Low Dimensional Koopman Generalized Eigenfunctions Representation: An Approach to Address Koopman High-Dimensionality Problem
This Paper introduces a methodology to achieve a lower dimensional Koopman quasi linear representation of nonlinear dynamics using Koopman generalized eigenfunctions. The methodology is presented for the analytically derived Koopman formulation of rigid body dynamics but can be generalized to any data-driven or analytically derived generalized eigenfunction set. The presented approach aim at achieving a representation for which the number of Koopman observables matches the number of input leading to an exact linearization solution instead of resorting to the least square approximation method. The methodology is tested by designing a linear quadratic (LQ) flight controller of a quadrotor unmanned aerial vehicle (UAV). Hardware in the loop simulations validate the applicability of this approach to real-time implementation in presence of noise and sensor delays.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators
We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolution of observables, Koopman operators tran…
Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition
This paper develops data-driven methods to identify eigenfunctions of the Koopman operator associated to a dynamical system and subspaces that are invariant under the operator. We build on Extended Dynamic Mode Decomposi…
On the algebra of Koopman eigenfunctions and on some of their infinities
For continuous-time dynamical systems with reversible trajectories, the nowhere-vanishing eigenfunctions of the Koopman operator of the system form a multiplicative group. Here, we exploit this property to accelerate the…
Deep learning for universal linear embeddings of nonlinear dynamics
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimat…
Deep LearningExtended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control
This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the fu…