Related papers: Enhancing Predictive Capabilities in Data-Driven D…
Analyzing the spectral properties of the Koopman operator is crucial for understanding and predicting the behavior of complex stochastic dynamical systems. However, the accuracy of data-driven estimation methods, such as Extended Dynamic…
Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
We propose a novel method for forecasting the temporal evolution of probability distributions observed at discrete time points. Extending the Dynamic Probability Density Decomposition (DPDD), we embed distributional dynamics into…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…
When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…
We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…
Extended dynamic mode decomposition (EDMD) is a data-driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method of order N and collocation method of order M.…
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…
The Dynamic Mode Decomposition (DMD) and the more general Extended DMD (EDMD) are powerful tools for computational analysis of dynamical systems in data-driven scenarios. They are built on the theoretical foundation of the Koopman…
The Koopman operator and extended dynamic mode decomposition (EDMD) as a data-driven technique for its approximation have attracted considerable attention as a key tool for modeling, analysis, and control of complex dynamical systems.…
Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…
This paper proposes Koopman operator-based Stochastic Model Predictive Control (K-SMPC) for enhanced lateral control of autonomous vehicles. The Koopman operator is a linear map representing the nonlinear dynamics in an infinite-dimensional…
Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…
Advanced autonomous driving systems require accurate vehicle dynamics modeling. However, identifying a precise dynamics model remains challenging due to strong nonlinearities and the coupled longitudinal and lateral dynamic characteristics.…
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and…
Nonlinear dynamical systems can be handily described by the associated Koopman operator, whose action evolves every observable of the system forward in time. Learning the Koopman operator and its spectral decomposition from data is enabled…
We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. For many DMD algorithms, the…
Advances in machine learning and the growing trend towards effortless data generation in real-world systems has led to an increasing interest for data-inferred models and data-based control in robotics. It seems appealing to govern robots…
We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…