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Minimax LQG control

Ian Petersen — 2006

International Journal of Applied Mathematics and Computer Science

This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under...

The rank of hyperelliptic Jacobians in families of quadratic twists

Sebastian Petersen — 2006

Journal de Théorie des Nombres de Bordeaux

The variation of the rank of elliptic curves over in families of quadratic twists has been extensively studied by Gouvêa, Mazur, Stewart, Top, Rubin and Silverberg. It is known, for example, that any elliptic curve over admits infinitely many quadratic twists of rank 1 . Most elliptic curves have even infinitely many twists of rank 2 and examples of elliptic curves with infinitely many twists of rank 4 are known. There are also certain density results. This paper studies the variation of the...

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