Examensarbete i matematik på grundnivå med inriktning mot optimeringslära och systemteori

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1 Examensarbete i matematik på grundnivå med inriktning mot optimeringslära och systemteori (kurskod SA104X, 15hp, VT15) Förkunskaper Det är ett krav att följa kursen i SF1811 Optimeringslära för F, under hösten 2014 såvida inte motsvarande kunskaper har förvärvats tidigare. Vidare rekommenderar vi att samtliga grundkurser i matematik är avklarade.

2 Optimeringslära och systemteori Ett spår i Tillämpad matematik och beräkningsmatematik Optimeringslära och systemteori är ett tillämpat matematiskt ämne Konsten att göra något så bra som möjligt under givna förutsättningar Teorin om matematisk modellering, analys och styrning av dynamiska system Verktyg från t.ex. linjär algebra, mekanik, differentialekvationer, optimeringslära, och stokastiska processer,. Tillämpningar inom Operationsanalys, ekonomi Biologi, robotik Reglerteknik och signalbehandling. Exempel på tillämpningar Strålbehandling av cancer Mobila manipuleringar Schemaläggning Formationsflygning

3 Projekt förslag Optimization A study of lumping in scheduled traffic Automatic generation of diversified groups Topology optimization of linearly elastic structures On the behavior of unnormalized Krylov methods for solving linear equations where the matrix is symmetric Networks and Control Continuous feedback control subject to discrete-time sensing Community detection in networks Localization of a cell phone: Uncertainty assessment and robust estimates Formation flying Signal Processing Analysis of audio signals of snoring Multi-pitch tone estimation via transportation distances

4 Optimization A study of lumping in scheduled traffic. This project will model the traffic and see if the lumping phenomenon will be produced and determine the main factors behind it. Automatic generation of diversified groups. Given data of different characteristics of a large number of individuals, the aim is to create a fixed number of groups such that the groups are as diversified as possible. Topology optimization of linearly elastic structures. This project deals with optimal design of load-carrying linearly elastic structures (like a bridge or a bicycle frame). The word "topology" is used since we, in addition to the optimal outer shape of the structure, are interested in the optimal number, location and shape of the holes in the structure. On the behavior of unnormalized Krylov methods for solving linear equations where the matrix is symmetric. An important problem in optimization and other areas is to solve a linear equation where the matrix is symmetric. If the matrix is positive definite, the conjugate-gradient method is one such method. The conjugate-gradient method may be viewed as a particular Krylov method which is normalized in each step.

5 Networks and Control Continuous feedback control subject to discrete-time sensing. In this project we study the problem of closing a feedback-loop using a continuous input signal constructed from the discrete-time sampling of an output signal, with attitude control as one of the applications. Community detection in networks. Many engineering and social systems can be viewed as interacting networks. The interaction can typically be represented by a graph. A very interesting problem regarding such graphs is community/cluster detection, namely organizing nodes in a graph into clusters, according to how the nodes interact with each other.

6 Networks and Control Localization of a cell phone: Uncertainty assessment and robust estimates. The location of a cell phone, communicating with an antenna in a cell phone tower, can be determined using spatial methods based on covariances. Here we will investigate this localization problem in order to assess the overall uncertainty and to determine how to make a robust location estimate. Formation flying. In this project we will study modeling and control for a group of quadcopters. A quadcopter (or quadrotor) is a multirotor minihelicopter that is lifted and propelled by four rotors and has found increasingly many real-world applications.

7 Signal Processing Analysis of audio signals of snoring. In signal processing, speech and music signals are often modeled as the output of a slowly time varying linear filter. This project will use the models to determine the different snoring phases based on audio recordings. For example, methods for discovering phases of apnea could be identified. Multi-pitch tone estimation via transportation distances. Ideally, harmonics should be perfect multiples of the pitch. However, in practice there are often small deviations, for example in sounds from stringed instruments. This causes problems in many traditional methods for multi-pitch estimation. Here we will investigate the use of transportation distances for multi-pitch estimation.