Hamzi - Eurandom

Extension to the Nonlinear Case
• The preceding suggests the following key observations in the linear
setting: Given an approximation ˆ Lc of Lc we obtain an approximation for
ρ∞ of the form
ˆρ∞(x) ∝ e − ˆ Lc(x)
• Although the above relationship between ρ∞ and Lc holds for only a
small class of systems (e.g. linear and some Hamiltonian systems), by
mapping a nonlinear system into a suitable reproducing kernel Hilbert
space we may reasonably extend this connection to a broad class of
nonlinear systems.
. . . . . .
Boumediene Hamzi (Imperial College) On Control and RDS in RKHS June 4th, 2012 44 / 55