Robust forward invariant sets for nonlinear systems

Mukhopadhyay, Shayok

Title:

Robust forward invariant sets for nonlinear systems

dc.contributor.advisor	Zhang, Fumin
dc.contributor.author	Mukhopadhyay, Shayok
dc.contributor.committeeMember	Taylor, David
dc.contributor.committeeMember	Vela, Patricio
dc.contributor.committeeMember	Wardi, Yorai
dc.contributor.committeeMember	Malisoff, Michael
dc.contributor.department	Electrical and Computer Engineering
dc.date.accessioned	2014-08-27T13:41:23Z
dc.date.available	2014-08-27T13:41:23Z
dc.date.created	2014-08
dc.date.issued	2014-07-01
dc.date.submitted	August 2014
dc.date.updated	2014-08-27T13:41:23Z
dc.description.abstract	The process of quantifying the robustness of a given nonlinear system is not necessarily trivial. If the dynamics of the system in question are not sufficiently involved, then a tight estimate of a bound on system performance may be obtained. As the dynamics of the system concerned become more and more involved, it is often found that using the results existing in the literature provides a very conservative bound on system performance. Therefore, the motivation for this work is to develop a general method to obtain a less conservative estimate of a bound on system performance, compared to the results already available in literature. The scope of this work is limited to two dimensions at present. Note that working in a two dimensional space does not necessarily make the objective easily achievable. This is because quantifying the robustness of a general nonlinear system perturbed by disturbances can very easily become intractable, even on a space with dimension as low as two. The primary contribution of this work is a computational algorithm, the points generated by which are conjectured to lie on the boundary of the smallest robust forward invariant set for a given nonlinear system. A well known path-planning algorithm, available in existing literature, is leveraged to make the algorithm developed computationally efficient. If the system dynamics are not accurately known, then the above computed approximation of an invariant set may cease to be invariant over the given finite time interval for which the computed set is expected to be invariant. Therefore, the secondary contribution of this work is an algorithm monitoring a computed approximation of an invariant set. It is shown that for a certain type of systems, this secondary monitoring algorithm can be used to detect that a computed approximation of an invariant set is about to cease to be invariant, even if the primary algorithm computed the set based on an unsophisticated dynamical model of a system under consideration. The work related to computing approximations of invariant sets is tested mainly with the curve tracking problem in two dimensions. The algorithm monitoring whether a computed approximation of an invariant set is about to cease to be invariant is inspired by work related to detecting Lithium-ion (Li-ion) battery terminal voltage collapse detection.
dc.description.degree	Ph.D.
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/1853/52311
dc.language.iso	en_US
dc.publisher	Georgia Institute of Technology
dc.subject	Nonlinear systems
dc.subject	Robust forward invariant sets
dc.subject	Path planning based computation of invariant sets
dc.subject	Computational algorithms
dc.subject	Instability detection
dc.subject	Battery terminal voltage collapse detection
dc.title	Robust forward invariant sets for nonlinear systems
dc.type	Text
dc.type.genre	Dissertation
dspace.entity.type	Publication
local.contributor.advisor	Zhang, Fumin
local.contributor.corporatename	School of Electrical and Computer Engineering
local.contributor.corporatename	College of Engineering
relation.isAdvisorOfPublication	65d2541f-4ce1-40d0-923b-09e66eb45b33
relation.isOrgUnitOfPublication	5b7adef2-447c-4270-b9fc-846bd76f80f2
relation.isOrgUnitOfPublication	7c022d60-21d5-497c-b552-95e489a06569
thesis.degree.level	Doctoral