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On (the existence of) Control Lyapunov Barrier Functions

Title data

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

Official URL: Volltext

Project information

Project title:
Project's official title
Project's id
Activating Lyapunov-Based Feedback - Nonsmooth Control Lyapunov Functions
G1500106

Project financing: ARC (Australian Research Council)

Abstract in another language

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
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
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 09 Dec 2017 22:00
Last Modified: 23 Mar 2021 09:12
URI: https://eref.uni-bayreuth.de/id/eprint/40899