The discovery of graphene in 2004 opened the door to the wonderful world of two-dimensional (2D) layered materials, and the properties and applications of these materials have been hot research topics ever since. The atomic-level thinness and layered structure of 2D materials give rise to extraordinary properties and enable novel functionalities, and they have exhibited great potential in various fields including electronics and optoelectronics. They are particularly promising for photodetection, and detectors from ultraviolet to terahertz wavelengths have been demonstrated based on these materials. However, low light absorption in 2D materials, which originates from their thin structure, has hindered their widespread application in photodetection. In this thesis, we demonstrate optical nanostructures that can significantly boost the interaction of light with 2D materials and thus improve their photodetection performance. Our focus is on infrared (IR) photodetectors which have applications in a wide range of areas that include biomedical and thermal imaging, telecommunication, spectroscopy, and many other modern technologies. First, we present a hybrid plasmonic structure for enhancing the light absorption in graphene in the long-wave IR (LWIR) spectral region. This structure, consisting of a metallic bull's eye grating and optical nanoantennas, employs surface plasmon polaritons and localized surface plasmons to concentrate light into a monolayer graphene flake with sub-wavelength lateral extent. Optical simulations show that this plasmonic structure provides a 558-fold light absorption enhancement in graphene and a 32-fold enhancement in the detectivity of the LWIR photodetector. It is also found that integrating this structure with an optical cavity substrate further boosts the device performance. Black phosphorus (bP), another 2D layered material with a narrow and direct bandgap of 0.31 eV, has great potential for IR optoelectronics. Nevertheless, the performance of bP-based photodetectors is limited by weak light absorption in bP, resulting from its thinness and optical anisotropy. In the next work, via optical simulations, we demonstrate hybrid plasmonic nanoantenna/optical cavity structures that boost the IR light absorption in multilayer bP through polarization conversion and light intensity enhancement. In a reciprocal manner, these nanostructures enhance the spontaneous emission from bP. Light absorption and emission enhancements of up to 185-fold and 18-fold, respectively, are achieved. Detectivity and electroluminescence efficiency of 2D material-based photodetectors and light-emitting diodes can be significantly enhanced employing these optical nanostructures. Recently, platinum diselenide (PtSe2), a 2D noble-transition-metal dichalcogenide, has also been investigated for IR detection. However, wavelengths up to the short-wave infrared region have been the main focus of these studies. In the last work, we present LWIR photodetectors based on multilayer PtSe2. We utilise a TiO2/Au optical cavity substrate for enhancing the LWIR light absorption in PtSe2. Responsivity values of up to 54 mA/W are obtained at 8.35 um. In addition, these devices show a fast photoresponse with a time constant of 54 ns to white light illumination. This study reveals the potential of multilayer PtSe2 for fast and broadband photodetection from visible to LWIR wavelengths. It also highlights the key role of the substrate in the performance of 2D material-based IR photodetectors.

Non-invasive fetal electrocardiography (NI-FECG) is an emerging technique that offers novel diagnostic potential for monitoring fetal wellbeing. As the timing and amplitude of cardiac electrical activity reflect both autonomic system development and changes in response to fetal distress, these signals allow for monitoring opportunities unattainable using current techniques. However, clinical translation using existing NI-FECG systems has been hampered by a large variability in signal quality and a poor understanding of the factors which contribute to these signal characteristics. The overarching aim of this thesis is to develop modelling techniques to address these challenges and advance the use of NI-FECG as a clinical tool. To achieve this, we first develop an integrated computational model of the maternal-fetal anatomy for generating simulated NI-FECG signals. To address limitations in existing models, we present an open-source process to generate NI-FECG recordings with exact specifications of the geometric and conductive properties of the maternal-fetal anatomy and sensor configuration. Using this model, we demonstrate that morphological ECG features currently used for assessing fetal wellbeing are significantly influenced by asymmetry in the anatomic structure. Next, we validate our computational model by assessing its ability for predicting surface potentials in clinical NI-FECG recordings. Using our model, we demonstrate agreement between simulated and experimental data and illustrate its utility for predicting a configuration of sensors to reliably extract the fetal heart rate. To further optimize the sensor configuration, we generate simulated data across a wide range of anatomic variations and propose an optimal NI-FECG sensor placement for future studies. Finally, we present a process to benchmark NI-FECG extraction algorithms using our model and provide recommendations to ensure morphological fetal ECG features are accurately captured. With the application of these findings to clinical practice, we expect these techniques will improve the reliability of NI-FECG and its utility for assessing fetal wellbeing.

Power systems worldwide are experiencing a radical transition from a traditional configuration based on conventional thermal prime movers with synchronous generators to systems increasingly dominated by variable renewable energy sources that are asynchronously connected to the system via power electronic interfaces. Consequently, the level of system synchronous inertia is rapidly decreasing, with potentially severe effects on frequency stability. In Australia, the recent decommission of large coal-fired power plants, recurrent brown-outs over hot summer days, in addition to a major blackout in the South Australia region in 2016, have thus raised significant concerns as to the capability of the current system and market arrangements to adapt to the varying technical, economic and environmental requirements. Also, Australia's weak grid faces a high risk of separation during extreme weather conditions or in the event of cascading failures. These contingencies may become particularly severe in low-inertia grids, where the sub-regions resulting after system split need to procure enough resources to respond to low (importing areas) and high (exporting areas) frequency conditions. In this work, a multi-service frequency response model is developed to represent the frequency behaviour of a system (or subsystems) considering different contingencies, frequency response resources, inertia availability and demand sensitivity to frequency changes. This model is used to build frequency response constraints that guarantee the allocation of the resources necessary to contain frequency deviations after load, generation and transmission contingencies. These frequency response constraints are used to assemble a multi-area security-constrained unit commitment, capable of minimising the total cost of operation considering the technical characteristics of synchronous units, renewable energy resources availability, DC power flows, transmission constraints, and the allocation of reserves (including fast frequency response resources) and inertia to comply with statutory limits for the rate of change of frequency, frequency nadir and zenith, and quasi-steady-state frequency. This unit commitment model, cast as a mixed-integer linear program, is investigated on test systems representing the Australian power system and validated via dynamic simulations. The results show how the system's frequency resilience to extreme events can be effectively enhanced for both high- and low-frequency conditions that arise in different areas after a generation, load or interconnector contingency. As decreasing inertia levels put pressure on the system frequency security adequacy, investing in technologies to support it becomes necessary. Using the unit commitment model as the framework to study low-inertia power system operation, this work presents an expansion model based on Dantzig-Wolfe decomposition and delayed column generation algorithm that inherently embeds the associated frequency security constraints in the expansion process. As a result, the expansion model guarantees minimum investment and operation cost decisions and frequency security adequacy. A case study application representing the actual characteristics of the Australian power system is presented, using the parameters provided by the Australian Energy Market Operator in the context of the Integrated System Plan. This work studies the optimal development paths for the system under uncertainty, considering the investment in transmission lines, battery energy storage systems, pumped-hydro storage systems, and synchronous condensers. The expansion model is validated and tested using different scenario trees that help identify the investment flexibility provided by various technologies in the presence of uncertainty. The novelties of this work include a multi-area security-constrained unit commitment model capable of allocating frequency security resources, including fast frequency response to withstand generation and load contingencies, and transmission contingencies leading to system split. Furthermore, the model can co-optimise the largest contingency size and guarantee the feasibility of transmission of contingency reserves through the interconnectors after contingency. It also presents a state-of-the-art security-constrained expansion planning model capable of making investment decisions that consider frequency response constraints and fast frequency response. To the best of the author's knowledge, this is the first time an expansion planning model with these characteristics has been presented and applied on a real system to make investment decisions not only on transmission and storage assets but also on synchronous condensers. Some of the novel elements presented in this work have had a substantial impact on real-world applications. The frequency response adequacy model has been used to analyse the frequency security of future energy scenarios in Australia in the context of the Independent Review into the Future Security of the National Electricity Market conducted by Australia's Chief Scientist. A graphical tool derived from the frequency adequacy model has been used by the Australian Energy Market Operator to analyse the frequency behaviour of the South West Interconnected System in Western Australia. Also, recently, UK's National Grid Electricity System Operator has started applying a new framework to evaluate investment decisions in new transmission assets based on the least worst weighted regret approach presented in this work.

Functional magnetic resonance imaging (fMRI) is a non-invasive imaging technique that has been extensively used in recent years to localize neural activities in the brain. Assuming a general linear model (GLM) to approximate recorded signals, classical maximum likelihood based estimators and detectors are used in the literature and their design is based on strong assumptions (e.g., Gaussianity of the noise). In the first part of this thesis, we extend the existing detectors and estimators using an alternative measure from information geometry called "alpha-divergence". This measure is used to obtain robustness against possible outliers or mismatches in observations and achieve more reliable results. Finally, in the second part, we consider existing knowledge about the data as prior information (e.g., low rank data, locally correlated noise) and develop detectors that are more adapted for such data types. After validation of our proposed techniques using simulations and synthetic data, we compare the performance of the proposed methods with existing methods in the literature in different imaging applications with the same data modeling (e.g., fMRI data, hyperspectral images, etc.)

The Central Pattern Generators (CPGs) are the neuronal circuits that can produce rhythmic activity without any sensory feedback or oscillatory input. They underlie stereotyped behaviours such as respiration, locomotion, and swallowing. The thesis presents CPGs from the modeller's perspective, defines the main conceptual building blocks, and discusses the possible rhythmogenic mechanisms in these circuits. Further, the thesis focuses on the respiratory and the swallowing circuits in particular. Respiration and swallowing are vital motor behaviours that require the coordination of the activity of two brainstem central pattern generators (r-CPG, sw-CPG). First, the previous models of the r-CPG are reviewed in detail. The previous models of r-CPG utilised biophysically detailed but computationally complex Hodgkin-Huxley neurons, and this thesis shows that the standard in the field model of the r-CPG can be reproduced utilising simpler Izhikevich neurons, thereby reducing the number of model parameters. Next, the thesis elaborates on the computational modelling of the neural substrate for breathing-swallowing coordination. We sequentially construct several computational models of the breathing-swallowing circuit. Starting from two interacting half-centre oscillators for each CPG, the connectivity between central sensory relay, sw- and r-CPG neuronal populations is progressively refined to match experimental data obtained in a perfused brainstem preparation. The neuronal nodes utilised in these models, representing the neuronal populations, have a parsimonious description of the intrinsic properties. The present model provides novel insights that can guide future experiments and the development of efficient treatments for breathing-swallowing disorders. Furthermore, partially motivated by the idea of learning a sequence of activity patterns in CPGs, this thesis presents a study conducted in Hopfield Networks. Similar to CPGs, Hopfield Networks can produce oscillatory behaviours. However, the thesis elaborates on discrete Hopfield networks whose dynamics converge to a fixed point. The thesis presents a unifying framework for the newly proposed and the previously developed learning algorithms from an optimisation standpoint. Lastly, the appendix of the thesis contains a description of practical routines for evaluating a phase response curve (PRC) of limit cycles --- an important tool for the analysis of systems with oscillatory behaviours.

As the penetration levels of residential-scale solar PV and battery energy storage systems (BESS) increase, net demand is reduced, and thus synchronous generators are displaced. This leads to a reduction in primary frequency response (PFR) resources and maintaining frequency excursions following a large generation contingency becomes increasingly difficult. Understanding the impacts of the reduction of PFR resources in the context of increasing PV and BESS penetrations presents the first challenge. Aggregating the individual customers and embedding the actual behind the meter operation of PV and BESS require proper modelling techniques. Since BESS can quickly inject active power, there is an opportunity for them to also provide PFR using droop settings. The second challenge, however, is that droop settings based on the rated capacity of residential BESS may not be effective. This is because their true ability to inject power depends on the demand, PV generation, charging/discharging power, state of charge, and fixed export limits at their connection point. Lastly, the distribution network that these BESS are connected to poses the final challenge. The ability of BESS to provide PFR depends on the ability of the distribution network to maintain its integrity in terms of voltage and thermal violations during these moments of injections. To address these challenges, and to quantify the techniques for BESS to provide PFR, the following research is carried out: For the first challenge, a bottom-up modelling approach is proposed to demonstrate the system-level impacts on power system characteristics (i.e., PFR reduction, frequency performance and generating cost) from residential PV and BESS. Results show that commercially available BESS modelled for self-consumption led to very similar generating costs compared to cases when only PV systems are considered. This is contrary to popular belief in the literature that adoption of BESS will charge large amounts of excess PV and thus reduce system-level operational costs of generating units. In terms of frequency performance of the power system, results show that the rate-of-change of frequency and the frequency nadir initially deteriorates with increasing penetrations of PV and BESS. However, as penetrations increase further, the trends reverse and improve due to significant reductions in the generation contingency size. For the second challenge, a two-part approach is required. Firstly, an analytical approach is proposed to quantify the injections required from residential BESS using droop settings based on installed capacity to provide PFR following a contingency at any given time. Results demonstrates the relationship among time, BESS droop and their rated power capacity to ensure the provision of the PFR. This approach gave insight into calculating droop settings for residential BESS to provide PFR and quantifies the injections for different penetration levels. In the second approach, a methodology is proposed that actively calculates droop settings for residential BESS based on their true ability to individually inject active power based on fixed export limits – as this is the current industry practice for limiting PV and BESS injections to mitigate network impacts. Instead of using the installed capacity, this methodology considers the demand, PV generation, charging/discharging power, state of charge, and the export limits at the connection point of customers. Results show that adopting fixed droop settings based on the rated capacity of BESS are ineffective in delivering PFR at times. Furthermore, larger contributions are possible when actively calculating droop settings thus highlighting the role of residential BESS in providing PFR. The final challenge of the distribution network constraints is then addressed by advanced considerations, where maximum injections are calculated for individual customers based on the physical limits of the DN (i.e., voltage and thermal limits). The proposed methodology uses these maximum injections as dynamic export limits instead of the fixed 5kW per phase. With dynamic export limits, further increases of PFR are unlocked, and by not exceeding these maximum injections, the network integrity is maintained. To assess the system-level impacts on power system characteristics, a modified IEEE 9-bus system with 73,000+ residential customers with real smart meter data is used. This proposed approach accurately models the behind the meter operation of individual customers and allow impact analyses that reflect their aggregated behaviour as penetration levels increase. The effectiveness of the analytical approach to calculate the droop settings and the active droop methodologies are applied to the IEEE 9-bus test system. For distribution network consideration, a three-phase optimal power flow analysis on a real Australian MV-LV network with 4,626 single-phase customers is performed.

Optical wireless communications use optical signals or light over the air for the transmission of information. With optical fibre components becoming mature, optical wireless communications operating at several tens of gigabits per second data rates have been explored recently for indoor applications, as an alternative to the most popular forms of wireless communications using radio frequencies. Unlike radio frequency transmission, optical wireless communications provide the unique advantages of offering higher, scalable and license-free communication bandwidth without RF interference. It is a promising solution to support the ever-increasing demand for high-bandwidth across indoor wireless applications, as highlighted by bandwidth challenges faced by people using Wi-Fi networks and mobile broadband networks during the recent COVID-19 pandemic. To realise optical wireless communication link operating at high data rates up to multi Gb/s, the line-of-sight link is preferred due to its high optical power efficiency and low multipath distortion that leads to high signal-to-noise-ratio performance. However, such line-of-sight links are susceptible to the obstructions of the optical beams due to objects or users shadowing the transmission of beams. The primary objective of this thesis is to address these challenges by investigating specific transmitter diversity techniques where multiple transmitters are introduced to improve the indoor optical wireless system performance. For optical wireless links with transmitter diversity, this thesis also investigates the delay-tolerant coding scheme to address the inter-symbol interference caused by multiple signals from transmitters and studies the spatial modulation techniques using multiple-inputs-single-output OWC links to increase the achievable system throughput with transmitter diversity. The thesis starts with the channel gain modelling of the indoor intensity modulation/direct detection-based line-of-sight optical wireless system as the foundation for the transmitter diversity investigation. The systematic investigation of two popular coding schemes, i.e., space-time-block-coding and repetition-coding, is then performed theoretically and experimentally to achieve transmitter diversity. These two schemes provide a fundamental framework to address the optical beam obstruction issue in the line-of-sight channel. Based on the superior performance of the repetition-coding scheme, a generalised delay-tolerant coding technique using the orthogonal-filters-based repetition-coding scheme with on-demand equalisation is further developed. This includes the development of the principle, a detailed theoretical analysis, and experimental demonstration, to tackle the channel delay caused by multi-channel optical wireless transmission. Moreover, to further increase the achievable system throughput in addition to the transmitter diversity, spatial modulation with signal space diversity is further proposed. The transmitter diversity performance of both signal space diversity scheme and the spatial modulation channel index detection impact are investigated using theoretical analysis and experimental demonstration. The thesis is finalised by reviewing all coding schemes’ bit-error-rate performance under different total channel gain distributions emulating various indoor line-of-sight optical wireless channel obstructions. In conclusion, the optical wireless communications with transmitter diversity principles have been investigated via analytical modelling and experimental demonstrations in this thesis. The transmitter diversity coding schemes proposed and investigated here have shown the capability of improving the communication performance and hence, provide a promising pathway to realise resilient optical wireless communications.

Networked systems are now playing central and important roles in many engineering applications. Although a lot of research efforts have been made to the control of such networked systems, some important questions still remain unanswered. The thesis aims to identify and address some of the theoretical challenges in the optimization and control of networked systems that are not explored by the existing literature. In particular, the three main contributions of the thesis are in the area of asynchronous distributed optimization, online optimization using coordinate descent methods, and security and privacy of networked systems. For asynchronous distributed optimization, we propose an asynchronous algorithm to minimize the sum of convex cost functions using dual decomposition and block coordinate subgradient methods. The prominent feature of our algorithm is that the communication, computation and stepsize update in the network is not coordinated. Moreover, we show that our asynchronous algorithm covers some existing results in the literature as special cases. Under assumptions weaker than those used in the literature, we are able to prove almost sure convergence of the asynchronous algorithm. A numerical example is provided to illustrate the effectiveness of the algorithm. In addition to traditional offline optimization problems, we also consider the problem of online optimization where the optimization problem may change over time. In this part, we use coordinate descent methods to solve the time-varying optimization problem online, in an adaptive fashion. Specifically, we consider three coordinate selection rules, namely, random coordinate descent, cyclic coordinate descent, and Gauss-Southwell coordinate descent, that are commonly used in the literature of coordinate descent algorithms and extend them to the online setting. In contrast to offline optimization where convergence to the optimal point is desired, we solve the time-varying problem partially at each step and use the notion of regret as the measure of performance of our online algorithms. We provide an in-depth regret analysis for online coordinate descent algorithms under different assumptions and show that they are comparable to existing regret bounds of online gradient descent in the same settings. Lastly, a time-varying quadratic problem is studied numerically to illustrate the main results. Finally, we address the security and privacy of networked systems. We design controllers for nonlinear networked control systems (NCSs) using semi-homomorphic encryption which enables control signal computation using encrypted signals directly. Thus, the security of the NCSs is further enhanced by preserving the privacy of information flowing through the network connecting the plant and the controller. By using Lyapunov based methods, we provide sufficient conditions on the encryption parameters that guarantee robust stability of the NCS in the presence of disturbances which covers the existing result on linear systems as a special case. Furthermore, we discuss the trade-offs between the required computational resources, security guarantees and the closed-loop performance. We test our controller on a numerical example to show the performance of the encryption based controller.

Structured numerical methods are developed for solving a class of constrained network optimal control problems with discrete-time dynamics arising from the path-graph interconnection of N heterogeneous sub-systems. Structured dynamics of this kind are relevant in the operation of irrigation channels, vehicle platoons, supply chains, and radial power networks and, also arise from the discretization of one-dimensional partial differential equations. The size of the optimization problem grows with increase in the number of sub-systems N and the time horizon T. To solve large instances of such problems, involving potentially millions of variables, it is imperative to exploit the special spatio-temporal structure. In this thesis, two numerical algorithms are developed to exploit the special problem structure, with a view to achieving decomposable computations and suppressing the computational effort required to solve it. To start, a structured splitting method, based on the alternating direction method of multipliers (ADMM), is developed. It is shown that the computations at each iteration involve structured matrix-vector products, which are decomposable across spatial and temporal dimension of the optimal control problem, into parallelizable sub-problems of size independent of N and T. The overall arithmetic complexity of each ADMM iteration is O(NT). Secondly, a structured preconditioned conjugate gradient (PCG) solver is developed for the Newton steps of second-order methods. The main innovation pertains to O(NT) arithmetic complexity of each PCG iteration. Again, the associated computations are decomposable across spatial and temporal dimensions of the optimal control problem, into mostly parallelizable sub-problems of size independent of N and T. Numerical results are provided for a mass-spring-damper chain and an automated irrigation channel to compare the proposed techniques against each other and existing approaches. It is observed that the ADMM approach can take a large number of iterations to converge with high accuracy. This can result in higher overall arithmetic complexity, and correspondingly higher data-exchange overhead if computations are distributed for parallel implementation, compared to an interior point method in which the proposed structured PCG solver is used to determine Newton directions.

As applications of deep learning continue to be discovered and implemented, the problem of robustness becomes increasingly important. It is well established that deep learning models have a serious vulnerability against adversarial attacks. Malicious attackers targeting learning models can generate so-called "adversarial examples'' that are able to deceive the models. These adversarial examples can be generated from real data by adding small perturbations in specific directions. This thesis focuses on the problem of explaining vulnerability (of neural networks) to adversarial examples, an open problem which has been addressed from various angles in the literature. The problem is approached geometrically, by considering adversarial examples as points which lie close to the decision boundary in a high-dimensional feature space. By invoking results from high-dimensional geometry, it is argued that adversarial robustness is impacted by high data dimensionality. Specifically, an upper bound on robustness which decreases with dimension is derived, subject to a few mathematical assumptions. To test this idea that adversarial robustness is affected by dimensionality, we perform experiments where robustness metrics are compared after training neural network classifiers on various dimension-reduced datasets. We use MNIST and two cognitive radio datasets for our experiments, and we compute the attack-based empirical robustness and attack-agnostic CLEVER score, both of which are approximations of true robustness. These experiments show correlations between adversarial robustness and dimension in certain cases.

Optimization-based approaches are developed for two problems in the management of dynamical systems. The first approach relates to the scheduling of rigid-profile inputs under constrained continuous-time dynamics. A parsimonious discretization is developed which yields a sub-optimal but feasible solution to this non-convex semi-infinite program. The second approach relates to uncertain preview in constrained receding horizon control. An approach to managing the interaction between the controller and the preview scheduler is developed to ensure recursive feasibility, with scope to balance control and scheduling objectives.

The integrity of the positioning system solution can be defined as a measure of trust one can put in the value of the estimated position. Some authors have called it ``a guarantee of safety''. Due to the safety implications, the Global Navigation Satellite Systems (GNSS) position integrity monitoring was first used in civil aviation. Integrity has become a key performance metric for Intelligent Transport Systems (ITS) given the ongoing efforts to develop more robust integrity monitoring algorithms for land-based applications in GNSS-challenged environments. However, ``a guarantee of safety'' cannot be given without any risk of misleading information associated with it. This risk exists due to the different error sources that impact the GNSS signals and needs to be up to a specified tolerable level that differs depending on the application. Any integrity monitoring algorithm proposed for ITS needs to be able to deal with problems specific to the urban environments: reduced measurement availability, satellite/user geometry and presence of large errors such as multipath. The algorithm proposed in this research is based on a robust, multi-sensor and cooperative positioning system with the Particle Filter (PF) as the underlying position estimator. This research proposes three novel integrity monitoring algorithms built on Bayesian Receiver Autonomous Integrity Monitoring (BRAIM). By using BRAIM, the need for measurement redundancy is mitigated. Although, BRAIM (with the PF as the underlying estimator) tests for different number and different magnitudes of faults through the employment of multiple particles (i.e., hypotheses), Fault Detection and Exclusion (FDE) is added to BRAIM. FDE is added to remove the impact of large biases on the a posteriori distribution used to bound the integrity risk estimate. This results in a novel FDE+BRAIM algorithm. In order to decrease the estimated integrity risk, a Spatial Feature Constraint (SFC) algorithm is implemented to constrain solutions to feasible locations within a road feature. By integrating SFC and BRAIM, the second novel algorithm is proposed: SFC+BRAIM. Lastly, a combination of both novel algorithms is proposed: the FDE+SFC+BRAIM algorithm. The performance of the proposed algorithms was evaluated for GPS only, multi-sensor and distributed cooperative data. The best performance is achieved by cooperative SFC+BRAIM. That method achieved the median probability of misleading information of 5.84*10^-9/epoch for the horizontal alarm limit of 5 m and integrity risk of 1*10^-7/epoch.