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.

From time immemorial, epilepsy has persisted to be one of the greatest impediments to human life for those stricken by it. As the fourth most common neurological disorder, epilepsy causes paroxysmal electrical discharges in the brain that manifest as seizures. Seizures have the effect of debilitating patients on a physical and psychological level. Although not lethal by themselves, they can bring about total disruption in consciousness which can, in hazardous conditions, lead to fatality. Roughly 1\% of the world population suffer from epilepsy and another 30 to 50 new cases per 100,000 increase the number of affected annually. Controlling seizures in epileptic patients has therefore become a great medical and, in recent years, engineering challenge.



In this study, the conditions of human seizures are recreated in an animal model of temporal lobe epilepsy. The rodents used in this study are chemically induced to become chronically epileptic. Their Electroencephalogram (EEG) data is then recorded and analyzed to detect and predict seizures; with the ultimate goal being the control and complete suppression of seizures.



Two methods, the maximum Lyapunov exponent and the Generalized Partial Directed Coherence (GPDC), are applied on EEG data to extract meaningful information. Their effectiveness have been reported in the literature for the purpose of prediction of seizures and seizure focus localization. This study integrates these measures, through some modifications, to robustly detect seizures and separately find precursors to them and in consequence provide stimulation to the epileptic brain of rats in order to suppress seizures. Additionally open-loop stimulation with biphasic currents of various pairs of sites in differing lengths of time have helped us create control efficacy maps. While GPDC tells us about the possible location of the focus, control efficacy maps tells us how effective stimulating a certain pair of sites will be.



The results from computations performed on the data are presented and the feasibility of the control problem is discussed. The results show a new reliable means of seizure detection even in the presence of artifacts in the data. The seizure precursors provide a means of prediction, in the order of tens of minutes, prior to seizures. Closed loop stimulation experiments based on these precursors and control efficacy maps on the epileptic animals show a maximum reduction of seizure frequency by 24.26\% in one animal and reduction of length of seizures by 51.77\% in another. Thus, through this study it was shown that the implementation of the methods can ameliorate seizures in an epileptic patient. It is expected that the new knowledge and experimental techniques will provide a guide for future research in an effort to ultimately eliminate seizures in epileptic patients.

For a sensor array, part of its elements may fail to work due to hardware failures. Then the missing data may distort in the beam pattern or decrease the accuracy of direction-of-arrival (DOA) estimation. Therefore, considerable research has been conducted to develop algorithms that can estimate the missing signal information. On the other hand, through those algorithms, array elements can also be selectively turned off while the missed information can be successfully recovered, which will save power consumption and hardware cost.

Conventional approaches focusing on array element failures are mainly based on interpolation or sequential learning algorithm. Both of them rely heavily on some prior knowledge such as the information of the failures or a training dataset without missing data. In addition, since most of the existing approaches are developed for DOA estimation, their recovery target is usually the co-variance matrix but not the signal matrix.

In this thesis, a new signal recovery method based on matrix completion (MC) theory is introduced. It aims to directly refill the absent entries in the signal matrix without any prior knowledge. We proposed a novel overlapping reshaping method to satisfy the applying conditions of MC algorithms. Compared to other existing MC based approaches, our proposed method can provide us higher probability of successful recovery. The thesis describes the principle of the algorithms and analyzes the performance of this method. A few application examples with simulation results are also provided.

Buck converters are electronic devices that changes a voltage from one level to a lower one and are present in many everyday applications. However, due to factors like aging, degradation or failures, these devices require a system identification process to track and diagnose their parameters. The system identification process should be performed on-line to not affect the normal operation of the device. Identifying the parameters of the system is essential to design and tune an adaptive proportional-integral-derivative (PID) controller.

Three techniques were used to design the PID controller. Phase and gain margin still prevails as one of the easiest methods to design controllers. Pole-zero cancellation is another technique which is based on pole-placement. However, although these controllers can be easily designed, they did not provide the best response compared to the Frequency Loop Shaping (FLS) technique. Therefore, since FLS showed to have a better frequency and time responses compared to the other two controllers, it was selected to perform the adaptation of the system.

An on-line system identification process was performed for the buck converter using indirect adaptation and the least square algorithm. The estimation error and the parameter error were computed to determine the rate of convergence of the system. The indirect adaptation required about 2000 points to converge to the true parameters prior designing the controller. These results were compared to the adaptation executed using robust stability condition (RSC) and a switching controller. Two different scenarios were studied consisting of five plants that defined the percentage of deterioration of the capacitor and inductor within the buck converter. The switching logic did not always select the optimal controller for the first scenario because the frequency response of the different plants was not significantly different. However, the second scenario consisted of plants with more noticeable different frequency responses and the switching logic selected the optimal controller all the time in about 500 points. Additionally, a disturbance was introduced at the plant input to observe its effect in the switching controller. However, for reasonable low disturbances no change was detected in the proper selection of controllers.

Utility scale solar energy is generated by photovoltaic (PV) cell arrays, which are often deployed in remote areas. A PV array monitoring system is considered where smart sensors are attached to the PV modules and transmit data to a monitoring station through wireless links. These smart monitoring devices may be used for fault detection and management of connection topologies. In this thesis, a compact hardware simulator of the smart PV array monitoring system is described. The voltage, current, irradiance, and temperature of each PV module are monitored and the status of each panel along with all data is transmitted to a mobile device. LabVIEW and Arduino board programs have been developed to display and visualize the monitoring data from all sensors. All data is saved on servers and mobile devices and desktops can easily access analytics from anywhere. Various PV array conditions including shading, faults, and loading are simulated and demonstrated.

Additionally, Electrical mismatch between modules in a PV array due to partial shading causes energy losses beyond the shaded module, as unshaded modules are forced to operate away from their maximum power point in order to compensate for the shading. An irradiance estimation algorithm is presented for use in a mismatch mitigation system. Irradiance is estimated using measurements of module voltage, current, and back surface temperature. These estimates may be used to optimize an array’s electrical configuration and reduce the mismatch losses caused by partial shading. Propagation of error in the estimation is examined; it is found that accuracy is sufficient for use in the proposed mismatch mitigation application.

Several music players have evolved in multi-dimensional and surround sound systems. The audio players are implemented as software applications for different audio hardware systems. Digital formats and wireless networks allow for audio content to be readily accessible on smart networked devices. Therefore, different audio output platforms ranging from multispeaker high-end surround systems to single unit Bluetooth speakers have been developed. A large body of research has been carried out in audio processing, beamforming, sound fields etc. and new formats are developed to create realistic audio experiences.

An emerging trend is seen towards high definition AV systems, virtual reality gears as well as gaming applications with multidimensional audio. Next generation media technology is concentrating around Virtual reality experience and devices. It has applications not only in gaming but all other fields including medical, entertainment, engineering, and education. All such systems also require realistic audio corresponding with the visuals.

In the project presented in this thesis, a new portable audio hardware system is designed and developed along with a dedicated mobile android application to render immersive surround sound experiences with real-time audio effects. The tablet and mobile phone allow the user to control or “play” with sound directionality and implement various audio effects including sound rotation, spatialization, and other immersive experiences. The thesis describes the hardware and software design, provides the theory of the sound effects, and presents demonstrations of the sound application that was created.

The research on the topology and dynamics of complex networks is one of the most focused area in complex system science. The goals are to structure our understanding of the real-world social, economical, technological, and biological systems in the aspect of networks consisting a large number of interacting units and to develop corresponding detection, prediction, and control strategies. In this highly interdisciplinary field, my research mainly concentrates on universal estimation schemes, physical controllability, as well as mechanisms behind extreme events and cascading failure for complex networked systems.

Revealing the underlying structure and dynamics of complex networked systems from observed data without of any specific prior information is of fundamental importance to science, engineering, and society. We articulate a Markov network based model, the sparse dynamical Boltzmann machine (SDBM), as a universal network structural estimator and dynamics approximator based on techniques including compressive sensing and K-means algorithm. It recovers the network structure of the original system and predicts its short-term or even long-term dynamical behavior for a large variety of representative dynamical processes on model and real-world complex networks.

One of the most challenging problems in complex dynamical systems is to control complex networks.

Upon finding that the energy required to approach a target state with reasonable precision

is often unbearably large, and the energy of controlling a set of networks with similar structural properties follows a fat-tail distribution, we identify fundamental structural ``short boards'' that play a dominant role in the enormous energy and offer a theoretical interpretation for the fat-tail distribution and simple strategies to significantly reduce the energy.

Extreme events and cascading failure, a type of collective behavior in complex networked systems, often have catastrophic consequences. Utilizing transportation and evolutionary game dynamics as prototypical

settings, we investigate the emergence of extreme events in simplex complex networks, mobile ad-hoc networks and multi-layer interdependent networks. A striking resonance-like phenomenon and the emergence of global-scale cascading breakdown are discovered. We derive analytic theories to understand the mechanism of

control at a quantitative level and articulate cost-effective control schemes to significantly suppress extreme events and the cascading process.

There has been tremendous technological advancement in the past two decades. Faster computers and improved sensing devices have broadened the research scope in computer vision. With these developments, the task of assessing the quality of human actions, is considered an important problem that needs to be tackled. Movement quality assessment finds wide range of application in motor control, health-care, rehabilitation and physical therapy. Home-based interactive physical therapy requires the ability to monitor, inform and assess the quality of everyday movements. Obtaining labeled data from trained therapists/experts is the main limitation, since it is both expensive and time consuming.

Motivated by recent studies in motor control and therapy, in this thesis an existing computational framework is used to assess balance impairment and disease severity in people suffering from Parkinson's disease. The framework uses high-dimensional shape descriptors of the reconstructed phase space, of the subjects' center of pressure (CoP) tracings while performing dynamical postural shifts. The performance of the framework is evaluated using a dataset collected from 43 healthy and 17 Parkinson's disease impaired subjects, and outperforms other methods, such as dynamical shift indices and use of chaotic invariants, in assessment of balance impairment.

In this thesis, an unsupervised method is also proposed that measures movement quality assessment of simple actions like sit-to-stand and dynamic posture shifts by modeling the deviation of a given movement from an ideal movement path in the configuration space, i.e. the quality of movement is directly related to similarity to the ideal trajectory, between the start and end pose. The S^1xS^1 configuration space was used to model the interaction of two joint angles in sit-to-stand actions, and the R^2 space was used to model the subject's CoP while performing dynamic posture shifts for application in movement quality estimation.

Information divergence functions, such as the Kullback-Leibler divergence or the Hellinger distance, play a critical role in statistical signal processing and information theory; however estimating them can be challenge. Most often, parametric assumptions are made about the two distributions to estimate the divergence of interest. In cases where no parametric model fits the data, non-parametric density estimation is used. In statistical signal processing applications, Gaussianity is usually assumed since closed-form expressions for common divergence measures have been derived for this family of distributions. Parametric assumptions are preferred when it is known that the data follows the model, however this is rarely the case in real-word scenarios. Non-parametric density estimators are characterized by a very large number of parameters that have to be tuned with costly cross-validation. In this dissertation we focus on a specific family of non-parametric estimators, called direct estimators, that bypass density estimation completely and directly estimate the quantity of interest from the data. We introduce a new divergence measure, the $D_p$-divergence, that can be estimated directly from samples without parametric assumptions on the distribution. We show that the $D_p$-divergence bounds the binary, cross-domain, and multi-class Bayes error rates and, in certain cases, provides provably tighter bounds than the Hellinger divergence. In addition, we also propose a new methodology that allows the experimenter to construct direct estimators for existing divergence measures or to construct new divergence measures with custom properties that are tailored to the application. To examine the practical efficacy of these new methods, we evaluate them in a statistical learning framework on a series of real-world data science problems involving speech-based monitoring of neuro-motor disorders.

In many applications, measured sensor data is meaningful only when the location of sensors is accurately known. Therefore, the localization accuracy is crucial. In this dissertation, both location estimation and location detection problems are considered.

In location estimation problems, sensor nodes at known locations, called anchors, transmit signals to sensor nodes at unknown locations, called nodes, and use these transmissions to estimate the location of the nodes. Specifically, the location estimation in the presence of fading channels using time of arrival (TOA) measurements with narrowband communication signals is considered. Meanwhile, the Cramer-Rao lower bound (CRLB) for localization error under different assumptions is derived. Also, maximum likelihood estimators (MLEs) under these assumptions are derived.

In large WSNs, distributed location estimation algorithms are more efficient than centralized algorithms. A sequential localization scheme, which is one of distributed location estimation algorithms, is considered. Also, different localization methods, such as TOA, received signal strength (RSS), time difference of arrival (TDOA), direction of arrival (DOA), and large aperture array (LAA) are compared under different signal-to-noise ratio (SNR) conditions. Simulation results show that DOA is the preferred scheme at the low SNR regime and the LAA localization algorithm provides better performance for network discovery at high SNRs. Meanwhile, the CRLB for the localization error using the TOA method is also derived.

A distributed location detection scheme, which allows each anchor to make a decision as to whether a node is active or not is proposed. Once an anchor makes a decision, a bit is transmitted to a fusion center (FC). The fusion center combines all the decisions and uses a design parameter $K$ to make the final decision. Three scenarios are considered in this dissertation. Firstly, location detection at a known location is considered. Secondly, detecting a node in a known region is considered. Thirdly, location detection in the presence of fading is considered. The optimal thresholds are derived and the total probability of false alarm and detection under different scenarios are derived.