Robust Controller for Delays and Packet Dropout Avoidance in Solar-Power Wireless Network

Solar Wireless Networked Control Systems (SWNCS) are a style of distributed control systems where sensors, actuators, and controllers are interconnected via a wireless communication network. This system setup has the benefit of low cost, flexibility, low weight, no wiring and simplicity of system diagnoses and maintenance. However, it also unavoidably calls some wireless network time delays and packet dropout into the design procedure. Solar lighting system offers a clean environment, therefore able to continue for a long period. SWNCS also offers multi Service infrastructure solution for both developed and undeveloped countries. The system provides wireless controller lighting, wireless communications network (WI-FI/WIMAX), CCTV surveillance, and wireless sensor for weather measurement which are all powered by solar energy

Analysis of Large-Scale Asynchronous Switched Dynamical Systems

This dissertation addresses research problems related to the switched system as well as its application to large-scale asynchronous dynamical systems. For decades, this switched system has been widely studied in depth, owing to the broad applicability of the switched system framework. For example, the switched system can be adopted for modeling the dynamics of numerous systems including power systems, manufacturing systems, aerospace systems, networked control systems, etc. Despite considerable research works that have been developed during last several decades, there are still remaining yet important and unsolved problems for the switched systems. In the first part of this dissertation, new methods are developed for uncertainty propagation of stochastic switched systems in the presence of the state uncertainty, represented by probability density functions(PDFs). The main difficulty of this problem is that the number of PDF components in the state increases exponentially under the stochastic switching, incurring the curse of dimensionality. This dissertation provides a novel method that circumvents the issue regarding the curse of dimensionality. As an extension of this research, the new method for the switching synthesis is presented in the second part, to achieve the optimal performance of the switched system. This research is relevant to developing the switching synthesis on how to switch between different switching modes. In the following chapters, some interesting applications that emerges as today's leading-edge technology in high-performance computing (HPC) will be introduced. Generally, the massive parallel computing entails idle process time in multi-core processors or distributed computing devices as up to 80% of total computation time, owing to the synchronization of the data. Thus, there is a trend toward relaxing such a restriction on synchronization penalty to overcome this bottleneck problem. This dissertation presents a synchronous computing algorithms as a key solution to Leverage the computing performance to the maximum capabilities. The price to Pay for adopting the asynchronous computing algorithms is, however, unpredictability of the solution due to the randomness in the behavior of asynchrony. In this dissertation, the switched system is employed to model the characteristics of the asynchrony in parallel computing, enabling analysis of the asynchronous algorithm. Particularly, the analysis will be performed for massively parallel asynchronous numerical algorithms implemented on 1D heat equation and large-scale asynchronous distributed quadratic programming problems. As another case study, this switched system is also implemented on the stability analysis of large-scaled is tribute networked control systems (DNCS) having random communication delays. For these problems, the convergence or stability analysis is carried out by the switched system framework. One of major concerns when adopting the switched system framework for analysis of these systems is the scalability issues associated with extremely large switching mode numbers. Due to the massive parallelism or large-scale distributed nodes, the switching mode numbers are beyond counting, leading to the computational intractability. The proposed methods are developed targeting the settlement of this scalability issue, which inevitably takes place in adopting the switched system framework. Thus, the primary emphasis of this dissertation is placed on the mathematical development of computationally efficient tools, particularly for analysis of the large-scale asynchronous switched dynamical system, which has broad applications including massively parallel asynchronous numerical algorithms to solve ODE/PDE problems, distributed optimization problems, and large-scale DNCS with random communication delays

Hybrid methodology for Markovian epidemic models

In this thesis, we introduce a hybrid discrete-continuous approach suitable for analysing a wide range of epidemiological models, and an approach for improving parameter estimation from data describing the early stages of an outbreak. We restrict our attention to epidemiological models with continuous-time Markov chain (CTMC) dynamics, a ubiquitous framework also commonly used for modelling telecommunication networks, chemical reactions and evolutionary genetics. We introduce our methodology in the framework of the well-known Susceptible–Infectious–Removed (SIR) model, one of the simplest approaches for describing the spread of an infectious disease. We later extend it to a variant of the Susceptible–Exposed–Infectious– Removed (SEIR) model, a generalisation of the SIR CTMC that is more realistic for modelling the initial stage of many outbreaks. Compartmental CTMC models are attractive due to their stochastic individual-to-individual representation of disease transmission. This feature is particularly important when only a small number of infectious individuals are present, during which stage the probability of epidemic fade out is considerable. Unfortunately, the simple SIR CTMC has a state space of order N², where N is the size of the population being modelled, and hence computational limits are quickly reached as N increases. There are a number of approaches towards dealing with this issue, most of which are founded on the principal of restricting one’s attention to the dynamics of the CTMC on a subset of its state space. However, two highly-efficient approaches published in 1970 and 1971 provide a promising alternative to these approaches. The fluid limit [Kurtz, 1970] and diffusion limit [Kurtz, 1971] are large-population approximations of a particular class of CTMC models which approximate the evolution of the underlying CTMC by a deterministic trajectory and a Gaussian diffusion process, respectively. These large-population approximations are governed by a compact system of ordinary differential equations and are suitably accurate so long as the underlying population is sufficiently large. Unfortunately, they become inaccurate if the population of at least one compartment of the underlying CTMC is close to an absorbing boundary, such as during the initial stages of an outbreak. It follows that a natural approach to approximating a CTMC model of a large population is to adopt a hybrid framework, whereby CTMC dynamics are utilised during the initial stages of the outbreak and a suitable large-population approximation is utilised otherwise. In the framework of the SIR CTMC, we present a hybrid fluid model and a hybrid diffusion model which utilise CTMC dynamics while the number of infectious individuals is low and otherwise utilises the fluid limit and the diffusion limit, respectively. We illustrate the utility of our hybrid methodology in computing two key quantities, the distribution of the duration of the outbreak and the distribution of the final size of the outbreak. We demonstrate that the hybrid fluid model provides a suitable approximation of the distribution of the duration of the outbreak and the hybrid diffusion model provides a suitable approximation of the distribution of the final size of the outbreak. In addition, we demonstrate that our hybrid methodology provides a substantial advantage in computational-efficiency over the original SIR CTMC and is superior in accuracy to similar hybrid large-population approaches when considering mid-sized populations. During the initial stages of an outbreak, calibrating a model describing the spread of the disease to the observed data is fundamental to understanding and potentially controlling the disease. A key factor considered by public health officials in planning their response to an outbreak is the transmission potential of the disease, a factor which is informed by estimates of the basic reproductive number, R₀, defined as the average number of secondary cases resulting from a single infectious case in a naive population. However, it is often the case that estimates of R₀ based on data from the initial stages of an outbreak are positively biased. This bias may be the result of various features such as the geography and demography of the outbreak. However, a consideration which is often overlooked is that the outbreak was not detected until such a time as it had established a considerable chain of transmissions, therefore effectively overcoming initial fade out. This is an important feature because the probability of initial fade out is often considerable, making the event that the outbreak becomes established somewhat unlikely. A straightforward way of accounting for this is to condition the model on a particular event, which models the disease overcoming initial fade out. In the framework of both the SIR CTMC and the SEIR CTMC we present a conditioned approach to estimating R₀ from data on the initial stages of an outbreak. For the SIR CTMC, we demonstrate that in certain circumstances, conditioning the model on effectively overcoming initial fade out reduces bias in estimates of R₀ by 0.3 on average, compared to the original CTMC model. Noting that the conditioned model utilises CTMC dynamics throughout, we demonstrate the flexibility of our hybrid methodology by presenting a conditioned hybrid diffusion approach for estimating R₀. We demonstrate that our conditioned hybrid diffusion approach still provides estimates of R₀ which exhibit less bias than under an unconditioned hybrid diffusion model, and that the diffusion methodology enables us to consider larger outbreaks then would have been computationally-feasible in the original conditioned CTMC framework. We demonstrate the flexibility of our conditioned hybrid approach by applying it to a variant of the SEIR CTMC and using it to estimate R₀ from a range of real outbreaks. In so doing, we utilise a truncation rule to ensure the initial CTMC dynamics are computationally-feasible.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 201

Vehicle Stability Control Considering the Driver-in-the-Loop

A driver‐in‐the‐loop modeling framework is essential for a full analysis of vehicle stability systems. In theory, knowing the vehicle’s desired path (driver’s intention), the problem is reduced to a standard control system in which one can use different methods to produce a (sub) optimal solution. In practice, however, estimation of a driver’s desired path is a challenging – if not impossible – task. In this thesis, a new formulation of the problem that integrates the driver and the vehicle model is proposed to improve vehicle performance without using additional information from the future intention of the driver. The driver’s handling technique is modeled as a general function of the road preview information as well as the dynamic states of the vehicle. In order to cover a variety of driving styles, the time‐ varying cumulative driver's delay and model uncertainties are included in the formulation. Given that for practical implementations, the driver’s future road preview data is not accessible, this information is modeled as bounded uncertainties. Subsequently, a state feedback controller is designed to counteract the negative effects of a driver’s lag while makes the system robust to modeling and process uncertainties. The vehicle’s performance is improved by redesigning the controller to consider a parameter varying model of the driver‐vehicle system. An LPV controller robust to unknown time‐varying delay is designed and the disturbance attenuation of the closed loop system is estimated. An approach is constructed to identify the time‐varying parameters of the driver model using past driving information. The obtained gains are clustered into several modes and the transition probability of switching between different driving‐styles (modes) is calculated. Based on this analysis, the driver‐vehicle system is modeled as a Markovian jump dynamical system. Moreover, a complementary analysis is performed on the convergence properties of the mode‐dependent controller and a tighter estimation for the maximum level of disturbance rejection of the LPV controller is obtained. In addition, the effect of a driver’s skills in controlling the vehicle while the tires are saturated is analyzed. A guideline for analysis of the nonlinear system performance with consideration to the driver’s skills is suggested. Nonlinear controller design techniques are employed to attenuate the undesirable effects of both model uncertainties and tire saturation

Air Traffic Control

Improving air traffic control and air traffic management is currently one of the top priorities of the global research and development agenda. Massive, multi-billion euro programs like SESAR (Single European Sky ATM Research) in Europe and NextGen (Next Generation Air Transportation System) in the United States are on their way to create an air transportation system that meets the demands of the future. Air traffic control is a multi-disciplinary field that attracts the attention of many researchers, ranging from pure mathematicians to human factors specialists, and even in the legal and financial domains the optimization and control of air transport is extensively studied. This book, by no means intended to be a basic, formal introduction to the field, for which other textbooks are available, includes nine chapters that demonstrate the multi-disciplinary character of the air traffic control domain

Linear robust H-infinity stochastic control theory on the insurance premium-reserve processes

This thesis deals with the stability analysis of linear discrete-time premium-reserve (P-R) systems in a stochastic framework. Such systems are characterised by a mixture of the premium pricing process and the medium- and long- term stability in the accumulated reserve (surplus) policy, and they play a key role in the modern actuarial literature. Although the mathematical and practical analysis of P-R systems is well studied and motivated, their stability properties have not been studied thoughtfully and they are restricted in a deterministic framework. In Engineering, during the last three decades, many useful techniques are developed in linear robust control theory. This thesis is the first attempt to use some useful tools from linear robust control theory in order to analyze the stability of these classical insurance systems. Analytically, in this thesis, P-R systems are first formulated with structural properties such that time-varying delays, random disturbance and parameter uncertainties. Then as an extension of the previous literature, the results of stabilization and the robust H-infinity control of P-R systems are modelled in stochastic framework. Meanwhile, the risky investment impact on the P-R system stability condition is shown. In this approach, the potential effects from changes in insurer's investment strategy is discussed. Next we develop regime switching P-R systems to describe the abrupt structural changes in the economic fundamentals as well as the periodic switches in the parameters. The results for the regime switching P-R system are illustrated by means of two different approaches: markovian and arbitrary regime switching systems. Finally, we show how robust guaranteed cost control could be implemented to solve an optimal insurance problem. In each chapter, Linear Matrix Inequality (LMI) sufficient conditions are derived to solve the proposed sub-problems and numerical examples are given to illustrate the applicability of the theoretical findings