2012/07/17 by Thomas L. Hunt, Hunt, Thomas, Arthur J. Krener +1
Computer Science · Engineering · Physics and Astronomy · #49-04 #49J15 #49J20 #49L99 #49M37 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gaussian Processes and Bayesian Inference #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1207.4232
openalex publication_date 2012/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a modification to the patchy method of Navasca and Krener for solving the stationary Hamilton Jacobi Bellman equation. The numerical solution that we generate is a set of polynomials that approximate the optimal cost and optimal control on a partition of the state space. We derive an error bound for our numerical method under the assumption that the optimal cost is a smooth strict Lyupanov function. The error bound is valid when the number of subsets in the partition is not too large.