Lagrangian Manifolds, Viscosity Solutions and Maslov Index
McCaffrey, D. and Banks, S.P.
(1999)
Lagrangian Manifolds, Viscosity Solutions and Maslov Index.
Research Report.
ACSE Research Report 749
.
Department of Automatic Control and Systems Engineering
Abstract
This paper considers a geometrical construction for stationary viscosity solutions based on Lagrangian manifolds. This has been proposed recently in the literature by M.V. Day. The construction involves a key assumption of Lipschitz continuity. We discuss in this paper how this assumption follows from the vanishing of the Maslov index on closed curves on the manifold, at least foe low dimensional manifolds. This is naturally satisfied for large portions of stable and unstable manifolds corresponding to hyperbolic equilibrium points. We discuss examples where this situation arises including infinite time control and nonlinear filtering. We also give an introduction to the Maslov index and outline the connections with canonical tunnelling operators and idempotent analysis approaches to deriving stationary solutions to Hamilton-Jacobi-Bellman equations.
Metadata
Item Type:
Monograph
Authors/Creators:
McCaffrey, D.
Banks, S.P.
Copyright, Publisher and Additional Information:
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