Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 20 for “"Koopman operator"”.
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Application of Koopman Operator Theory to Legged Locomotion
… 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 …
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Koopman Operator Theory Applied to Lambert’s Problem with a Spectral Behavior Analysis
… have constraints in their applications. Using operator theory to simplify a system’s nonlinear dynamics presents a promising avenue for research. This Thesis bridges the gap in implementing operator theory to effectively solve Lambert’s problem. The Koopman Operator is used to embed the …
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Applications of the Koopman Operator: Novel Methods and Formulations for Lifted Linear Models
… It has been shown that through the use of the Koopman Operator, these nonlinear systems can be lifted to a higher order state space, and with this lifted representation, the system's dynamics behave linearly. In this thesis, we explore the use of existing methods for constructing the Koopman …
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Robust Identification, Estimation, and Control of Electric Power Systems using the Koopman Operator-Theoretic Framework
… dynamical systems via the spectrum of the Koopman operator has emerged as a paradigm shift, from the Poincaré's geometric picture that centers the attention on the evolution of states, to the Koopman operator's picture that focuses on the evolution of observables. The Koopman …
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Power System Stability Improvement with Decommissioned Synchronous Machine Using Koopman Operator Based Model Predictive Control
… for the nonlinear controller design using Koopman operator-based framework is proposed. Besides, the time delay embedding technique is adopted together with Koopman operator theory for the nonlinear system identification. Koopman operator provides a linear representation of the system and …
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Robust and Data-Driven Uncertainty Quantification Methods as Real-Time Decision Support in Data-Driven Models
… data-driven. In dynamical analysis, the Koopman operator represents nonlinear system dynamics as linear systems by lifting state functions, enabling data-driven estimation through its applied form. By analyzing its spectral properties—eigenvalues, eigenfunctions, and modes—the Koopman …
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Power System Coherency Identification Using Nonlinear Koopman Mode Analysis
In this thesis, we apply nonlinear Koopman mode analysis to decompose the swing dynamics of a power system into modes of oscillation, which are identified by analyzing the Koopman operator, a linear infinite-dimensional operator that may be defined for any nonlinear dynamical system. Specifically, …
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Wavelet-based Dynamic Mode Decomposition in the Context of Extended Dynamic Mode Decomposition and Koopman Theory
Koopman theory is widely used for data-driven modeling of nonlinear dynamical systems. One of the well-known algorithms that stem from this approach is the Extended Dynamic Mode Decomposition (EDMD), a data-driven algorithm for uncontrolled systems. In this thesis, we will start by discussing the …
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Nonparametric sparse learning of dynamical systems
Transfer operators such as the Koopman operator and the Perron-Frobenius operator provide a rich framework for representing the dynamics of very general, nonlinear dynamical systems. In this dissertation, we develop a nonparametric approach to learning the system dynamics via transfer operators in …
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Latent Space Modeling for Environmental Systems
… heterogeneity. The second part delves into the Koopman Invertible Autoencoders (KIA), a model based on the Koopman operator theory. KIA is adept at capturing both forward and backward dynamics in infinite-dimensional Hilbert space, leading to more precise long-term predictions. This model’s …
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Efficient Sampling Methods of, by, and for Stochastic Dynamical Systems
… exploits the relationship between the stochastic Koopman operator and the Kolmogorov backward equation to derive optimal importance sampling and multilevel splitting estimators. By expressing an indicator function over a rare event in terms of the eigenfunctions of the stochastic Koopman operator, …
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A Koopman-Based Reduced-Order State Observer for Visual Localization of Robots
A reduced-order observer using Koopman lifting linearization is developed for localization of a robot guided by a vision system. The Koopman operator is a powerful method for representing nonlinear robot dynamics as a linear model in a lifted space. Koopman faces two main challenges with robot …
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On the Application of Machine Learning and Physical Modeling Theory to Causal Lifting Linearizations of Nonlinear Dynamical Systems with Exogenous Input and Control
… through lifting linearization underpinned by Koopman operator and physical system modeling theory are presented. Outputs of a nonlinear control system, called observables, may be functions of state and input, Φ(x,u). These input-dependent observables cannot be used for lifting the system, …
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Unsteady Metric Based Grid Adaptation using Koopman Expansion
… complex nonlinear flows, given its links to the Koopman operator, and also its easy mathematical implementation. This research proposes the integration of DMD into the process of anisotropic grid adaptation to dynamically adjust the mesh in response to evolving flow features. The effectiveness of …
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Animal Motion Analysis and Approximation for Robotics
… extended dynamic mode decomposition, or even Koopman method to understand and compare the motion across different species. Thus, the goal of this thesis is to further develop the methods mentioned above to analyze and characterize animal motion. The algorithms derived should apply regardless …
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Modeling the Sit-to-Stand Transition using Koopman Lifting Linearization and Human State Estimation
… a dynamic modeling methodology inspired by Koopman operator theory, to subsume segmented local dynamics in a globally linear dynamic model. A novel class of lifting linearization basis functions, termed “State-Membership Product (SMP)” observables, enables both the seamless blending of local …
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Integration of Control and Dynamical Systems Perspectives to Machine Learning
… With a novel problem formulation with the Koopman operator, which is cast as a generalization of pole assignments to nonlinear decision making, a diverse array of dynamic behaviors are realized. Thirdly, as an additional highlight of exploration, I present the successful extension of RL …
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Implications of seasonality and asymmetry for ENSO’s predictability and future changes
… evaluate an alternative framework – based on the Koopman operator – for representing asymmetry and seasonality in a highly idealized, conceptual model of ENSO. While conceptual ENSO models are widely used to diagnose ENSO stability in observations and global climate models, they rely on nonlinear …
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Learning and decision-making in spatiotemporally varying domains
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms
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Advancements in Model Predictive Control for Real-Time Applications With Economic and Conflicting Control Objectives
L'abstract è presente nell'allegato / the abstract is in the attachment