M. R. Jovanovic.
Modeling, Analysis, and Control of Spatially Distributed Systems.
PhD thesis,
University of California at Santa Barbara,
2004.
Abstract: |
Spatially distributed dynamical systems arise in a variety of science and engineering problems. These systems are typically described by Partial Integro-Differential Equations (P(I)DEs), or by a finite or infinite number of coupled Ordinary Differential Equations (ODEs). In this dissertation, we model spatially distributed dynamical systems and present new tools for their analysis and design. All theoretical tools that we develop are applicable to classes of systems characterized by their structural properties. We exploit these structural properties and provide non-conservative results. Part I of the dissertation is devoted to the distributed systems theory. We derive an explicit formula for the Hilbert–Schmidt norm of the frequency response operator for a class of P(I)DEs. Our method avoids the need for spatial discretization and provides an exact reduction of an infinite dimensional problem to a problem in which only matrices of finite dimensions are involved. We also develop tools for analysis of stability and input-output system norms of linear P(I)DEs with spatially periodic coefficients. We illustrate how stability properties and input-output norms of spatially invariant systems can be changed when a spatially periodic feedback is introduced. In Part II, we use system theoretic approach to model and analyze the transition and turbulence in plane channel flows. We utilize a componentwise frequency response analysis to reveal distinct resonant mechanisms for subcritical transition. We further illustrate that the spatio-temporal impulse responses of the Linearized Navier-Stokes equations contain many qualitative features of early stages of turbulent spots. Part III considers distributed control of systems on lattices. We utilize backstepping as a tool for distributed control of these systems. We discuss architecture induced by distributed backstepping design and demonstrate that backstepping yields controllers with inherent degree of spatial localization. Also, we revisit several widely cited results in the control of vehicular platoons and show that they are inherently ill-posed. Finally, we remark on phenomenon of peaking in the control of vehicular platoons and demonstrate how to avoid it. |
@PhdThesis{phd-04-mrj,
author = "M.\ R.\ Jovanovi\'c",
title = "Modeling, Analysis, and Control of Spatially Distributed Systems",
school = "University of California at Santa Barbara",
pdf = http://ccec.mee.ucsb.edu/pdf/phd-04-mrj.pdf,
year = 2004,
abstract = {Spatially distributed dynamical systems arise in a variety of science and engineering problems. These systems are typically described by Partial Integro-Differential Equations (P(I)DEs), or by a finite or infinite number of coupled Ordinary Differential Equations (ODEs). In this dissertation, we model spatially distributed dynamical systems and present new tools for their analysis and design. All theoretical tools that we develop are applicable to classes of systems characterized by their structural properties. We exploit these structural properties and provide non-conservative results. Part I of the dissertation is devoted to the distributed systems theory. We derive an explicit formula for the Hilbert–Schmidt norm of the frequency response operator for a class of P(I)DEs. Our method avoids the need for spatial discretization and provides an exact reduction of an infinite dimensional problem to a problem in which only matrices of finite dimensions are involved. We also develop tools for analysis of stability and input-output system norms of linear P(I)DEs with spatially periodic coefficients. We illustrate how stability properties and input-output norms of spatially invariant systems can be changed when a spatially periodic feedback is introduced. In Part II, we use system theoretic approach to model and analyze the transition and turbulence in plane channel flows. We utilize a componentwise frequency response analysis to reveal distinct resonant mechanisms for subcritical transition. We further illustrate that the spatio-temporal impulse responses of the Linearized Navier-Stokes equations contain many qualitative features of early stages of turbulent spots. Part III considers distributed control of systems on lattices. We utilize backstepping as a tool for distributed control of these systems. We discuss architecture induced by distributed backstepping design and demonstrate that backstepping yields controllers with inherent degree of spatial localization. Also, we revisit several widely cited results in the control of vehicular platoons and show that they are inherently ill-posed. Finally, we remark on phenomenon of peaking in the control of vehicular platoons and demonstrate how to avoid it.}
}
R. M. Zurakowski.
Exploiting Immune Response Dynamics in HIV Therapy.
PhD thesis,
University of California at Santa Barbara,
2004.
Abstract: |
The Human Immunodeficiency Virus (HIV) infects cells involved in the regulation of the adaptive immune response. Untreated infection usually leads to severe immunodeficiency and death from opportunistic infections. However, recent experimental work has shown that the natural immune response to HIV can be enhanced through the use of schedules of interrupted therapy. In some cases, this enhancement is sufficient to induce a persistent, drug-free state in which the virus is controlled to low levels and the patient exhibits no progressive deterioration of the immune system. Clinical trials attempting to use interrupted treatment schedules to exploit this phenomenon have had mixed results. Recent modeling work that explains the behavior shows that the immune response to HIV is governed by nonlinear dynamics that are sensitive to small parameter variations. It is unlikely, therefore, that a single schedule of interrupted treatment would yield consistent results across a number of patients. In order to successfully induce immune-mediated control of HIV infection with a greater degree of success, it will likely be necessary to use a method of calculating interruption schedules that will accommodate variations unique to the patient based on measurements made during treatment. We introduce a framework based on nonlinear Model Predictive Control to determine appropriate interruption schedules for exploiting the natural immune response to HIV. This framework incorporates models of the immune response, and uses feedback measurements to provide robustness to the modeling and measurement errors inherent in the application. The method is designed to be implementable in a clinical setting. |
@PhdThesis{phd-04-rmz,
author = "R. M. Zurakowski",
title = "Exploiting Immune Response Dynamics in {HIV} Therapy",
school = "University of California at Santa Barbara",
pdf = http://ccdc.mee.ucsb.edu/pdf/phd-04-rmz.pdf,
year = 2004,
abstract = {The Human Immunodeficiency Virus (HIV) infects cells involved in the regulation of the adaptive immune response. Untreated infection usually leads to severe immunodeficiency and death from opportunistic infections. However, recent experimental work has shown that the natural immune response to HIV can be enhanced through the use of schedules of interrupted therapy. In some cases, this enhancement is sufficient to induce a persistent, drug-free state in which the virus is controlled to low levels and the patient exhibits no progressive deterioration of the immune system. Clinical trials attempting to use interrupted treatment schedules to exploit this phenomenon have had mixed results. Recent modeling work that explains the behavior shows that the immune response to HIV is governed by nonlinear dynamics that are sensitive to small parameter variations. It is unlikely, therefore, that a single schedule of interrupted treatment would yield consistent results across a number of patients. In order to successfully induce immune-mediated control of HIV infection with a greater degree of success, it will likely be necessary to use a method of calculating interruption schedules that will accommodate variations unique to the patient based on measurements made during treatment. We introduce a framework based on nonlinear Model Predictive Control to determine appropriate interruption schedules for exploiting the natural immune response to HIV. This framework incorporates models of the immune response, and uses feedback measurements to provide robustness to the modeling and measurement errors inherent in the application. The method is designed to be implementable in a clinical setting.}
}