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Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear…

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…

The advent of easy access to large amount of data has sparked interest in directly developing the relationships between input and output of dynamic systems. A challenge is that in addition to the applied input and the measured output, the…

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…

Nonlinearity in dynamics has long been a major challenge in robotics, often causing significant performance degradation in existing control algorithms. For example, the navigation of bipedal robots can exhibit nonlinear behaviors even under…

The gap between our ability to collect interesting data and our ability to analyze these data is growing at an unprecedented rate. Recent algorithmic attempts to fill this gap have employed unsupervised tools to discover structure in data.…

Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by…

The Koopman framework is a popular approach to transform a finite dimensional nonlinear system into an infinite dimensional, but linear model through a lifting process, using so-called observable functions. While there is an extensive…

In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust…

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…

We present a novel approach to shared control of human-machine systems. Our method assumes no a priori knowledge of the system dynamics. Instead, we learn both the dynamics and information about the user's interaction from observation…

We study nonlinear dynamics of the Earth's tropical climate system. For that, we apply a recently developed technique for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. The method…

Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has…

Soft robots are challenging to model due in large part to the nonlinear properties of soft materials. Fortunately, this softness makes it possible to safely observe their behavior under random control inputs, making them amenable to…

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…

Automated driving applications require accurate vehicle specific models to precisely predict and control the motion dynamics. However, modern vehicles have a wide array of digital and mechatronic components that are difficult to model,…

Nonlinear Negative Imaginary (NI) systems arise in various engineering applications, such as controlling flexible structures and air vehicles. However, unlike linear NI systems, their theory is not well-developed. In this paper, we propose…

This paper presents a class of linear predictors for nonlinear controlled dynamical systems. The basic idea is to lift the nonlinear dynamics into a higher dimensional space where its evolution is approximately linear. In an uncontrolled…

Data-driven modeling of non-Markovian dynamics is a recent topic of research with applications in many fields such as climate research, molecular dynamics, biophysics, or wind power modeling. In the frequently used standard Langevin…

In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to…