High-order numerical solutions to Bellman's equation of optimal control
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.
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.Collections
Related items
Showing items related by title, author, creator and subject.
-
Vibration Reduction for Flexible Spacecraft Attitude Control Using PWPF Modulator and Smart Structures
Song, Gangbing; Agrawal, Brij N. (1999);This paper presents a new approach to vibration reduction of flexible spacecraft during attitude control by using Pulse Width Pulse Frequency (PWPF) Modulator for thruster firing and smart materials for active vibration ... -
Chris Eagle: Ripples in the Gene Pool - Creating Genetic: Mutations to Survive the Vulnerability Window [video]
Eagle, Chris (2006-10-24);Reverse engineers often like to argue that a prime motivator for their activities is the desire to discover and patch vulnerabilities in closed-source binary software. Given the veritable plethora.. nay, Katrina-like flood ... -
Chris Eagle: Ripples in the Gene Pool - Creating Genetic: Mutations to Survive the Vulerability Window
Eagle, Chris (2006-10-24);Reverse engineers often like to argue that a prime motivator for their activities is the desire to discover and patch vulnerabilities in closed-source binary software. Given the veritable plethora.. nay, Katrina-like flood ...