Discrete Mechanics and Optimal Control

Authors:	Junge Oliver, University of Paderborn, Germany Marsden Jerrold E., California Institute of Technology, Pasadena, United States Ober-Bloebaum Sina, University of Paderborn, Germany
Topic:	2.3 Non-Linear Control Systems
Session:	Optimal Control in Nonlinear Systems I
Keywords:	discrete mechanics, variational analysis, optimal control

Abstract

A new approach to the solution of optimal control problems for mechanical systems is proposed. It is based on a direct discretization of the Lagrange-d'Alembert principle for the system (as opposed to using, for example, collocation or multiple shooting to enforce the equations of motion as constraints). The resulting forced discrete Euler-Lagrange equations then serve as constraints for the optimization of a given cost functional. We numerically illustrate the method by optimizing a low thrust satellite orbit transfer as well as the reconfiguration of a group of hovercraft in the plane.