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In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we treat the uncertain ...
In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer n≥3, we define e(n) to be the minimum positive integer such that an ...
Generalized linear models, where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform z = A x, arise in a range of applications in nonlinear filtering and regression. Approximate message passing (AMP) methods, b ...
It is known that for a convex body K in R-d of volume one, the expected volume of random simplices in K is minimized if K is an ellipsoid, and for d = 2, maximized if K is a triangle. Here we provide corresponding stability estimates. ...
Path-following tasks, which refer to dynamic motion planning along pre-specified geometric references, are frequently encountered in applications such as milling, robot-supported measurements, and trajectory planning for autonomous vehicles. Different conv ...
A water bell is formed by fluid flowing in a thin, coherent sheet in the shape of a bell. Experimentally, a water bell is created via the impact of a cylindrical jet on a flat surface. Its shape is set by the splash angle (the separation angle) of the resu ...
We show that the maximum total perimeter of k plane convex bodies with disjoint interiors lying inside a given convex body C is equal to , in the case when C is a square or an arbitrary triangle. A weaker bound is obtained for general plane convex bodies. ...
We show how any labeled convex polygon associated to a compact semi-toric system, as de fined by V (u) over tilde Ngoc, determines Karshon's labeled directed graph which classifies the underlying Hamiltonian S-1-space up to isomorphism. Then we characteriz ...
Haptic exploration has received a great deal of attention of late thanks to the variety of commercially available tactile sensors. While the majority of previous works consider control of a single contact point at a time, we tackle simultaneous control of ...
The problem of finding "small" sets that meet every straight-line which intersects a given convex region was initiated by Mazurkiewicz in 1916. We call such a set an opaque set or a barrier for that region. We consider the problem of computing the shortest ...
