Title data
Yegorov, Ivan ; Dower, Peter ; Grüne, Lars:
A characteristics based curseofdimensionalityfree approach for approximating control Lyapunov functions and feedback stabilization.
Bayreuth ; Melbourne
,
2018
.  8 S.


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Project information
Project title: 
Project's official title Project's id Activating LyapunovBased Feedback  Nonsmooth Control Lyapunov Functions DP160102138 No information FA23861614066 

Project financing: 
ARC (Australian Research Council) AFOSR/AOARD 
Abstract
This paper develops a curseofdimensionalityfree numerical approach to construct control Lyapunov functions (CLFs) and stabilizing feedback strategies for deterministic con trol systems described by systems of ODEs. An extension of the Zubov method is used to represent a CLF as the value function for an appropriate infinitehorizon optimal control problem. The infinitehorizon stabilization problem is approximated by an exit time problem, with target set given by a sufficiently small closed neighborhood of the origin in the state space. In order to compute the related value function and optimal feedback control law separately at different initial states and thereby to attenuate the curse of dimensionality, an extension of a recently developed characteristics based framework is proposed. Theoretical foundations of the developed approach are given together with practical discussions regarding its implementation, and numerical examples are also provided. In particular, it is pointed out that the curse of complexity may remain a significant issue even if the curse of dimensionality is avoided.