Lyapunov Stabilizability of Controlled Diffusions via a Superoptimality Principle for Viscosity Solutions
Journal Article
·
· Applied Mathematics and Optimization
- Dipartimento di Matematica P. e A., Universita di Padova, via Belzoni 7, 35131 Padova (Italy)
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 the Lyapunov function to study stochastic open loop stabilizability in probability and local and global asymptotic stabilizability (or asymptotic controllability). Finally, we illustrate the theory with some examples.
- OSTI ID:
- 21064215
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 53; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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