Deterministic Methods in Stochastic Optimal Control.
Abstract
In this paper a new approach to the control of systems represented by stochastic differential equations (SDEs) is developed in which stochastic control is viewed as deterministic control with a particular form of constraint structure. Specifically, the characteristic non-anticipativity property of the control processes is formulated as an equality constraint on the set of possibly anticipative processes. The optimal non-anticipative control is then recovered by minimizing, over the class of possibly anticipating processes, a cost function modified by the inclusion of a Lagrange multiplier term to enforce the nonanticipativity constraint. This unconstrained minimization is carried out pathwise-i.e., separately for each value of a certain random parameter and hence reduces to a parameterized family of deterministic optimal control problems. Solution of the controlled SDEs with anticipative controls are defined by a decomposition method. It is shown that the value function of the control problem is the unique global solution of a robust equation (random partial differential equation) associated to a linear backward Hamilton-Jacobi-Bellman stochastic partial differential equation (HJB SPDE).
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1992
- Accession Number
- ADA260478
Entities
People
- Gabriel Burstein
- Mark H. Davis
Organizations
- Imperial College London