Control Occupation Kernel Regression for Nonlinear ControlAffine Systems
Abstract
This manuscript presents an algorithm for obtaining an approximation of nonlinear high order control affine dynamical systems, that leverages the controlled trajectories as the central unit of information. As the fundamental basis elements leveraged in approximation, higher order control occupation kernels represent iterated integration after multiplication by a given controller in a vector valued reproducing kernel Hilbert space. In a regularized regression setting, the unique optimizer for a particular optimization problem is expressed as a linear combination of these occupation kernels, which converts an infinite dimensional optimization problem to a finite dimensional optimization problem through the representer theorem. Interestingly, the vector valued structure of the Hilbert space allows for simultaneous approximation of the drift and control effectiveness components of the control affine system. Several experiments are performed to demonstrate the effectiveness of the approach.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2106.00103
 Bibcode:
 2021arXiv210600103A
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Machine Learning;
 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Functional Analysis