120,752 research outputs found
DeepKoCo: Efficient latent planning with a task-relevant Koopman representation
No full textThis paper presents DeepKoCo, a novel modelbased agent that learns a latent Koopman representation from images. This representation allows DeepKoCo to plan efficiently using linear control methods, such as linear model predictive control. Compared to traditional agents, DeepKoCo learns taskrelevant dynamics, thanks to the use of a tailored lossy autoencoder network that allows DeepKoCo to learn latent dynamics that reconstruct and predict only observed costs, rather than all observed dynamics. As our results show, DeepKoCo achieves a similar final performance as traditional model-free methods on complex control tasks, while being considerably more robust to distractor dynamics, making the proposed agent more amenable for real-life applications.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Learning & Autonomous Contro
Global and Koopman modes analysis of sound generation in mixing layers
No full textIt is now well established that linear and nonlinear instability waves play a significant role in the noise generation process for a wide variety of shear flows such as jets or mixing layers. In that context, the problem of acoustic radiation generated by spatially growing instability waves of two-dimensional subsonic and supersonic mixing layers are revisited in a global point of view, i.e., without any assumption about the base flow, in both a linear and a nonlinear framework by using global and Koopman mode decompositions. In that respect, a timestepping technique based on disturbance equations is employed to extract the most dynamically relevant coherent structures for both linear and nonlinear regimes. The present analysis proposes thus a general strategy for analysing the near-field coherent structures which are responsible for the acoustic noise in these configurations. In particular, we illustrate the failure of linear global modes to describe the noise generation mechanism associated with the vortex pairing for the subsonic regime whereas they appropriately explain the Mach wave radiation of instability waves in the supersonic regime. By contrast, the Dynamic Mode Decomposition (DMD) analysis captures both the near-field dynamics and the far-field acoustics with a few number of modes for both configurations. In addition, the combination of DMD and linear global modes analyses provides new insight about the influence on the radiated noise of nonlinear interactions and saturation of instability waves as well as their interaction with the mean flow
Schoenus L
No full textGenus 2. Schoenus L., Sp. Pl.: 42 (1753). L e c t o t y p u s: Schoenus nigricans L. 1 (2). Schoenus nigricans L., Sp. Pl.: 43 (1753). 2 (3). Schoenus ferrugineus L., Sp. Pl.: 43 (1753). Tribus 3. Rhynchosporeae Nees, Linnaea 9: 294 (1834). T y p u s: Rhynchospora VahlPublished as part of Danylyk, Ivan M. & Koopman, Jacob, 2023, Cyperaceae of Ukraine: taxonomy and linear classification, pp. 93-111 in Phytotaxa 578 (1) on page 96, DOI: 10.11646/phytotaxa.578.1.5, http://zenodo.org/record/751773
On Koopman Operator for Burgers' Equation
No full textWe consider the flow of Burgers' equation on an open set of (small) functions in . We derive explicitly the Koopman decomposition of the Burgers' flow. We identify the frequencies and the coefficients of this decomposition as eigenvalues and eigenfunctionals of the Koopman operator. We prove the convergence of the Koopman decomposition for for small Cauchy data, and up to for regular Cauchy data. The convergence up to } leads to a `completeness' property for the basis of Koopman modes. We construct all modes and eigenfunctionals, including the eigenspaces involved in geometric multiplicity. This goes beyond the summation formulas provided by (Page & Kerswell, 2018), where only one term per eigenvalue was given. A numeric illustration of the Koopman decomposition is given and the Koopman eigenvalues compared to the eigenvalues of a Dynamic Mode Decomposition (DMD)
Smooth Koopman eigenfunctions
No full textAny dynamical system, whether it is generated by a differential equation or a
transformation rule on a manifold, induces a dynamics on functional-spaces. The
choice of functional-space may vary, but the induced dynamics is always linear,
and codified by the Koopman operator. The eigenfunctions of the Koopman
operator are of extreme importance in the study of the dynamics. They provide a
clear distinction between the mixing and non-mixing components of the dynamics,
and also reveal embedded toral rotations. The usual choice of functional-space
is , a class of square integrable functions. A fundamental problem with
eigenfunctions in is that they are often extremely discontinuous,
particularly if the system is chaotic. There are some prototypical systems
called skew-product dynamics in which Koopman eigenfunctions are also
smooth. The article shows that under general assumptions on an ergodic system,
these prototypical examples are the only possibility. Moreover, the smooth
eigenfunctions can be used to create a change of variables which explicitly
characterizes of the weakly mixing component
Lie group valued Koopman eigenfunctions
No full text© 2023 IOP Publishing Ltd & London Mathematical Society cc-byEvery continuous-time flow on a topological space has associated to it a Koopman operator, which operates by time-shifts on various spaces of functions, such as C r , L 2, or functions of bounded variation. An eigenfunction of the vector field (and thus for the Koopman operator) can be viewed as an S 1-valued function, which also plays the role of a semiconjugacy to a rigid rotation on S 1. This notion of Koopman eigenfunctions will be generalized to Lie-group valued eigenfunctions, and we will discuss the dynamical aspects of these functions. One of the tools that will be developed to aid the discussion, is a concept of exterior derivative for Lie group valued functions, which generalizes the notion of the differential d f of a real valued function f. The extended notion of Koopman eigenfunctions utilizes a geometric property of usual eigenfunctions. We show that the generalization in a geometric sense can be used to reveal fundamental properties of usual Koopman eigenfunctions, such as their behaviour under time-rescaling, and as submersions
Lie group valued Koopman eigenfunctions
No full textEvery continuous-time flow on a topological space has associated to it a
Koopman operator, which operates by time-shifts on various spaces of functions,
such as , , or functions of bounded variation. An eigenfunction of
the vector field (and thus for the Koopman operator) can be viewed as an
-valued function, which also plays the role of a semiconjugacy to a rigid
rotation on . This notion of Koopman eigenfunctions will be generalized to
Lie-group valued eigenfunctions, and we will discuss the dynamical aspects of
these functions. One of the tools that will be developed to aid the discussion,
is a concept of exterior derivative for Lie group valued functions, which
generalizes the notion of the differential of a real valued function .
The extended notion of Koopman eigenfunctions utilizes a geometric property of
usual eigenfunctions. We show that the generalization in a geometric sense can
be used to reveal fundamental properties of usual Koopman eigenfunctions, such
as their behavior under time-rescaling, and as submersions
Application of Koopman Operator Theory to Legged Locomotion
No full textNonlinearities from complicated robot systems and harsh contact dynamics have long impeded the effectiveness of optimal control strategies for legged robots. In this work, we present a linearized simple walking model using Koopman Operator Theory, and its usage in Linear Model Predictive Control (L-MPC). Various walking and contact models were evaluated, but ultimately the rimless wheel was selected due to its inherent stability and low dimensionality, and a nonlinear viscoelastic model was used to accurately capture floor contact and impact dynamics. Koopman models were developed using both Radial Basis Functions (RBFs) and neural network-generated observables for the passive rimless wheel. A novel actuation method with linear actuators, combined with the Control Coherent Koopman methodology, resulted in accurate linear models that effectively enabled L-MPC to control the wheel on flat ground. This model outperformed those created using the more traditional Dynamic Mode Decomposition with Control method. This work demonstrates the power of Koopman linearization to produce a unified set of linear dynamical equations that encompass various contact and non-contact configurations and demonstrates the effectiveness of the Control Coherent Koopman methodology in generating an accurate input matrix across these different contact modes.S.M
On one-parameter Koopman groups
No full textWe characterize Koopman one-parameter C0-groups, in the class of all unitary one-parameter C0-groups on L2(X), as those that preserve L∞(X) and for which the infinitesimal generator is a derivation on the bounded functions in its domain
Who\u27s Sanctioning Whom? The Continuing Evolution of the Federal Faith-Based Initiative
No full textTrends in American Politics and Public Life, given by Dr. Douglas Koopman
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