Accession Number:

ADA619703

Title:

Galerkin Optimal Control

Descriptive Note:

Master's thesis

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CA

Personal Author(s):

Report Date:

2014-12-01

Pagination or Media Count:

217.0

Abstract:

A Galerkin-based family of numerical formulations is presented for solving nonlinear optimal control problems. This dissertation introduces a family of direct methods that calculate optimal trajectories by discretizing the system dynamics using Galerkin numerical techniques and approximate the cost function with Gaussian quadrature. In this numerical approach, the analysis is based on L2-norms. An important result in the theoretical foundation is that the feasibility and consistency theorems are proved for problems with continuous andor piecewise continuous controls. Galerkin methods may be formulated in a number of ways that allow for efficiency andor improved accuracy while solving a wide range of optimal control problems with a variety of state and control constraints. Numerical formulations using Lagrangian and Legendre test functions are derived. One formulation allows for a weak enforcement of boundary conditions, which imposes end conditions only up to the accuracy of the numerical approximation itself. Additionally, the multi-scale formulation can reduce the dimension of multi-scale optimal control problems, those in which the states and controls evolve on different timescales. Finally, numerical examples are shown to demonstrate the versatile nature of Galerkin optimal control.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE