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Safe Controller Synthesis for Data-Driven Differential Inclusions

Ahmadi, Mohamadreza and Israel, Arie and Topcu, Ufuk (2020) Safe Controller Synthesis for Data-Driven Differential Inclusions. IEEE Transactions on Automatic Control . ISSN 0018-9286. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20200131-082224462

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Abstract

We consider the problem of designing finite-horizon safe controllers for a dynamical system for which no explicit analytical model exists and limited data only along a single trajectory of the system are available. Given samples of the states and inputs of the system, and additional side information in terms of regularity of the evolution of the states, we synthesize a controller such that the evolution of the states avoid some pre-specified unsafe set over a given finite horizon. Motivated by recent results on Whitney's extension theorem, we use piecewise-polynomial approximations of the trajectories based on the data along with the regularity side information to formulate a data-driven differential inclusion model that can predict the evolution of the trajectories. For these classes of data-driven differential inclusions, we propose a safety analysis theorem based on barrier certificates. As a corollary of this theorem, we demonstrate that we can design controllers ensuring safety of the solutions to the data-driven differential inclusion over a finite horizon. From a computational standpoint, our results are cast into a set of sum-of-squares programs whenever the certificates are parametrized by polynomials of fixed degree and the sets are semi-algebraic.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/tac.2020.2969713DOIArticle
ORCID:
AuthorORCID
Ahmadi, Mohamadreza0000-0003-1447-3012
Additional Information:© 2019 IEEE. The work has been supported partly by AFOSR FA9550-19-1-0005 and NSF 1646522.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-19-1-0005
NSFCNS-1646522
Record Number:CaltechAUTHORS:20200131-082224462
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200131-082224462
Official Citation:M. Ahmadi, A. Israel and U. Topcu, "Safe Controller Synthesis for Data-Driven Differential Inclusions," in IEEE Transactions on Automatic Control. doi: 10.1109/TAC.2020.2969713
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101026
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:31 Jan 2020 18:05
Last Modified:03 Aug 2020 21:25

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