Finite horizon backward reachability analysis and control synthesis for uncertain nonlinear systems

He Yin, Andrew Packard, Murat Arcak, Peter Seiler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations


We present a method for synthesizing controllers to steer trajectories from an initial set to a target set on a finite time horizon. The proposed control synthesis problem is decomposed into two steps. The first step under-approximates the backward reachable set (BRS) from the target set, using level sets of storage functions. The storage function is constructed with an iterative algorithm to maximize the volume of the under-approximated BRS. The second step obtains a control law by solving a pointwise min-norm optimization problem using the pre-computed storage function. A closed-form solution of this min-norm optimization can be computed through the KKT conditions. This control synthesis framework is then extended to uncertain nonlinear systems with parametric uncertainties and L2 disturbances. The computation algorithm for all cases is derived using sum-of-squares (SOS) programming and the S-procedure. The proposed method is applied to several examples, including robotic systems.

Original languageEnglish (US)
Title of host publication2019 American Control Conference, ACC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages7
ISBN (Electronic)9781538679265
StatePublished - Jul 2019
Event2019 American Control Conference, ACC 2019 - Philadelphia, United States
Duration: Jul 10 2019Jul 12 2019

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2019 American Control Conference, ACC 2019
Country/TerritoryUnited States

Bibliographical note

Funding Information:
*This work was funded in part by the ONR grant N00014-18-1-2209.

Publisher Copyright:
© 2019 American Automatic Control Council.

Copyright 2020 Elsevier B.V., All rights reserved.


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