Forward-Backward Rapidly-Exploring Random Trees for Stochastic Optimal Control
- Resource Type
- Conference
- Authors
- Hawkins, Kelsey P.; Pakniyat, Ali; Theodorou, Evangelos; Tsiotras, Panagiotis
- Source
- 2021 60th IEEE Conference on Decision and Control (CDC) Decision and Control (CDC), 2021 60th IEEE Conference on. :912-917 Dec, 2021
- Subject
- Aerospace
Bioengineering
Communication, Networking and Broadcast Technologies
Components, Circuits, Devices and Systems
Power, Energy and Industry Applications
Robotics and Control Systems
Signal Processing and Analysis
Transportation
Monte Carlo methods
Conferences
Optimal control
Differential equations
Trajectory
Feedback control
Function approximation
- Language
- ISSN
- 2576-2370
We propose a numerical method for the computation of the forward-backward stochastic differential equations (FBSDE) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. By the use of the Girsanov change of probability measures, it is demonstrated how a rapidly-exploring random tree (RRT) can be utilized for the forward integration pass, as long as the controlled drift term is appropriately compensated in the backward integration pass. A numerical approximation of the value function is proposed by solving a series of function approximation problems backwards in time along the edges of the constructed RRT. Moreover, a local entropy-weighted least squares Monte Carlo (LSMC) method is developed to concentrate function approximation accuracy in regions most likely to be visited by optimally controlled trajectories.