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- Adaptive Control (1)
- Backstepping (1)
- Control systems (1)
- Curve Tracking (1)
- Dynamical systems (1)
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- Fracture (1)
- General Black-Sholes model (1)
- Itô's formula (1)
- Low-frequency (1)
- Minimum action method (1)
- Near-martingale (1)
- Non-local Methods (1)
- Orthogonal polynomials (1)
- Parameter Identification (1)
- Peridynamics (1)
- Quantum trees (1)
- Robin spectrum (1)
- Sampling (1)
- Sequential predictors (1)
- Stochastic differential equation (1)
- Stochastic integral (1)
- Time-varying systems (1)
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Curve Tracking Control Under State Constraints And Uncertainties, Robert Kelly Sizemore
Curve Tracking Control Under State Constraints And Uncertainties, Robert Kelly Sizemore
LSU Doctoral Dissertations
We study a class of steering control problems for free-moving particles tracking a curve in the plane and also in a three-dimensional environment, which are central problems in robotics. In the two-dimensional case, we provide adaptive controllers for curve tracking under unknown curvatures and control uncertainty. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature to form the augmented error dynamics. This nonlinear dependence puts our curvature identification objective outside the scope of existing adaptive tracking and parameter identification results that were limited to cases where the unknown parameters …
Non-Local Methods In Fracture Dynamics, Eyad Said
Non-Local Methods In Fracture Dynamics, Eyad Said
LSU Doctoral Dissertations
We first introduce a regularized model for free fracture propagation based on non-local potentials. We work within the small deformation setting and the model is developed within a state based peridynamic formulation. At each instant of the evolution we identify the softening zone where strains lie above the strength of the material. We show that deformation discontinuities associated with flaws larger than the length scale of non-locality $\delta$ can become unstable and grow. An explicit inequality is found that shows that the volume of the softening zone goes to zero linearly with the length scale of non-local interaction. This scaling …
Backstepping And Sequential Predictors For Control Systems, Jerome Avery Weston
Backstepping And Sequential Predictors For Control Systems, Jerome Avery Weston
LSU Doctoral Dissertations
We provide new methods in mathematical control theory for two significant classes of control systems with time delays, based on backstepping and sequential prediction. Our bounded backstepping results ensure global asymptotic stability for partially linear systems with an arbitrarily large number of integrators. We also build sequential predictors for time-varying linear systems with time-varying delays in the control, sampling in the control, and time-varying measurement delays. Our bounded backstepping results are novel because of their use of converging-input-converging-state conditions, which make it possible to solve feedback stabilization problems under input delays and under boundedness conditions on the feedback control. Our …
Spectra Of Quantum Trees And Orthogonal Polynomials, Zhaoxia Wang
Spectra Of Quantum Trees And Orthogonal Polynomials, Zhaoxia Wang
LSU Doctoral Dissertations
We investigate the spectrum of regular quantum-graph trees, where the edges are endowed with a Schr\"odinger operator with self-adjoint Robin vertex conditions. It is known that, for large eigenvalues, the Robin spectrum approaches the Neumann spectrum. In this research, we compute the lower Robin spectrum. The spectrum can be obtained from the roots of a sequence of orthogonal polynomials involving two variables. As the length of the quantum tree increases, the spectrum approaches a band-gap structure. We find that the lowest band tends to minus infinity as the Robin parameter increases, whereas the rest of the bands remain positive. Unexpectedly, …
General Stochastic Integral And Itô Formula With Application To Stochastic Differential Equations And Mathematical Finance, Jiayu Zhai
LSU Doctoral Dissertations
A general stochastic integration theory for adapted and instantly independent stochastic processes arises when we consider anticipative stochastic differential equations. In Part I of this thesis, we conduct a deeper research on the general stochastic integral introduced by W. Ayed and H.-H. Kuo in 2008. We provide a rigorous mathematical framework for the integral in Chapter 2, and prove that the integral is well-defined. Then a general Itô formula is given. In Chapter 3, we present an intrinsic property, near-martingale property, of the general stochastic integral, and Doob-Meyer's decomposition for near-submartigales. We apply the new stochastic integration theory to several …