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Data‐driven predictive control for a class of uncertain control‐affine systems
Author(s) -
Li Dan,
Fooladivanda Dariush,
Martínez Sonia
Publication year - 2022
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.6430
Subject(s) - affine transformation , model predictive control , mathematical optimization , computer science , class (philosophy) , set (abstract data type) , optimization problem , control (management) , probability distribution , limit (mathematics) , sample (material) , control theory (sociology) , mathematics , artificial intelligence , statistics , mathematical analysis , chemistry , chromatography , pure mathematics , programming language
Abstract This article studies a data‐driven predictive control for a class of control‐affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are feasible and provide superior performance guarantees with high probability. This results into the formulation of a stochastic optimization problem (P), which is intractable due to the unknown distribution of the uncertainty variables. By developing a distributionally robust optimization framework, we present an equivalent and yet tractable reformulation of (P). Further, we propose an efficient algorithm that provides online suboptimal data‐driven solutions and guarantees performance with high probability. To illustrate the effectiveness of the proposed approach, we consider a highway speed‐limit control problem. We then develop a set of data‐driven speed controls that allow us to prevent traffic congestion with high probability. Finally, we employ the resulting control method on a traffic simulator to illustrate the effectiveness of this approach numerically.