Title data
Yegorov, Ivan ; Dower, Peter ; Grüne, Lars:
A characteristics based curseofdimensionalityfree approach for approximating control Lyapunov functions and feedback stabilization.
In:
Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems. 
Hong Kong
,
2018
.  pp. 342349
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Project financing: 
ARC (Australian Research Council) AFOSR/AOARD 
Abstract in another language
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.
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A characteristics based curseofdimensionalityfree approach for approximating control Lyapunov functions and feedback stabilization. (deposited 17 Feb 2018 22:00)
 A characteristics based curseofdimensionalityfree approach for approximating control Lyapunov functions and feedback stabilization. (deposited 15 Aug 2018 06:34) [Currently Displayed]