Learning of Causal Observable Functions for KoopmanDFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation
Abstract
Effective and causal observable functions for loworder lifting linearization of nonlinear controlled systems are learned from data by using neural networks. While Koopman operator theory allows us to represent a nonlinear system as a linear system in an infinitedimensional space of observables, exact linearization is guaranteed only for autonomous systems with no input, and finding effective observable functions for approximation with a loworder linear system remains an open question. DualFaceted Linearization uses a set of effective observables for loworder lifting linearization, but the method requires knowledge of the physical structure of the nonlinear system. Here, a datadriven method is presented for generating a set of nonlinear observable functions that can accurately approximate a nonlinear control system to a loworder linear control system. A caveat in using data of measured variables as observables is that the measured variables may contain input to the system, which incurs a causality contradiction when lifting the system, i.e. taking derivatives of the observables. The current work presents a method for eliminating such anticausal components of the observables and lifting the system using only causal observables. The method is applied to excavation automation, a complex nonlinear dynamical system, to obtain a loworder lifted linear model for control design.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 arXiv:
 arXiv:2104.02004
 Bibcode:
 2021arXiv210402004S
 Keywords:

 Computer Science  Robotics
 EPrint:
 The contents of this paper were also selected by the CASE 2021 Program Committee for presentation at the conference