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On (the existence of) Control Lyapunov Barrier Functions

URN to cite this document: urn:nbn:de:bvb:703-epub-3522-6

Title data

Braun, Philipp ; Kellett, Christopher M.:
On (the existence of) Control Lyapunov Barrier Functions.
Newcastle, Australia , 2017 . - 19 S.

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Project information

Project title:
Project's official titleProject's id
Activating Lyapunov-Based Feedback - Nonsmooth Control Lyapunov FunctionsG1500106

Project financing: ARC (Australian Research Council)

Abstract

Recently, [17] proposed control Lyapunov barrier functions (CLBFs) for the stabilization of nonlinear dynamical systems with state constraints. Under the assumption of the existence of a smooth CLBF, Sontag's universal formula was used to define a continuous feedback ensuring that the constraints are satisfied. However, as we demonstrate in this paper, the above approach neglects the necessity of discontinuous controllers in the case of state constraints. Additionally, we show that the assumption of a smooth CLBF limits the state constraints to those defined by unbounded sets. Consequently, we introduce the notion of nonsmooth complete control Lyapunov functions (CCLFs) and indicate how they may be used for stabilization in the presence of state constraints.

Further data

Item Type: Preprint, postprint
Keywords: (nonsmooth) control Lyapunov functions; control of constrained systems; asymptotic stabilization
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: No
URN: urn:nbn:de:bvb:703-epub-3522-6
Date Deposited: 04 Dec 2017 07:23
Last Modified: 18 Mar 2019 10:24
URI: https://epub.uni-bayreuth.de/id/eprint/3522

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