1,816 research outputs found
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Bound and Conquer: Improving Triangulation by Enforcing Consistency
We study the accuracy of triangulation in multi-camera systems with respect
to the number of cameras. We show that, under certain conditions, the optimal
achievable reconstruction error decays quadratically as more cameras are added
to the system. Furthermore, we analyse the error decay-rate of major
state-of-the-art algorithms with respect to the number of cameras. To this end,
we introduce the notion of consistency for triangulation, and show that
consistent reconstruction algorithms achieve the optimal quadratic decay, which
is asymptotically faster than some other methods. Finally, we present
simulations results supporting our findings. Our simulations have been
implemented in MATLAB and the resulting code is available in the supplementary
material.Comment: 8 pages, 4 figures, Submitted to IEEE Transactions on Pattern
Analysis and Machine Intelligenc
- …