Optimal experimental design for parameter identification and model selection

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2014

Optimal control of a Stefan problem with gradient-based methods in FEniCS

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Masterarbeit, 2016

The achievable region approach to the optimal control of stochastic systems

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances(the achievable region) of the system of interest, and (ii) optimisingthe overall system-wide performance objective over this space. This isradically different from conventional formulations based on dynamicprogramming. The approach is explained with reference to a simpletwo-class queueing system. Powerful new methodologies due to the authorsand co-workers are deployed to analyse a general multiclass queueingsystem with parallel servers and then to develop an approach to optimalload distribution across a network of interconnected stations. Finally,the approach is used for the first time to analyse a class of intensitycontrol problems.

Genomewide association study using a high-density single nucleotide polymorphism array and case-control design identifies a novel essential hypertension susceptibility locus in the promoter region of endothelial NO synthase.

Essential hypertension is a multifactorial disorder and is the main risk factor for renal and cardiovascular complications. The research on the genetics of hypertension has been frustrated by the small predictive value of the discovered genetic variants. The HYPERGENES Project investigated associations between genetic variants and essential hypertension pursuing a 2-stage study by recruiting cases and controls from extensively characterized cohorts recruited over many years in different European regions. The discovery phase consisted of 1865 cases and 1750 controls genotyped with 1M Illumina array. Best hits were followed up in a validation panel of 1385 cases and 1246 controls that were genotyped with a custom array of 14 055 markers. We identified a new hypertension susceptibility locus (rs3918226) in the promoter region of the endothelial NO synthase gene (odds ratio: 1.54 [95% CI: 1.37-1.73]; combined P=2.58 · 10(-13)). A meta-analysis, using other in silico/de novo genotyping data for a total of 21 714 subjects, resulted in an overall odds ratio of 1.34 (95% CI: 1.25-1.44; P=1.032 · 10(-14)). The quantitative analysis on a population-based sample revealed an effect size of 1.91 (95% CI: 0.16-3.66) for systolic and 1.40 (95% CI: 0.25-2.55) for diastolic blood pressure. We identified in silico a potential binding site for ETS transcription factors directly next to rs3918226, suggesting a potential modulation of endothelial NO synthase expression. Biological evidence links endothelial NO synthase with hypertension, because it is a critical mediator of cardiovascular homeostasis and blood pressure control via vascular tone regulation. This finding supports the hypothesis that there may be a causal genetic variation at this locus.

FPGA-Based Control Design for Power Electronic Applications

Tehoelektoniikkalaitteella tarkoitetaan ohjaus- ja säätöjärjestelmää, jolla sähköä muokataan saatavilla olevasta muodosta haluttuun uuteen muotoon ja samalla hallitaan sähköisen tehon virtausta lähteestä käyttökohteeseen. Tämä siis eroaa signaalielektroniikasta, jossa sähköllä tyypillisesti siirretään tietoa hyödyntäen eri tiloja. Tehoelektroniikkalaitteita vertailtaessa katsotaan yleensä niiden luotettavuutta, kokoa, tehokkuutta, säätötarkkuutta ja tietysti hintaa. Tyypillisiä tehoelektroniikkalaitteita ovat taajuudenmuuttajat, UPS (Uninterruptible Power Supply) -laitteet, hitsauskoneet, induktiokuumentimet sekä erilaiset teholähteet. Perinteisesti näiden laitteiden ohjaus toteutetaan käyttäen mikroprosessoreja, ASIC- (Application Specific Integrated Circuit) tai IC (Intergrated Circuit) -piirejä sekä analogisia säätimiä. Tässä tutkimuksessa on analysoitu FPGA (Field Programmable Gate Array) -piirien soveltuvuutta tehoelektroniikan ohjaukseen. FPGA-piirien rakenne muodostuu erilaisista loogisista elementeistä ja niiden välisistä yhdysjohdoista.Loogiset elementit ovat porttipiirejä ja kiikkuja. Yhdysjohdot ja loogiset elementit ovat piirissä kiinteitä eikä koostumusta tai lukumäärää voi jälkikäteen muuttaa. Ohjelmoitavuus syntyy elementtien välisistä liitännöistä. Piirissä on lukuisia, jopa miljoonia kytkimiä, joiden asento voidaan asettaa. Siten piirin peruselementeistä voidaan muodostaa lukematon määrä erilaisia toiminnallisia kokonaisuuksia. FPGA-piirejä on pitkään käytetty kommunikointialan tuotteissa ja siksi niiden kehitys on viime vuosina ollut nopeaa. Samalla hinnat ovat pudonneet. Tästä johtuen FPGA-piiristä on tullut kiinnostava vaihtoehto myös tehoelektroniikkalaitteiden ohjaukseen. Väitöstyössä FPGA-piirien käytön soveltuvuutta on tutkittu käyttäen kahta vaativaa ja erilaista käytännön tehoelektroniikkalaitetta: taajuudenmuuttajaa ja hitsauskonetta. Molempiin testikohteisiin rakennettiin alan suomalaisten teollisuusyritysten kanssa soveltuvat prototyypit,joiden ohjauselektroniikka muutettiin FPGA-pohjaiseksi. Lisäksi kehitettiin tätä uutta tekniikkaa hyödyntävät uudentyyppiset ohjausmenetelmät. Prototyyppien toimivuutta verrattiin vastaaviin perinteisillä menetelmillä ohjattuihin kaupallisiin tuotteisiin ja havaittiin FPGA-piirien mahdollistaman rinnakkaisen laskennantuomat edut molempien tehoelektroniikkalaitteiden toimivuudessa. Työssä on myösesitetty uusia menetelmiä ja työkaluja FPGA-pohjaisen säätöjärjestelmän kehitykseen ja testaukseen. Esitetyillä menetelmillä tuotteiden kehitys saadaan mahdollisimman nopeaksi ja tehokkaaksi. Lisäksi työssä on kehitetty FPGA:n sisäinen ohjaus- ja kommunikointiväylärakenne, joka palvelee tehoelektroniikkalaitteiden ohjaussovelluksia. Uusi kommunikointirakenne edistää lisäksi jo tehtyjen osajärjestelmien uudelleen käytettävyyttä tulevissa sovelluksissa ja tuotesukupolvissa.

Optimal control theory for a unitary operation under dissipative evolution

We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared to the complete basis of Liouville space that is commonly believed necessary for this task. The reduction is based on two observations: the target is not a general dynamical map but a unitary operation; and the time evolution of two properly chosen states is sufficient to distinguish any two unitaries. We illustrate gate optimization employing a reduced set of states for a controlled phasegate with trapped atoms as qubit carriers and a iSWAP gate with superconducting qubits.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Optimal inverter design for an induction machine using resonant frequency matching

The frequency responses of two 50 Hz and one 400 Hz induction machines have been measured experimentally over a frequency range of 1 kHz to 400 kHz. This study has shown that the stator impedances of the machines behave in a similar manner to a parallel resonant circuit, and hence have a resonant point at which the Input impedance of the machine is at a maximum. This maximum impedance point was found experimentally to be as low as 33 kHz, which is well within the switching frequency ranges of modern inverter drives. This paper investigates the possibility of exploiting the maximum impedance point of the machine, by taking it into consideration when designing an inverter, in order to minimize ripple currents due to the switching frequency. Minimization of the ripple currents would reduce torque pulsation and losses, increasing overall performance. A modified machine model was developed to take into account the resonant point, and this model was then simulated with an inverter to demonstrate the possible advantages of matching the inverter switching frequency to the resonant point. Finally, in order to experimentally verify the simulated results, a real inverter with a variable switching frequency was used to drive an induction machine. Experimental results are presented.

The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.