Numerical calculation of nonsmooth control Lyapunov functions via piecewise affine approximation

Robert Baier; Philipp Braun; Lars Grüne; Christopher M. Kellett

doi:10.1016/j.ifacol.2019.11.808

Numerical calculation of nonsmooth control Lyapunov functions via piecewise affine approximation

Robert Baier
, Philipp Braun
, Lars Grüne
, Christopher M. Kellett

Research output: Contribution to journal › Conference article › peer-review

5 Citations (Scopus)

Abstract

We review the numerical computation of control Lyapunov functions for switched systems in the Filippov sense and in the sample-and-hold sense. The computed (control) Lyapunov functions are piecewise affine and the decrease conditions involve either generalized gradients or the Dini subderivate. Further conditions for stabilization or stabilizability yield a (mixed-integer) linear program.

Original language	English
Pages (from-to)	370-375
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	52
Issue number	16
DOIs	https://doi.org/10.1016/j.ifacol.2019.11.808
Publication status	Published - Sept 2019
Externally published	Yes
Event	11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 - Vienna, Austria Duration: 4 Sept 2019 → 6 Sept 2019

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10.1016/j.ifacol.2019.11.808

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@article{947d49637ace47398320fd28f4f347c1,

title = "Numerical calculation of nonsmooth control Lyapunov functions via piecewise affine approximation",

abstract = "We review the numerical computation of control Lyapunov functions for switched systems in the Filippov sense and in the sample-and-hold sense. The computed (control) Lyapunov functions are piecewise affine and the decrease conditions involve either generalized gradients or the Dini subderivate. Further conditions for stabilization or stabilizability yield a (mixed-integer) linear program.",

keywords = "(control) Lyapunov function, Asymptotic stability, Controllability, Linear programming, Mixed-integer problems, Piecewise linear analysis, Switched systems",

author = "Robert Baier and Philipp Braun and Lars Gr{\"u}ne and Kellett, \{Christopher M.\}",

note = "Publisher Copyright: {\textcopyright} 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.; 11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 ; Conference date: 04-09-2019 Through 06-09-2019",

year = "2019",

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doi = "10.1016/j.ifacol.2019.11.808",

language = "English",

volume = "52",

pages = "370--375",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Numerical calculation of nonsmooth control Lyapunov functions via piecewise affine approximation

AU - Baier, Robert

AU - Braun, Philipp

AU - Grüne, Lars

AU - Kellett, Christopher M.

PY - 2019/9

Y1 - 2019/9

N2 - We review the numerical computation of control Lyapunov functions for switched systems in the Filippov sense and in the sample-and-hold sense. The computed (control) Lyapunov functions are piecewise affine and the decrease conditions involve either generalized gradients or the Dini subderivate. Further conditions for stabilization or stabilizability yield a (mixed-integer) linear program.

AB - We review the numerical computation of control Lyapunov functions for switched systems in the Filippov sense and in the sample-and-hold sense. The computed (control) Lyapunov functions are piecewise affine and the decrease conditions involve either generalized gradients or the Dini subderivate. Further conditions for stabilization or stabilizability yield a (mixed-integer) linear program.

KW - (control) Lyapunov function

KW - Asymptotic stability

KW - Controllability

KW - Linear programming

KW - Mixed-integer problems

KW - Piecewise linear analysis

KW - Switched systems

UR - https://www.scopus.com/pages/publications/85077460733

U2 - 10.1016/j.ifacol.2019.11.808

DO - 10.1016/j.ifacol.2019.11.808

M3 - Conference article

AN - SCOPUS:85077460733

SN - 2405-8963

VL - 52

SP - 370

EP - 375

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 16

T2 - 11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019

Y2 - 4 September 2019 through 6 September 2019

ER -

Numerical calculation of nonsmooth control Lyapunov functions via piecewise affine approximation

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