-2 was resistant to rituximab therapy at 8 or 16 weeks after start of treatment. Furthermore expression of IL-1 beta in the synovial tissue remained unchanged, while IL-6 tended to decrease after therapy. Conclusions: Therapy with B cell depleting agents, although efficient in achieving good clinical and radiographic response in RA patients, leaves important inflammatory pathways in the rheumatoid synovium essentially unaffecte

Sparse initial data indentification for parabolic pde and its finite element approximations

We address the problem of inverse source identification for parabolic equations from the optimal control viewpoint employing measures of minimal norm as initial data. We adopt the point of view of approximate controllability so that the target is not required to be achieved exactly but only in an approximate sense. We prove an approximate inversion result and derive a characterization of the optimal initial measures by means of duality and the minimization of a suitable quadratic functional on the solutions of the adjoint system. We prove the sparsity of the optimal initial measures showing that they are supported in sets of null Lebesgue measure. As a consequence, approximate controllability can be achieved efficiently by means of controls that are activated in a finite number of pointwise locations. Moreover, we discuss the finite element numerical approximation of the control problem providing a convergence result of the corresponding optimal measures and states as the discretization parameters tend to zero.The first author was supported by Spanish Ministerio de Economía y Competitividad under project MTM2011-22711. The third author was supported by the Advanced Grant NUMERIWAVES/FP7-246775 of the European Research Council Executive Agency, FA9550-14-1-0214 of the EOARD-AFOSR, FA9550-15-1-0027 of AFOSR, the BERC 2014-2017 program of the Basque Government, the MTM2011-29306 and SEV-2013-0323 Grants of the MINECO, the CIMI-Toulouse Excellence Chair in PDEs, Control and Numerics and a Humboldt Award at the University of Erlangen-Nürnberg