Related papers: Auxiliary Functions as Koopman Observables: Data-D…
In this paper we develop a new data-driven closure approximation method to compute the statistical properties of quantities of interest in high-dimensional stochastic dynamical systems. The new method relies on estimating conditional…
Koopman operator theory provides a powerful data-driven technique for modeling nonlinear dynamical systems in a linear framework, in comparison to computationally expensive and highly nonlinear physics-based simulations. However, Koopman…
The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such…
This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique…
In recent years data-driven analysis of dynamical systems has attracted a lot of attention and transfer operator techniques, namely, Perron-Frobenius and Koopman operators are being used almost ubiquitously. Since data is always obtained in…
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…
Stabilization, disturbance rejection, and control of optical beams and optical spots are ubiquitous problems that are crucial for the development of optical systems for ground and space telescopes, free-space optical communication…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
The Koopman operator lifts nonlinear dynamical systems into a functional space of observables, where the dynamics are linear. In this paper, we provide three different Koopman representations for hybrid systems. The first is specific to…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
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…
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…
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…
The internal state of a dynamical system, a set of variables that defines its evolving configuration, is often hidden and cannot be fully measured, posing a central challenge for real-time monitoring and control. While observers are…
The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept$\unicode{x2013}$representing highly nonlinear dynamical systems by infinite-dimensional linear…
Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…
Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of…
The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying linear function space representations of nonlinear dynamics from…
The aim of this survey is to present the main important techniques and tools from variational analysis used for first and second order dynamical systems of implicit type for solving monotone inclusions and non-smooth optimization problems.…
The accurate modeling and control of nonlinear dynamical effects are crucial for numerous robotic systems. The Koopman formalism emerges as a valuable tool for linear control design in nonlinear systems within unknown environments. However,…