Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control

@article{Korda2018LinearPF,
  title={Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control},
  author={Milan Korda and Igor Mezi{\'c}},
  journal={Autom.},
  year={2018},
  volume={93},
  pages={149-160}
}
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References

SHOWING 1-10 OF 29 REFERENCES
Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control
TLDR
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.
Linear identification of nonlinear systems: A lifting technique based on the Koopman operator
TLDR
The proposed linear identification technique is efficient to recover (polynomial) vector fields of different classes of systems, including unstable, chaotic, and open systems, and robust to noise, well-suited to model low sampling rate datasets, and able to infer network topology and dynamics.
Linear observer synthesis for nonlinear systems using Koopman Operator framework
A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
TLDR
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.
Generalizing Koopman Theory to Allow for Inputs and Control
TLDR
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).
Constrained model predictive control: Stability and optimality
Extending Data-Driven Koopman Analysis to Actuated Systems
Applied Koopmanism.
TLDR
The Koopman framework is showing potential for crossing over from academic and theoretical use to industrial practice, and the paper highlights its strengths in applied and numerical contexts.
Chaos as an intermittently forced linear system
TLDR
A universal, data-driven decomposition of chaos as an intermittently forced linear system is presented, combining delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates.
Spectral Properties of Dynamical Systems, Model Reduction and Decompositions
In this paper we discuss two issues related to model reduction of deterministic or stochastic processes. The first is the relationship of the spectral properties of the dynamics on the attractor of…
...
1
2
3
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