On Control and Estimation of Large and Uncertain Systems

This thesis contains an introduction and six papers about the control and estimation of large and uncertain systems. The first paper poses and solves a deterministic version of the multiple-model estimation problem for finite sets of linear systems. The estimate is an interpolation of Kalman filter estimates. It achieves a provided energy gain bound from disturbances to the point-wise estimation error, given that the gain bound is feasible. The second paper shows how to compute upper and lower bounds for the smallest feasible gain bound. The bounds are computed via Riccati recursions. The third paper proves that it is sufficient to consider observer-based feedback in output-feedback control of linear systems with uncertain parameters, where the uncertain parameters belong to a finite set. The paper also contains an example of a discrete-time integrator with unknown gain. The fourth paper argues that the current methods for analyzing the robustness of large systems with structured uncertainty do not distinguish between sparse and dense perturbations and proposes a new robustness measure that captures sparsity. The paper also thoroughly analyzes this new measure. In particular, it proposes an upper bound that is amenable to distributed computation and valuable for control design. The fifth paper solves the problem of localized state-feedback L2 control with communication delay for large discrete-time systems. The synthesis procedure can be performed for each node in parallel. The paper combines the localized state-feedback controller with a localized Kalman filter to synthesize a localized output feedback controller that stabilizes the closed-loop subject to communication constraints. The sixth paper concerns optimal linear-quadratic team-decision problems where the team does not have access to the model. Instead, the players must learn optimal policies by interacting with the environment. The paper contains algorithms and regret bounds for the first- and zeroth-order information feedback

Minimax Performance Limits for Multiple-Model Estimation

This article concerns the performance limits of strictly causal state estimation for linear systems with fixed, but uncertain, parameters belonging to a finite set. In particular, we provide upper and lower bounds on the smallest achievable gain from disturbances to the point-wise estimation error. The bounds rely on forward and backward Riccati recursions -- one forward recursion for each feasible model and one backward recursion for each pair of feasible models. We give simple examples where the lower and upper bounds are tight.Comment: Accepted by the European Control Conference, to be held 2024 in Stockholm, Swede

Minimax Adaptive Estimation for Finite Sets of Linear Systems

For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained quadratic programming. The estimator tends to learn the dynamics of the system, and once the uncertain parameters have been sufficiently estimated, the estimator behaves like a standard Kalman filter.Comment: Accompanying code: https://github.com/kjellqvist/MinimaxEstimation.j

Thermodynamic modelling of the Cr–Fe–Ni–O system

There is a need to describe the influence of oxygen on high alloyed steels, both regarding oxidation processes – as in the formation of oxide layers – and regarding steel/slag processes in a metallurgical context. As a first step and in order to be able to perform calculations and simulations on these different processes, the thermodynamic properties need to be described, as done for the Cr–Fe–Ni–O system. Previous attempts to describe this system has resulted in an inconsistent description, more specifically concerning the spinel phase. The aim of the present study is to obtain a consistent thermodynamic database for the Cr–Fe–Ni–O system with an emphasis on the modelling of the spinel phase. The solid phases are described using the compound energy formalism and the metallic and ionized liquid is modelled using the ionic two-sublattice model. A complete list of all binary and higher order parameters is included

Determining cattle pasture utilization using GPS-collars

This study was conducted in Jaboticabal, Brazil, on Nelore cattle. Three heifers on the same pasture were equipped with GPS-collars registering position and activity, allowing us to calculate distance to the other collars and distance to the water source. After one week the GPS-collars were taken of and put on three heifers on another pasture. This was repeated on seven different pastures on total 21 heifers. The results indicate that the cattle are more active during the afternoons than in the mornings and have a shorter avtiviyu period during the night. In conjunction with the results of Einemo (2008) it is concluded that the high activity during the afternoon means the animals are mainly grazing during that period. Results show the cattle spread out when active but like to huddle up together while resting. Compared to when active, the animals also seem to prefer to rest at a distance from the water.Denna studie skedde i Jaboticabal, Brasilien på boskap av rasen Nelore. Tre kvigor på samma bete blev utrustade med GPS-halsband som registrerade djurens position och aktivitet så att vi kunde beräkna avståndet mellan de andra halsbanden och till djurens vattenbehållare. Efter en vecka togs halsbanden av och sattes på tre andra kvigor på ett nytt bete. Totalt användes sju betesmarker och 21 kvigor. Resultaten visar att djuren är mer aktiva under eftermiddagarna än under morgon och förmiddag samt under en kortare perido på natten. Kombinerat med resultaten av Einemo (2008) drar jag slutsatsen att den höga aktiviteten under eftermiddagen betyder att djuren främst spenderar den tiden med att beta. Resultaten visar att djuren är utspridda medan de betar men vilar tillsammans i grupp. Jämfört med deras aktiva tid verkar djuren föredra att vila på avstånd från vattenkällan

A thermodynamic database for simulation of CMAS and TBC interactions

A thermodynamic database has been developed for calculating thermochemical interaction of thermal barrier coatings, namely 7YSZ (yttria partially stabilized zirconia), with CaO-MgO-Al2O3-SiO2 (CMAS) deposits. CaO-MgO-Al2O3-SiO2-Y2O3-ZrO2 is thus the core system for understanding and modeling of processes occurring between CMAS and TBC. A good thermodynamic description of all phases in the system is essential in modeling related to materials design and process optimization. An efficient technique used to obtain a self-consistent thermodynamic database is called the CALPHAD method [1], where the Gibbs energy of each phase is described with a mathematical model. The Gibbs energy of the total system is then minimized with respect to temperature and composition in order to predict the most stable phases under equilibrium conditions. In this work Y2O3-ZrO2 was incorporated into an existing description [2] of the CaO-MgO-Al2O3-SiO2 system. Many pseudo-binaries and ternaries are assessed within the CaO-MgO-Al2O3-SiO2-Y2O3-ZrO2 system. Two examples on calculated phase diagrams are shown below. The compound energy formalism [3] is used to model solid oxide solutions such as spinels, monoxide, corundum, zirconia, yttria etc. The ionic two-sublattice liquid model [4,5] is used to model molten slags

Landskapsord och synvinklar

Den här kandidatuppsatsen handlar om hur landskapsarkitektur uppfattas i svensk media. Utgångspunkten är frågeställningen Hur förhåller sig samtida debatt om landskapsarkitektur till begreppen ekologi, sociologi, estetik samt genius loci? Med ett urval från både fackpress och dagspress sovrades de aktuella artiklarna ut. De handlar om det prisade området Hammarby Sjöstad i sydvästra Stockholm och skrevs år 2000–2010. Samtliga artiklar beskriver genomförda gestaltningar. Undersökningen visar hur författarna formulerar sig kring landskapsarkitektur utifrån sociologiska, ekologiska och estetiska aspekter samt utifrån begreppet genius loci. Aspekterna definierades utifrån tidigare forskning och ett protokoll upprättades för var och en av dem. Citat som beskrev de olika aspekterna togs ut från artiklarna och sorterades in i protokollet. Resultatet visar vilka aspekter som beskrevs mest respektive minst i media. Studien visar att det inte finns särskilt mycket värdering i artiklarna och att det är svårt att göra värderingar av landskapsarkitektur. Genius loci är det begrepp som ger artiklarna mest djup och bäst förmedlar en förståelse för platsen till läsaren.This essay reflects on the conception of landscape architecture in Swedish media. The study aims to answer the question How does contemporary debate about landscape architecture relate to the terms ecology, sociology, aesthetics and genius loci? Focusing on articles from both Swedish magazines specialized in architecture and the everyday news, a number of articles were selected. The articles concern the prized area of Hammarby Sjöstad southwest of Stockholm city center and were written in 2000-2010. They are all about a project in the area. I investigated how the authors treated the landscape architectural visualizations in terms of sociological, ecological and aesthetical aspects as well as the term genius loci. Earlier scientific research defined the aspects further and a protocol was developed. Quotes describing the different aspects were taken from the articles and interpreted for the protocol. Hence the results showed which aspects were more frequently mentioned in media. The conclusion tells that there is not very much valuing in the articles read and the term genius loci is the aspect that gives the articles most depth

Från hjul till fots : en undersökning av en alternativ planeringsmetod söder om Sahara - fallet the Axis i Nairobi i Kenya

Rapid urbanisation is putting strains on both the landscape and the city dwellers and the pressure on planning for sustainable and equitable cities is crucial. As many cities in Sub-Saharan Africa are expanding, city planning has trouble keeping up to meet the needs of the growing amount of urban dwellers. Many cities have also been planned with the cars in focus and the needs and comfort of the pedestrians have been overlooked. The capacity of institutions is limited due to centralized government and bureaucracy, as well as corruption. Planning is erratically implemented and it is difficult to know what will happen. Sustainability is of great importance but in fast-growing low-income countries the social, ecological and cultural sustainability is easily ignored. The aim of this essay is to find an alternative approach for planning in these countries with people and their activities as a priority. By recognizing the street as an important public space issues concerning social, ecological, economical and cultural needs can be addressed. Inclusiveness in terms of walkability can make the street become a public space within the infrastructure of the city. This can, in addition to parks and squares, be a tool to create a more sustainable city. In contrast to making big plans and working from above, the Small change approach described by Hamdi (2004) is a way to work from bottom upwards. He describes two types of structures in the city: designed structures and emerging structures. By designing for the current need with small solutions, the emerging structures appear, and the change isn’t so big that it needs big investments. This approach is very valuable when working in a limited planning context since small means can change things quickly. Using a street in Nairobi, Kenya as an example the work in this thesis consists of developing a toolkit for how to achieve a sustainable city planning by using a small step approach. The toolkit consists of the Pillars of Planning and Design Principles, guidelines and building blocks. The Axis as the street is called, runs through the central industrial area and ends in CBD, making up the only available overpass over the railways in a radius of a couple of kilometres. The history of Nairobi is of a colonial character and throughout history, both racial and social segregation have been practised while planning the city. Through observations, the needs of the city become visible and are considered in the design proposal of the Axis.Den snabba urbaniseringen påverkar både stadsborna och landskapet omkring städerna vilket gör at det blir alltmer viktigt att planera för hållbara och rättvisa städer. Många städer i Afrika söder om Sahara expanderar och stadsplaneringen har svårt att anpassa sig till, samt tillgodose behoven hos den växande urbana befolkningen. Länge har planeringen fokuserat på framkomlighet med bil medan fotgängarnas behov och komfort har förbisetts. Planeringsinstitutionernas möjligheter är ofta begränsade på grund av centraliserade regeringar, byråkrati och korruption. Detta leder till att planering och implementering sker på ett oförutsägbart vis och det är svårt att veta vad som kommer hända. Hållbar utveckling är av stor betydelse men i snabbväxande låginkomstländer är social, ekologisk och kulturell hållbarhet ofta lågt prioriterad. Syftet med denna uppsats är att hitta en alternativ metod för planering i länder söder som Sahara där människor och deras aktiviteter prioriteras. När gatan erkänns som en viktig offentlig plats kan frågor som rör sociala, ekologiska, ekonomiska och kulturella behov uppmärksammas och integreras i planeringen. Med mer utrymme för fotgängare på gångvänliga gator inkluderas alla invånare i staden och gatorna kan bli nya offentliga platser i stadens infrastruktur. Tillsammans med parker och torg kan mer gångvänliga gator vara ett tillvägagångssätt för att skapa en mer hållbar stad. Istället för att göra stora planer och arbeta uppifrån är ”den lilla förändringen” som beskrivs av Hamdi (2004) ett sätt att jobba från botten och uppåt. Han beskriver två typer av strukturer i staden: designade strukturer och framväxande strukturer. Genom att designa för det nuvarande behovet med små lösningar kan andra positiva processer ske. Detta tillvägagångssätt är mycket värdefullt när man arbetar i ett låginkomstland eftersom små medel kan förändra saker och ting snabbt. Med en gata i Nairobi i Kenya som exempel har arbetet i denna uppsats bestått av att utveckla en verktygslåda för hur man kan närma sig en hållbar stadsplanering med hjälp av en småstegsprincip. Verktygslådan består av Pillars of Planning och Design Principles, riktlinjer för planering respektive byggstenar för design. Axis, som gatan kallas, går genom ett centralt beläget industriområde och slutar i Central Business District och är den enda passagen över järnvägen på ett par kilometers radie. Under Nairobis koloniala historia har både ras- och social segregation praktiserats när man har planerat och byggt staden. Genom observationer, gångturanalyser och samtal har stadsbornas behov försökts synliggöras och beaktas i designförslaget för Axis

Strategies for High-Temperature Corrosion Simulations of Fe-Based Alloys Using the Calphad Approach: Part I

The environmental degradation of materials at high temperatures limits the useful life of different industrial components and hinders the development of more economical and environmentally friendly processes for the energy production. Despite the importance of this phenomena, a model to predict lifetime of materials that degrade due to high-temperature corrosion has up till now been lacking due to limitations of the computational possibilities and the complex nature of oxidation. In the present work we develop some strategies to model high-temperature corrosion in Fe-based alloys using the Calphad (Calculation of Phase Diagrams) approach. It is proposed that kinetic-based simulations for oxidation of Al and Cr can accurately represent the lifetime of the protective layers in FeCrAl and FeCr alloys at different temperatures in air. The oxide systems are in addition investigated by equilibrium calculations. The corrosion mechanisms of FeCr and FeCrAl alloys are discussed based on theoretical and experimental knowledge