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arXiv · 2304.11755

Control of Discrete-Time LTI Systems using Stochastic Ensemble Systems

Nirabhra Mandal·Mohammad Khajenejad·Sonia Martinez
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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.

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Nirabhra Mandal, Mohammad Khajenejad, Sonia Martinez. 2023-04-23. Control of Discrete-Time LTI Systems using Stochastic Ensemble Systems. https://arxiv.org/abs/2304.11755

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