Control Occupation Kernel Regression for Nonlinear Control-Affine Systems
This work addresses system identification for control-affine systems, which is incremental as it builds on existing kernel methods but introduces a novel embedding approach.
The paper tackles the problem of approximating nonlinear high-order control-affine dynamical systems by developing an algorithm that uses controlled trajectories embedded in a vector-valued reproducing kernel Hilbert space, achieving effective system identification through a finite-dimensional optimization solution.
This manuscript presents an algorithm for obtaining an approximation of a nonlinear high order control affine dynamical system. Controlled trajectories of the system are leveraged as the central unit of information via embedding them in vector-valued reproducing kernel Hilbert space (vvRKHS). The trajectories are embedded as the so-called higher order control occupation kernels which represent an operator on the vvRKHS corresponding to iterated integration after multiplication by a given controller. The solution to the system identification problem is then the unique solution of an infinite dimensional regularized regression problem. The representer theorem is then used to express the solution as finite linear combination of these occupation kernels, which converts an infinite dimensional optimization problem to a finite dimensional optimization problem. 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 developed approach.