A class of nonlinear, stochastic staticization control problems (including minimization problems with smooth, convex, coercive payoffs) driven by diffusion dynamics with constant diffusion coefficient is considered. A fundamental solution form is obtained where the same solution can be used for a limited variety of terminal costs without re-solution of the problem. One may convert this fundamental solution form from a stochastic control problem form to a deterministic control problem form. This yields an equivalence between certain second-order (in space) Hamilton-Jacobi partial differential equations (HJ PDEs) and associated first-order HJ PDEs. This reformulation has substantial numerical implications.
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Conversion of a Class of Stochastic Control Problems to Fundamental-Solution Deterministic Control Problems
A class of nonlinear, stochastic staticization control
problems (including minimization problems with smooth, convex,
coercive payoffs) driven by diffusion dynamics and constant
diffusion coefficient is considered. Using dynamic programming
and tools from static duality, a fundamental solution form is
obtained where the same solution can be used for a variety of
terminal costs without re-solution of the problem. Further, this
fundamental solution takes the form of a deterministic control
problem rather than a stochastic control problem.
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« less
- Award ID(s):
- 1908918
- NSF-PAR ID:
- 10171194
- Date Published:
- Journal Name:
- Proceedings of the American Control Conference
- ISSN:
- 0743-1619
- Page Range / eLocation ID:
- 2814-2819
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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