Quadratic integral penalty methods for numerical trajectory optimization
File(s)
Author(s)
Neuenhofen, Martin Peter
Type
Thesis
Abstract
This thesis presents new mathematical algorithms for the numerical solution of a mathematical
problem class called dynamic optimization problems . These are mathematical optimization
problems, i.e., problems in which numbers are sought that minimize an expression subject to
obeying equality and inequality constraints. Dynamic optimization problems are distinct from
non-dynamic problems in that the sought numbers may vary over one independent variable.
This independent variable can be thought of as, e.g., time.
This thesis presents three methods, with emphasis on algorithms, convergence analysis, and
computational demonstrations. The fi rst method is a direct transcription method that is based
on an integral quadratic penalty term. The purpose of this method is to avoid numerical
artifacts such as ringing or erroneous/spurious solutions that may arise in direct collocation
methods. The second method is a modifi ed augmented Lagrangian method that leverages
ideas from augmented Lagrangian methods for the solution of optimization problems with
large quadratic penalty terms, such as they arise from the prior direct transcription method.
Lastly, we present a direct transcription method with integral quadratic penalties and integral
logarithmic barriers. All methods are motivated with applications and examples, analyzed with
complete proofs for their convergence, and practically verifi ed with numerical experiments.
problem class called dynamic optimization problems . These are mathematical optimization
problems, i.e., problems in which numbers are sought that minimize an expression subject to
obeying equality and inequality constraints. Dynamic optimization problems are distinct from
non-dynamic problems in that the sought numbers may vary over one independent variable.
This independent variable can be thought of as, e.g., time.
This thesis presents three methods, with emphasis on algorithms, convergence analysis, and
computational demonstrations. The fi rst method is a direct transcription method that is based
on an integral quadratic penalty term. The purpose of this method is to avoid numerical
artifacts such as ringing or erroneous/spurious solutions that may arise in direct collocation
methods. The second method is a modifi ed augmented Lagrangian method that leverages
ideas from augmented Lagrangian methods for the solution of optimization problems with
large quadratic penalty terms, such as they arise from the prior direct transcription method.
Lastly, we present a direct transcription method with integral quadratic penalties and integral
logarithmic barriers. All methods are motivated with applications and examples, analyzed with
complete proofs for their convergence, and practically verifi ed with numerical experiments.
Version
Open Access
Date Issued
2022-03
Date Awarded
2022-08
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Kerrigan, Eric
Publisher Department
Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)