Zobrazeno 1 - 10
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pro vyhledávání: '"Kvalheim, Matthew D."'
Autor:
Kvalheim, Matthew D.
The author's extensions of Brockett's and Coron's necessary conditions for stabilizability are shown to be independent in the fiber bundle picture of control, but the latter is shown to be stronger in the vector bundle picture if the state space is o
Externí odkaz:
http://arxiv.org/abs/2312.16752
Deep neural network autoencoders are routinely used computationally for model reduction. They allow recognizing the intrinsic dimension of data that lie in a $k$-dimensional subset $K$ of an input Euclidean space $\mathbb{R}^n$. The underlying idea i
Externí odkaz:
http://arxiv.org/abs/2310.02250
Autor:
Arathoon, Philip, Kvalheim, Matthew D.
A frequently repeated claim in the "applied Koopman operator theory'' literature is that a dynamical system with multiple isolated equilibria cannot be linearized in the sense of admitting a smooth embedding as an invariant submanifold of a linear dy
Externí odkaz:
http://arxiv.org/abs/2306.15126
Autor:
Kvalheim, Matthew D., Arathoon, Philip
We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on a finite-dimensional Euclidean space. We solve this problem for dynam
Externí odkaz:
http://arxiv.org/abs/2305.18288
In this work, we give sufficient conditions for the almost global asymptotic stability of a cascade in which the subsystems are only almost globally asymptotically stable. The result is extended to upper triangular systems of arbitrary size. In parti
Externí odkaz:
http://arxiv.org/abs/2303.15535
Mechanical systems naturally evolve on principal bundles describing their inherent symmetries. The ensuing factorization of the configuration manifold into a symmetry group and an internal shape space has provided deep insights into the locomotion of
Externí odkaz:
http://arxiv.org/abs/2209.11869
Autor:
Kvalheim, Matthew D.
Necessary conditions for asymptotic stability and stabilizability of subsets for dynamical and control systems are obtained. The main necessary condition is homotopical and is in turn used to obtain a homological one. A certain extension is ruled out
Externí odkaz:
http://arxiv.org/abs/2205.07840
Autor:
Kvalheim, Matthew D.
The Hopf theorem states that homotopy classes of continuous maps from a closed connected oriented smooth $n$-manifold $M$ to the $n$-sphere are classified by their degree. Such a map is equivalent to a section of the trivial $n$-sphere bundle over $M
Externí odkaz:
http://arxiv.org/abs/2203.10371
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series expansion w
Externí odkaz:
http://arxiv.org/abs/2203.04498
The "Phase Response Curve" (PRC) is a common tool used to analyze phase resetting in the natural sciences. We make the observation that the PRC with respect to a coordinate $y\in\mathbb{R}$ actually depends on the full choice of coordinates $(x,y)$,
Externí odkaz:
http://arxiv.org/abs/2111.06511