201,511 research outputs found
Output Regulation of Nonlinear Systems in a Koopman Operator Framework
No full textThis thesis considers the problem of nonlinear output regulation in a Koopman operator framework. The goal of output regulation is to asymptotically track a reference and/or simultaneously reject a disturbance signal, both generated by some external autonomous system called the exosystem. The nonlinear output regulation problem is solvable if and only if a set of partial differential equations (PDE) are satisfied. From the solution, a feedback law can be obtained that achieves output regulation. However, solving the PDE is difficult. In this thesis, we instead aim to construct a feedback law by utilizing the Koopman operator instead.The Koopman operator associated with a state-space model of a (nonlinear) dynamical system describes the evolution of functions of the states, called observable functions, by propagating the state forward in time according to the flow of the system, and evaluating this at each possible observable function. The space of observables is an infinite-dimensional vector field. Therefore, the Koopman operator is infinite-dimensional and linear. The Koopman operator of an autonomous system associated with a nonlinear control system provides a bilinear description of the control system instead. The use of the Koopman operator to tackle the output regulation problem has not been done before in the literature. We identify conditions under which the Koopman operator can be used to rephrase the nonlinear output regulation problem as a bilinear output regulation problem. We then show when the bilinear output regulation problem is solved using linear dynamic error feedback. In particular, a Lyapunov-based approach is used to characterize a set of initial conditions for which the output is regulated. Finally, to verify the results, a numerical example is presented.Mechanical Engineering | Systems and Contro
Applying Koopman Methods for Nonlinear Reachability Analysis
No full textIn this thesis we investigate the possibilities for applying Koopman methods for reachability analysis. Reachability analysis is a verification process used to determine that a dynamical system starting in an initial set X0 cannot reach a certain set of dangerous states D within a time interval [0,T]. Koopman methods seem promising, because they predict nonlinear behaviour using linear techniques. However they have not been widely applied to reachability analysis.We describe three different Koopman methods: data-driven, Polyflow and Carleman. We use the Polyflow method combined with ideas from several other methods to create a new reachability tool: PolyReach. Next, we analyse the performance of PolyReach by comparing it with a state-of-the-art reachability algorithm Flow* on various nonlinear systems. Finally, we summarize the strengths and weaknesses of the PolyReach tool and discuss ideas for further improvement.Mechanical Engineering | Systems and Contro
Representer Theorem for Learning Koopman Operators
No full textIn this work, we consider the problem of learning the Koopman operator for discrete-time autonomous systems. The learning problem is formulated as a generic constrained regularized empirical loss minimization in the infinite-dimensional space of linear operators. We show that a representer theorem holds for the introduced learning problem under certain but general conditions, which allows convex reformulation of the problem in a specific finite-dimensional space without any approximation and loss of precision. We discuss the inclusion of various forms of regularization and constraints in the learning problem, such as the operator norm, the Frobenius norm, the operator rank, the nuclear norm, and the stability. Subsequently, we derive the corresponding equivalent finite-dimensional problem. Furthermore, we demonstrate the connection between the proposed formulation and the extended dynamic mode decomposition. We present several numerical examples to illustrate the theoretical results and verify the performance of regularized learning of the Koopman operators.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.Team Khosrav
Koopman Subspace Identification in the Presence of Measurement Noise
No full textThe ability to compute models that correctly predict the trajectories of a nonlinear system can become a significant challenge in systems and control. The introduction of Koopman operator theory helped to deal with this challenge. The Koopman operator is a composition operator that globally describes a nonlinear system in an infinite-dimensional linear framework. To implement this theory, the usual approach is to approximate the Koopman operator through data-driven methods. These algorithms use measurements of the nonlinear system to compute the approximated operator. Generally, noise can be present in real-world scenarios. Noisy measurements can have a considerable deteriorating effect on the data-driven approximation of Koopman operators. The approximation of this operator in presence of noisy training data is a necessary step for its implementation to a wider spectrum of real-world applications. Many robust numerical methods were designed to solve this issue. Koopman subspace identification (KSI) is a promising approach. As the name suggests, this algorithm employs subspace identification modeling to compute the matrix approximation of the Koopman operator. In this work, we test KSI against other state-of-the-art techniques. Additionally, we improve its performance in predicting the state trajectories of the nonlinear system in presence of noisy measurements. To this end, we propose a reducing-order routine that computes the most robust model against measurement noise. Furthermore, a randomized singular value decomposition is adopted to reduce computational times. The improved KSI is then compared against the other state-of-the-art algorithms in the presence of noisy data sets. We will show that the upgraded KSI outperforms most of the other techniques.Mechanical Engineering | Systems and 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
Studies in colorectal cancer metastases: implications for clinical practice
No full textContains fulltext :
106976.pdf (Publisher’s version ) (Open Access)Radboud Universiteit Nijmegen, 16 april 2013Promotores : Punt, C.J.A., Nagtegaal, I.D. Co-promotor : Koopman, M
Hipposideros curtus G. M. Allen 1921
No full textHipposideros curtus G. M. Allen, 1921. Rev. Zool. Afr., 9:194. TYPE LOCALITY: Cameroon, Sakbayeme. DISTRIBUTION: Cameroon, Bioko, perhaps Nigeria. SYNONYMS: sandersoni. COMMENTS: Includes sandersoni; see Hill (1963b:60).Published as part of Karl F. Koopman, 1993, Order Chiroptera, pp. 137-241 in Mammal Species of the World (2 nd Edition), Washington and London :Smithsonian Institution Press on page 172, DOI: 10.5281/zenodo.735306
A synopsis of the Malagasy endemic genus<i>Megistostegium</i>Hochr. (Hibisceae, Malvaceae)
No full textFIG. 1. — Floral and habit photographs of the three species of Megistostegium Hochr.: A, M. microphyllum Hochr.; B, M. nodulosum (Drake) Hochr.; C, M. perrieri Hochr. Scale bar for flowers: 2 cm.Published as part of Koopman, Margaret M., 2011, A synopsis of the Malagasy endemic genus Megistostegium Hochr. (Hibisceae, Malvaceae), pp. 101-113 in Adansonia (3) 33 (1) on page 103, DOI: 10.5252/a2011n1a7, http://zenodo.org/record/519705
Rhinolophus rex G. M. Allen 1923
No full textRhinolophus rex G. M. Allen, 1923. Am. Mus. Novit., 85:3. TYPE LOCALITY: China, Szechwan, Wanhsien. DISTRIBUTION: SW China.Published as part of Karl F. Koopman, 1993, Order Chiroptera, pp. 137-241 in Mammal Species of the World (2 nd Edition), Washington and London :Smithsonian Institution Press on page 168, DOI: 10.5281/zenodo.735306
Lonchophylla hesperia G. M. Allen 1908
No full textLonchophylla hesperia G. M. Allen, 1908. Bull. Mus. Comp. Zool., 52:35. TYPE LOCALITY: Peru, Tumbes, Zorritos. DISTRIBUTION: N Peru, Ecuador. COMMENTS: Known only from five specimens; see Gardner (1976:5).Published as part of Karl F. Koopman, 1993, Order Chiroptera, pp. 137-241 in Mammal Species of the World (2 nd Edition), Washington and London :Smithsonian Institution Press on page 181, DOI: 10.5281/zenodo.735306
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