In this study, the entrainment of brain dynamics in epilepsy was investigated in a thorough, systematic way. In the first part of the study, diagnosis of epilepsy, elements from the theory of chaos were used to measure the brain dynamics over time from EEGs (electroencephalograms) recorded in humans with either epileptic or non-epileptic seizures. In the second part of the study, treatment of epilepsy, data from rats undergoing VNS (vagus nerve stimulation) treatment were analyzed in the same way. The results suggest that a) the differential diagnosis in humans with epileptic and non-epileptic seizures can be significantly improved by analysis of brain dynamics, and b) the Vagus Nerve Stimulation may be working by controlling the entrainment level of brain dynamics.

Distributed wireless sensor networks (WSNs) have attracted researchers recently due to their advantages such as low power consumption, scalability and robustness to link failures. In sensor networks with no fusion center, consensus is a process where

all the sensors in the network achieve global agreement using only local transmissions. In this dissertation, several consensus and consensus-based algorithms in WSNs are studied.

Firstly, a distributed consensus algorithm for estimating the maximum and minimum value of the initial measurements in a sensor network in the presence of communication noise is proposed. In the proposed algorithm, a soft-max approximation together with a non-linear average consensus algorithm is used. A design parameter controls the trade-off between the soft-max error and convergence speed. An analysis of this trade-off gives guidelines towards how to choose the design parameter for the max estimate. It is also shown that if some prior knowledge of the initial measurements is available, the consensus process can be accelerated.

Secondly, a distributed system size estimation algorithm is proposed. The proposed algorithm is based on distributed average consensus and L2 norm estimation. Different sources of error are explicitly discussed, and the distribution of the final estimate is derived. The CRBs for system size estimator with average and max consensus strategies are also considered, and different consensus based system size estimation approaches are compared.

Then, a consensus-based network center and radius estimation algorithm is described. The center localization problem is formulated as a convex optimization problem with a summation form by using soft-max approximation with exponential functions. Distributed optimization methods such as stochastic gradient descent and diffusion adaptation are used to estimate the center. Then, max consensus is used to compute the radius of the network area.

Finally, two average consensus based distributed estimation algorithms are introduced: distributed degree distribution estimation algorithm and algorithm for tracking the dynamics of the desired parameter. Simulation results for all proposed algorithms are provided.

This thesis addresses control design for fixed-wing air-breathing aircraft. Four aircraft with distinct dynamical properties are considered: a scram-jet powered hypersonic (100foot long, X-43 like, wedge shaped) aircraft with flexible modes operating near Mach 8, 85k ft, a NASA HiMAT (Highly Maneuverable Aircraft Technology) F-18 aircraft,

a McDonnell Douglas AV-8A Harrier aircraft, and a Vought F-8 Crusader aircraft. A two-input two-output (TITO) longitudinal LTI (linear time invariant) dynamical model is used for each aircraft. Control design trade studies are conducted for each of the aircraft. Emphasis is placed on the hypersonic vehicle because of its complex nonlinear (unstable, non-minimum phase, flexible) dynamics and uncertainty associated with hypersonic flight (Mach $>$ 5, shocks and high temperatures on leading edges). Two plume models are used for the hypersonic vehicle – an old plume model and a new plume model. The old plume model is simple and assumes a typical decaying pressure distribution for aft nozzle. The new plume model uses Newtonian impact theory and a nonlinear solver to compute the aft nozzle pressure distribution. Multivariable controllers were generated using standard weighted $H_{\inf}$ mixed-sensitivity optimization as well as a new input disturbance weighted mixed-sensitivity framework that attempts to achieve good multivariable properties at both the controls (plant inputs) as well as the errors (plant outputs). Classical inner-outer (PD-PI) structures (partially centralized and decentralized) were also used. It is shown that while these classical (sometimes partially centralized PD-PI) structures could be used to generate comparable results to the multivariable controllers (e.g. for the hypersonic vehicle, Harrier, F-8), considerable tuning (iterative optimization) is often essential. This is especially true for the highly coupled hypersonic vehicle – thus justifying the need for a good multivariable control design tool. Fundamental control design tradeoffs for each aircraft are presented – comprehensively for the hypersonic aircraft. In short, the thesis attempts to shed light on when complex controllers are essential and when simple structures are sufficient for achieving control designs with good multivariable loop properties at both the errors (plant outputs) and the controls (plant inputs).

Distributed estimation uses many inexpensive sensors to compose an accurate estimate of a given parameter. It is frequently implemented using wireless sensor networks. There have been several studies on optimizing power allocation in wireless sensor networks used for distributed estimation, the vast majority of which assume linear radio-frequency amplifiers. Linear amplifiers are inherently inefficient, so in this dissertation nonlinear amplifiers are examined to gain efficiency while operating distributed sensor networks. This research presents a method to boost efficiency by operating the amplifiers in the nonlinear region of operation. Operating amplifiers nonlinearly presents new challenges. First, nonlinear amplifier characteristics change across manufacturing process variation, temperature, operating voltage, and aging. Secondly, the equations conventionally used for estimators and performance expectations in linear amplify-and-forward systems fail. To compensate for the first challenge, predistortion is utilized not to linearize amplifiers but rather to force them to fit a common nonlinear limiting amplifier model close to the inherent amplifier performance. This minimizes the power impact and the training requirements for predistortion. Second, new estimators are required that account for transmitter nonlinearity. This research derives analytically and confirms via simulation new estimators and performance expectation equations for use in nonlinear distributed estimation. An additional complication when operating nonlinear amplifiers in a wireless environment is the influence of varied and potentially unknown channel gains. The impact of these varied gains and both measurement and channel noise sources on estimation performance are analyzed in this paper. Techniques for minimizing the estimate variance are developed. It is shown that optimizing transmitter power allocation to minimize estimate variance for the most-compressed parameter measurement is equivalent to the problem for linear sensors. Finally, a method for operating distributed estimation in a multipath environment is presented that is capable of developing robust estimates for a wide range of Rician K-factors. This dissertation demonstrates that implementing distributed estimation using nonlinear sensors can boost system efficiency and is compatible with existing techniques from the literature for boosting efficiency at the system level via sensor power allocation. Nonlinear transmitters work best when channel gains are known and channel noise and receiver noise levels are low.

The ease of use of mobile devices and tablets by students has generated a lot of interest in the area of engineering education. By using mobile technologies in signal analysis and applied mathematics, undergraduate-level courses can broaden the scope and effectiveness of technical education in classrooms. The current mobile devices have abundant memory and powerful processors, in addition to providing interactive interfaces. Therefore, these devices can support the implementation of non-trivial signal processing algorithms. Several existing visual programming environments such as Java Digital Signal Processing (J-DSP), are built using the platform-independent infrastructure of Java applets. These enable students to perform signal-processing exercises over the Internet. However, some mobile devices do not support Java applets. Furthermore, mobile simulation environments rely heavily on establishing robust Internet connections with a remote server where the processing is performed. The interactive Java Digital Signal Processing tool (iJDSP) has been developed as graphical mobile app on iOS devices (iPads, iPhones and iPod touches). In contrast to existing mobile applications, iJDSP has the ability to execute simulations directly on the mobile devices, and is a completely stand-alone application. In addition to a substantial set of signal processing algorithms, iJDSP has a highly interactive graphical interface where block diagrams can be constructed using a simple drag-n-drop procedure. Functions such as visualization of the convolution operation, and an interface to wireless sensors have been developed. The convolution module animates the process of the continuous and discrete convolution operations, including time-shift and integration, so that users can observe and learn, intuitively. The current set of DSP functions in the application enables students to perform simulation exercises on continuous and discrete convolution, z-transform, filter design and the Fast Fourier Transform (FFT). The interface to wireless sensors in iJDSP allows users to import data from wireless sensor networks, and use the rich suite of functions in iJDSP for data processing. This allows users to perform operations such as localization, activity detection and data fusion. The exercises and the iJDSP application were evaluated by senior-level students at Arizona State University (ASU), and the results of those assessments are analyzed and reported in this thesis.

The demand for handheld portable computing in education, business and research has resulted in advanced mobile devices with powerful processors and large multi-touch screens. Such devices are capable of handling tasks of moderate computational complexity such as word processing, complex Internet transactions, and even human motion analysis. Apple's iOS devices, including the iPhone, iPod touch and the latest in the family - the iPad, are among the well-known and widely used mobile devices today. Their advanced multi-touch interface and improved processing power can be exploited for engineering and STEM demonstrations. Moreover, these devices have become a part of everyday student life. Hence, the design of exciting mobile applications and software represents a great opportunity to build student interest and enthusiasm in science and engineering. This thesis presents the design and implementation of a portable interactive signal processing simulation software on the iOS platform. The iOS-based object-oriented application is called i-JDSP and is based on the award winning Java-DSP concept. It is implemented in Objective-C and C as a native Cocoa Touch application that can be run on any iOS device. i-JDSP offers basic signal processing simulation functions such as Fast Fourier Transform, filtering, spectral analysis on a compact and convenient graphical user interface and provides a very compelling multi-touch programming experience. Built-in modules also demonstrate concepts such as the Pole-Zero Placement. i-JDSP also incorporates sound capture and playback options that can be used in near real-time analysis of speech and audio signals. All simulations can be visually established by forming interactive block diagrams through multi-touch and drag-and-drop. Computations are performed on the mobile device when necessary, making the block diagram execution fast. Furthermore, the extensive support for user interactivity provides scope for improved learning. The results of i-JDSP assessment among senior undergraduate and first year graduate students revealed that the software created a significant positive impact and increased the students' interest and motivation and in understanding basic DSP concepts.