Speaker
Description
The behavioral setting [1] is suited for data-driven algorithms since
systems are viewed as sets of trajectories. A classical result in this
framework, known as /Willems' fundamental lemma/ [2], states the
conditions that allow to represent all the system trajectories
from an observed one. This result makes possible to perform
data-driven simulations [3], that is simulation of the future system
trajectories directly from the observed data (without estimating a
system model).
The classical theory about the topic was developed for the class of
linear time-invariant systems only.
We discuss recent results [4,5] on how to switch from linear to
nonlinear systems.
[1] J. W. Polderman and J. C. Willems. Introduction to Mathematical
Systems Theory, volume 26 of Texts in Applied Mathematics. Springer
New York, New York, NY, 1998.
[2] J. C. Willems, P. Rapisarda, I. Markovsky, and B. De Moor. A note
on persistency of excitation. Syst. Control Lett.,
54(4):325–329, 2005.
[3] I. Markovsky and P. Rapisarda, “Data-driven simulation and control,”
Int. J. Control, vol. 81, pp. 1946–1959, 2008.
[4] I. Markovsky. Data-driven simulation of generalized bilinear
systems via linear time-invariant embedding. IEEE
Trans. Automat. Contr., 2023.
[5] A. Fazzi and A. Chiuso. Data-driven prediction and control for
NARX systems. Submitted.
