Control of discrete time LTI systems via Stochastic Ensembles

Nirabhra Mandal and Mohammad Khajenejad and Sonia Martínez
Proceedings of the 2023 SIAM Conference on Control Systems and Its Applications, July 2023

Abstract:

In this paper, we study the control properties of a new class of stochastic ensemble systems that consists of families of random variables. These random variables provide an increasingly good approximation of an unknown discrete, linear-time invariant (DLTI) system, and can be obtained by a standard, data-driven procedure. Our first result relates the reachability properties of the stochastic ensemble system with that of the limiting DLTI system. We then provide a method to combine the control inputs obtained from the stochastic ensemble systems to compute a control input for the DLTI system. Later, we deal with a particular kind of stochastic ensemble system generated from realizing Bernoulli random variables. For this, we characterize the variance of the computed state and control. We also do the same for a situation where the data is updated sequentially in a streaming fashion. We illustrate the results numerically in various simulation examples.

File: main.pdf

Bib-tex entry:

@InProceedings{NM-MK-SM:23-siam,
author = {N. Mandal and M. Khajenejad and S. Mart{\'\i}nez},
title = {Control of discrete time LTI systems via Stochastic Ensembles},
booktitle = {2023 SIAM Control Theory and Its Applications Conference},
pages = {},
year = {2023},
address = {Philadelphia, PA, USA},
month = {July}
}