Upper and lower bounds for singularly perturbed linear quadratic optimal control problems
File(s)
Author(s)
Howe, Sei
Type
Thesis
Abstract
The question of how to optimally control a large scale system is widely considered to be difficult to solve due to the size of the problem. This difficulty is further compounded when a system exhibits a two time-scale structure where some components evolve slowly and others evolve quickly. When this occurs, the optimal control problem is regarded as singularly perturbed with a perturbation parameter epsilon representing the ratio of the slow time-scale to the fast time-scale. As epsilon goes to zero, the system becomes stiff resulting in a computationally intractable problem. In this thesis, we propose an analytic method for constructing bounds on the minimum cost of a singularly perturbed, linear-quadratic optimal control problem that hold for any arbitrary value of epsilon.
Version
Open Access
Date Issued
2017-07
Date Awarded
2017-11
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Parpas, Panos
Rustem, Berc
Publisher Department
Computing
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)