Approximate nonlinear optimal control methodologies
File(s)
Author(s)
Jones, Adam
Type
Thesis
Abstract
This research has focused on finding extensions to methodologies for application in finding approximate solutions to nonlinear optimal control problems, with particular focus on the Nonlinear Quadratic Regulator (NLQR) problem. This has involved introducing the main results in the field of optimal control, and a brief literature review of the available methods and their limitations when applied to nonlinear problems. The first core idea of this thesis is in the development of an algorithm which adds optimal control theoretical developments to the State-Dependent Riccati Equation (SDRE) method through a constrained optimisation step. Secondly, the Albrecht method for solving the Hamilton Jacobi Bellman (HHB) equation via a series expansion method is extended to address its limitations in applications to problems which start suitably far away from the origin. The s0-called series extension can make use of numerical or algebraic polynomial system solvers and its applicability is discussed and exemplified through application to some chosen multivariable nonlinear problems. A discussion is made of the merits and disadvantages of the different approximate optimal control methodologies in order to summarise the work undertaken.
Version
Open Access
Date Issued
2025-04-25
Date Awarded
2026-03-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Astolfi, Alessandro
Sponsor
Defence Science and Technology Laboratory (Great Britain)
Publisher Department
Department of Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)