Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 18 of 18 for “"singular perturbation theory"”.
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Learning-based Optimal Control of Time-Varying Linear Systems Over Large Time Intervals
… using reinforcement learning. Leveraging singular perturbation theory techniques, we transform the time-varying optimal control problem into two time-invariant subproblems. This allows the utilization of an off-policy iteration method to learn the controller gains. We show that the …
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Theoretical Analysis of Nonlinear Differential Equations
… nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, or lack thereof, of each …
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Analysis and implementation of robust numerical methods to solve mathematical models of HIV and Malaria co-infection
… the dynamics of the model, we use the geometric singular perturbation theory to couple the fast and slow models from the full model. Finally, since the governing models are very complex, they cannot be solved analytically and hence we develop and analyze a special class of numerical methods to …
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A Dynamical Study of the Poisson-Nernst-Planck System for Three Ions
… charge zero. The PNP system can be treated as singularly perturbed system that has two limiting systems: inner and outer systems (termed fast and slow system in geometric singular perturbation theory). A complete set of integrals for the inner system is presented that provides information for …
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A Mathematical Model for the Transition in Firing Patterns Across Puberty of a Gonadotropin-Releasing Hormone Neuron
… the underlying dynamical system. Using geometric singular perturbation theory methods and mathematical software packages I analyze the MMOs arising in the GnRH model. This analysis is presented through a sequence of theorems that comprise the core results of my thesis.</p>
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Two-patch herbivore/vegetation models with density-dependent migration
… changes in the system. We used the geometric singular perturbation theory in order to reduce the dimension of the system. Using the continuation software AUTO we provided bifurcation diagrams for the reduced systems and we also provided some numerical illustrations to show the dynamics of the …
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The control of frequency of a conditional oscillator simultaneously subjected to multiple oscillatory inputs
… are obtained analytically using geometric singular perturbation theory and an analytic approximation of the frequency is obtained. The results are validated through numerical simulations of the model and are shown to extend to a detailed Hodgkin-Huxley type compartmental model of the …
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Rate-induced tipping to metastable Zombie fires
… technique with concepts from geometric singular perturbation theory. This framework allows us to reduce a reversible R-tipping problem due to crossing a quasithreshold to a heteroclinic orbit problem in a singular limit. Thus, we identify generic cases of such R-tipping via: (i) …
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Control and design of flexible-link manipulators
… is based on the concept of integral manifolds in singular perturbation theory, and the second is based on input-output decoupling in nonlinear systems theory. The practical implementation issues for the former require the inconvenient measurement of flexural rates. An observation strategy is …
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The role of short term synamptic plasticity in temporal coding of neuronal networks
… neurons and we use techniques from geometric singular perturbation theory to show that any n-cluster solution must satisfy a set of consistency conditions that can be geometrically derived. The results of both problems are validated using numerical simulations.
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Variable structure and singular perturbation control of elastic dynamical systems
… craft (spacecraft-beam-tip body configuration), singular perturbation technique is used. Based on nonlinear inversion, a control law is derived to decouple the attitude angle and the dominant flexible modes from the remaining elastic modes. The inverse control law decomposes the spacecraft …
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Time-optimal and saturating controls with application to flexible structures
… problem is formulated and solved using singular-perturbation theory. The solution procedures are illustrated with an example solved using the MACSYMA symbolic manipulation language. Regular-perturbation theory is then used to find the open-loop hard-constrained time-optimal control for a …
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Output feedback adaptive control in the presence of unmodeled dynamics
… of all signals is shown utilizing concepts of singular perturbation theory by treating the filter as a fast subsystem and the system dynamics together with weight update law as a slow subsystem. The design procedure is evaluated by augmenting an existing observer based controller with an …
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Analysis and reduction of a modeled bursting neuron
… was analyzed using methods based upon geometric singular perturbation theory. The mathematical mechanism of bursting in the model consisted of two slow variables traversing the state-space across a saddle-node bifurcation that defined an interface between quiescence and periodic spiking of the …
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State space modeling of differential-algebraic systems using singularly perturbed sliding manifolds
… often referred to as descriptor, implicit, or singular systems present a number of difficult problems in simulation and control. One of the key difficulties is that DAEs are not expressed in an explicit state space form required by many simulation and control design methods. This is …
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Composite load modeling for power systems: Model reduction, identification, and application to conservation voltage reduction
… order reduction technique is developed based on singular perturbation theory for the WECC CMLD. Specially, a solid accuracy assessment criterion is proposed and strictly proved. By embedding the criterion into the order reduction process as a correction procedure, the accuracy of the obtained …
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Dynamically orthogonal field equations for stochastic fluid flows and particle dynamics
… an increasing number of problems in continuum theory have been treated using stochastic dynamical theories. This is because dynamical systems governing real processes always contain some elements characterized by uncertainty or stochasticity. Uncertainties may arise in the system parameters, …