Lyapunov Stabilizability of Controlled Diffusions via a Superoptimality Principle for Viscosity Solutions

Journal Article · Sun Jan 15 00:00:00 EST 2006 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-005-0834-1· OSTI ID:21064215

Cesaroni, Annalisa ^[1]

---

1. 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, Vol. 53, Issue 1; Other Information: DOI: 10.1007/s00245-005-0834-1; Copyright (c) 2006 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
CONTROL THEORY
DIFFUSION
FUNCTIONS
HAMILTON-JACOBI EQUATIONS
LYAPUNOV METHOD
PROBABILITY
STABILITY
STOCHASTIC PROCESSES
VISCOSITY