Lyapunov stabilizability of controlled diffusions via a superoptimality principle for viscosity solutions

Details Lyapunov stabilizability of controlled diffusions via a superoptimality principle for viscosity solutions Lyapunov stabilizability of controlled diffusions via a superoptimality principle for viscosity solutions

2004-05-10

arxiv.org/abs/math/0405169v2

Mathematics

Optimization and Control

22 pages

Scientific paper

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.

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