Year: 2020
Type: preprint
Abstract: A warm start method is developed for efficiently solving complex chance constrained optimal control problems. The warm start method addresses the computational challenges of solving chance constrained optimal control problems using biased kernel density estimators and Legendre-Gauss-Radau collocation with an $hp$ adaptive mesh refinement method. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished by tuning a parameter of the kernel density estimator, as well as implementing a kernel switch as part of the solution process. Additionally, the number of samples for the biased kernel density estimator is set to incrementally increase through a series of mesh refinement iterations. Thus, the warm start method is a combination of tuning a parameter, a kernel switch, and an incremental increase in sample size. This warm start method is successfully applied to solve two challenging chance constrained optimal control problems in a computationally efficient manner using biased kernel density estimators and Legendre-Gauss-Radau collocation.
Source: arXiv (Cornell University)
Authors: Kiel, Rachel E., Kumar, Mrinal, Rao, Anil V.
Institutions: University of Florida, The Ohio State University
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Awards: Fast Sparse Nonlinear Optimization and Its Application to Optimal Control, Polyhedral Techniques for Fast Sparse Nonlinear Optimization and their Application to Nonsmooth Optimal Control, G770836262, A Novel Framework for the Efficient and Accurate Solutions of Complex Chance-Constrained Optimal Control Problems
OpenAlex ID: W3045332205