Structural Completeness of a Multi-channel Linear System with Dependent Parameters

It is well known that the "fixed spectrum" {i.e., the set of fixed modes} of a multi-channel linear system plays a central role in the stabilization of such a system with decentralized control. A parameterized multi-channel linear system is said to be "structurally complete" if it has no fixed spectrum for almost all parameter values. Necessary and sufficient algebraic conditions are presented for a multi-channel linear system with dependent parameters to be structurally complete. An equivalent graphical condition is also given for a certain type of parameterization

Elucidating fundamental mechanisms in energy generation and energy storage materials - A Raman spectroscopic study

Fundamental mechanisms that enhance the performance of thermoelectric (TE) materials, for example, charged grain boundaries in nano-structured n-type Bi2Te2:7Se0:3 and strong anharmonic phonon scattering effects in single crystalline SnSe, were investigated via micro-Raman spectroscopy. In n-type Bi2Te2:7Se0:3, I observed the presence of a forbidden IR-active mode in the Raman spectra of chemically and mechanically exfoliated (C/ME) n-type Bi2Te2:7Se0:3 flakes, due to the creation of sub-quintuples and consequent lowering of crystal symmetry. Furthermore, a previous study hypothesized that charged grain boundaries are formed upon restacking and densifying the C/ME processed flakes via spark-plasma-sintering, and I directly observed this by Kelvin Probe Force Microscopy as discussed in chapter 4. A record high TE performance was reported in single crystalline SnSe which is primarily attributed to its low thermal conductivity, originating from strong anharmonicity. I undertook a temperature dependent Raman study of fully dense SnSe, which revealed a relatively higher softening of the phonon modes in the b-c plane (by a factor of six) compared to the phonon mode softening along the a axis, as well as ultrashort phonon lifetimes (~0.1 ps). Analysis of the Raman peak frequencies and linewidths showed phonon decay to be dominated by a three-phonon scattering process. The anharmonic coeffcients αR and αC calculated from the Raman and heat capacity measurements, respectively, are in excellent agreement with each other as discussed in chapter 5. This study provides a deeper understanding of phonon-phonon interaction and anharmonicity in SnSe leading to outstanding thermal transport properties. In addition to using Raman spectroscopy to study thermoelectric materials, I also used in situ micro-Raman spectroscopy to elucidate the charge/discharge mechanism in sulfurized polyacrylonitrile (SPAN) based cathodes for lithium sulfur batteries (LSBs). From the irreversible Raman intensity of the 475 cm – 1 peak which I observed during the first discharge cycle, it can be inferred that the S-S bond linkages cleaved, resulting in the formation of radicals in SPAN with negative S sites. The reversible Raman peak intensities of the electrolyte in LSBs allowed me to monitor Li+ ion concentration and diffusion in the diffusion layer near the surface of SPAN-graphene foam (GF) cathode. Unlike cathodes containing elemental sulfur, the radicals in SPAN react reversibly with Li+ ions instead of forming polysulfide intermediates and Li2S/Li2S2 discharge products. Owing to the lightweight and porous structure of 3-dimensional GF, the LSBs with SPAN-GF cathodes exhibited a rate capacity of 900-1000 mAh/g at 0.1C over a large range of sulfur loadings (1.1-10.6 mg cm – 2). An areal capacity of 17.1 mAh cm – 2 was achieved with a sulfur loading of 19.7 mg cm – 2 The LSBs prepared in this study delivered simultaneously a gravimetric energy density of ~366 Wh Kg – 1 and a power density of ~580 W Kg – 1 at the electrode level as discussed in chapter 6

Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Additive Noise

In this paper, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state covariance with minimal control energy. The additive noise may include a combination of white Gaussian noise and abrupt "jump noise" that is discontinuous in time. We first establish the controllability of the state covariance for linear time-varying stochastic systems. We then turn to the derivation of the optimal control, which entails solving two dynamically coupled matrix ordinary differential equations (ODEs) with split boundary conditions. We show the existence and uniqueness of the solution to these coupled matrix ODEs, and thus those of the optimal control.Comment: 8 pages, 2 figure

Optimal Covariance Steering for Discrete-Time Linear Stochastic Systems

In this paper we study the optimal control for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a quadratic cost function. Then, we develop efficient computational methods for solving for the optimal control law, which is identified as the solution to a semi-definite program. During the analysis, we also obtain some useful results on a matrix Riccati difference equation, which may be of independent interest

Determination of Non-Darcy Porous Flow Boundary Value in Formation Type III

With the oil industrialization area increasing and the fine Petrophysics block decreasing, the oil field is faced with the situation that isn’t enough potential, thus it’s necessary to begin effective developing in formation type III, which has high potential, strong heterogeneity and low permeability. It’s important for reservoir development to understand porous flow law in formation type III. There is a large reserve in formation type III of X block in Daqing Oil Field, whose main formation type is thin and poor formation with thin thickness and poor Petrophysics. To find the boundary value for Non-Darcy porous flow in formation type III, we study the pressure number to recognize Non-Darcy porous flow and Non-Darcy porous flow index in characteristic curve for porous flow. We also study the Non-Darcy porous flow boundary value with two methods, pressure number method whose result is 107 mD, Non-Darcy porous flow index method whose result is 120 mD. The two values are similar, thus the Non-Darcy porous flow degree increases sharply when permeability is less than 10 mD. The study provides theory guide for improving residual oil potential and enhancing development effect in formation type III.Key Words: Thin and poor formation; Non-Darcy porous flow boundary value; Pressure number; Non-Darcy porous flow index