Log In Sign Up

Control Occupation Kernel Regression for Nonlinear Control-Affine Systems

by   Moad Abudia, et al.

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.


page 1

page 2

page 3

page 4


Regularised Least-Squares Regression with Infinite-Dimensional Output Space

We present some learning theory results on reproducing kernel Hilbert sp...

Metric on random dynamical systems with vector-valued reproducing kernel Hilbert spaces

The development of a metric on structural data-generating mechanisms is ...

Handling Hard Affine SDP Shape Constraints in RKHSs

Shape constraints, such as non-negativity, monotonicity, convexity or su...

Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space

We introduce a novel data-driven order reduction method for nonlinear co...

Kernel Methods for the Approximation of Nonlinear Systems

We introduce a data-driven order reduction method for nonlinear control ...

Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems

We present the Koopman State Estimator (KoopSE), a framework for model-f...