• Corpus ID: 54024507

Dynamic mode decomposition for interconnected control systems

@article{Heersink2017DynamicMD,
  title={Dynamic mode decomposition for interconnected control systems},
  author={Byron Heersink and Michael A. Warren and Heiko Hoffmann},
  journal={arXiv: Optimization and Control},
  year={2017}
}
Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the dynamics from an estimate of the Koopman operator obtained from data. Recent work of Proctor, Brunton, and Kutz has extended DMD and Koopman theory to accommodate systems with control inputs: dynamic mode decomposition with control (DMDc) and Koopman with inputs… 

Figures from this paper

Data-Driven Predictive Control of Interconnected Systems Using the Koopman Operator

Interconnected systems are widespread in modern technological systems. Designing a reliable control strategy requires modeling and analysis of the system, which can be a complicated, or even

Koopman Spectrum and Stability of Cascaded Dynamical Systems

This chapter investigates the behavior of cascaded dynamical systems through the lens of the Koopman operator and, in particular, its so-called principal eigenfunctions. It is shown that there exist

Data-driven operator-theoretic analysis of weak interactions in synchronized network dynamics

A data-driven approach to extracting interactions among oscillators in synchronized networks by solving a multiparameter eigenvalue problem associated with the Koopman operator on vector-valued function spaces is proposed.

Introduction to the Koopman Operator in Dynamical Systems and Control Theory

This introductory chapter provides an overview of the Koopman operator framework. We present basic notions and definitions, including those related to the spectral properties of the operator. We also

Experimental Applications of the Koopman Operator in Active Learning for Control

This chapter examines the Koopman operator, its application in active learning, and its relationship to alternative learning techniques, such as Gaussian processes and kernel ridge regression.

References

SHOWING 1-10 OF 33 REFERENCES

Dynamic Mode Decomposition with Control

This work develops a new method which extends dynamic mode decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models.

Generalizing Koopman Theory to Allow for Inputs and Control

A new generalization of Koopman operator theory that incorporates the effects of inputs and control is developed that is rigorously connected and generalizes a recent development called Dynamic Mode Decomposition with control (DMDc).

On dynamic mode decomposition: Theory and applications

A theoretical framework in which dynamic mode decomposition is defined as the eigendecomposition of an approximating linear operator, which generalizes DMD to a larger class of datasets, including nonsequential time series, and shows that under certain conditions, DMD is equivalent to LIM.

A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

This approach is an extension of dynamic mode decomposition (DMD), which has been used to approximate the Koopman eigenvalues and modes, and if the data provided to the method are generated by a Markov process instead of a deterministic dynamical system, the algorithm approximates the eigenfunctions of the Kolmogorov backward equation.

Spectral analysis of nonlinear flows

We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

This work presents a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space and demonstrates the usefulness of nonlinear observable subspaces in the design of Koop man operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Multiresolution Dynamic Mode Decomposition

We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multiresolution analysis allows for a decomposition method capable of robustly separating complex

Applied Koopman Operator Theory for Power Systems Technology

This paper presents a series of applications of the Koopman operator theory to power systems technology: coherency identification of swings in coupled synchronous generators, precursor diagnostic of instabilities in the coupled swing dynamics, and stability assessment of power systems without any use of mathematical models.