Applications of Second-Order Necessary and Sufficient Conditions to Optimal Trajectories

"A recent advance in sufficient conditions for a weak local minimum in optimal control problems is used to develop a procedure for applying second-order necessary and sufficient conditions for a minimum of a cost functional. For a system with n state variables, an improved Riccati equation solution method is used to transform a test for the unboundedness of a n x n matrix into a test for a scalar being zero. Application to one important second-order necessary and sufficient condition, the Jacobi no-conjugate-point condition, is introduced using the ""Shortest path between two points on a sphere"" problem. Second-order necessary and sufficient conditions are applied to various optimal control problems, including spacecraft trajectory problems with constant thrust acceleration and with time-varying low thrust acceleration for a power-limited rocket engine. A solution that simultaneously maximizes final orbit energy and minimizes propellant consumption is found that satisfies the usual first-order necessary conditions, but is non-optimal. Other example variational problems are investigated: Hamilton's Principle for several dynamic systems, including a circular orbit in an inverse-square gravitational field and projectile motion in a uniform field, as well as a simple example of Zermelo's problem. For those solutions that satisfy first-order necessary conditions but are non-optimal, a Genetic Algorithm is successfully used to find a global near-optimal solution of lower cost."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Aerospace Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Jo, Jang-Won

Contributors dc:contributor

• Prussing, John E.

• Operations Research

Language dc:language

eng

Identifier

(MiAaPQ)AAI9737146

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/85124