Generalized Solutions in Optimal Stochastic Control,
Abstract
Generalized solutions in calculus of variations were introduced many years ago by L. C. Young. By doing so, he obtained solutions in some wider sense to problems which have no ordinary solution. Similar ideas reappeared in optimal control theory under such names as relaxed controls, chattering controls, or sliding regimes. Under appropriate assumptions a relaxed optimal control was shown to exist. If, in addition, a Filippov-type convexity condition holds, the methods show that there is an optimal control in the ordinary sense. The author makes straightforward adaptation of the idea of relaxed control, to a class of problems which are stochastic perturbations of the standard Pontryagin control problem. He proves the existence of a relaxed optimal control. That result applies if the controller has complete information at each time t, and also if the control is open loop.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1976
- Accession Number
- ADA033090
Entities
People
- Wendell Fleming
Organizations
- Brown University