Lyapunov stabilizability of controlled diffusions via a superoptimality principle for viscosity solutions
Optimization and Control
2007-05-23 v2 Analysis of PDEs
Abstract
We prove optimality principles for semicontinuous bounded viscosity solutions of Hamilton-Jacobi-Bellman equations. In particular we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle control problems. This result is applied to extend the Lyapunov direct method for stability to controlled Ito stochastic differential equations. We define the appropriate concept of Lyapunov function to study the stochastic open loop stabilizability in probability and the local and global asymptotic stabilizability (or asymptotic controllability). Finally we illustrate the theory with some examples.
Cite
@article{arxiv.math/0405169,
title = {Lyapunov stabilizability of controlled diffusions via a superoptimality principle for viscosity solutions},
author = {Annalisa Cesaroni},
journal= {arXiv preprint arXiv:math/0405169},
year = {2007}
}
Comments
22 pages