Infinite dimensional nonlinear systems with state-dependent delays and state suprema: Analysis, observer design and applications

Ahmed, Aftab

Title:

Infinite dimensional nonlinear systems with state-dependent delays and state suprema: Analysis, observer design and applications

dc.contributor.advisor	Verriest, Erik I.
dc.contributor.author	Ahmed, Aftab
dc.contributor.committeeMember	Feron, Eric M.
dc.contributor.committeeMember	Zhang, Fumin
dc.contributor.committeeMember	Egerstedt, Magnus
dc.contributor.committeeMember	De La Llave, Rafael
dc.contributor.committeeMember	Gaylord, Thomas K.
dc.contributor.department	Electrical and Computer Engineering
dc.date.accessioned	2017-06-07T17:47:37Z
dc.date.available	2017-06-07T17:47:37Z
dc.date.created	2017-05
dc.date.issued	2017-04-10
dc.date.submitted	May 2017
dc.date.updated	2017-06-07T17:47:37Z
dc.description.abstract	The prime objective of this research is to investigate systems with state-dependent delays in a unified, well rounded, global and coherent framework from first principles. Such systems are inherently nonlinear and infinite dimensional in nature. The delay may either depend explicitly or implicitly on the state of the system. Our goal and contribution is four-fold. Firstly, to give an information structure i.e., to define the Cauchy problem and characterize the state space for such systems. We use the framework of Banach function spaces with the topology of uniform convergence. In systems with time-varying and/or state-dependent delays, causality plays a crucial role. Throughout the analysis and synthesis problems in this research, causality of the system is ensured. Secondly, we perform the inversion of the state-dependent delay i.e., we use the information on the delay and retrieve the state vector of the system. We use our newly established technique of Delay Injection to recover the state of the system and solve the observer design problem. Thirdly, we analyze and design controllers and observers for a special class of systems with state-dependent delays namely systems evolving with state suprema. We nail down the rich structure possessed by these systems and show that the discrete counterpart of these systems can be expressed as Multi-Mode Multi-Dimensional (M3D) systems. Fourthly, we investigate the spectrum of higher order linear time delay systems in the framework of matrix Lambert W functions and give some counter examples to show that the already existing well established literature suffers from some serious limitations. We support our theory with practical applications including estimator design for a subsonic rocket car for soft landing, nonlinear observer design for a turning process for high precision machining and temperature control of a tank with state-dependent delay; and analysis of gene expression.
dc.description.degree	Ph.D.
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/1853/58302
dc.language.iso	en_US
dc.publisher	Georgia Institute of Technology
dc.subject	Time delay systems
dc.subject	State-dependent delays
dc.subject	Stability
dc.subject	Observer design
dc.subject	Controller synthesis
dc.subject	State suprema
dc.subject	Nonlinear systems
dc.subject	Infinite dimensional
dc.subject	Functional differential equations
dc.subject	Spectrum
dc.title	Infinite dimensional nonlinear systems with state-dependent delays and state suprema: Analysis, observer design and applications
dc.type	Text
dc.type.genre	Dissertation
dspace.entity.type	Publication
local.contributor.advisor	Verriest, Erik I.
local.contributor.corporatename	School of Electrical and Computer Engineering
local.contributor.corporatename	College of Engineering
relation.isAdvisorOfPublication	5ae2e093-5b84-4da1-a625-f513a542173f
relation.isOrgUnitOfPublication	5b7adef2-447c-4270-b9fc-846bd76f80f2
relation.isOrgUnitOfPublication	7c022d60-21d5-497c-b552-95e489a06569
thesis.degree.level	Doctoral