High-order numerical solutions to Bellman's equation of optimal control
Loading...
Authors
Aguilar, Cesar O.
Krener, Arthur J.
Subjects
Advisors
Date of Issue
2012
Date
Publisher
Language
Abstract
In this paper we develop a numerical method to compute high-order approximate solutions to Bellman's dynamic programming equation that arises in the optimal regulation of discrete-time nonlinear control systems. The method uses a patchy technique to build Taylor polynomial approximations defined on small domains which are then patched together to create a piecewise-smooth approximation. Using the values of the computed cost function as the step-size, levels of patches are constructed such that their radial boundaries are level sets of the computed cost functions and their lateral boundaries are invariants sets of the closed loop dynamics. To minimize the computational effort, an adaptive scheme is used to determine the number of patches on each level depending on the relative error of the computed solutions.
Type
Article
Description
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funding
Format
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.