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Choice-based conjoint experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. This method involves the design of profiles on the basis of attributes specified at certain levels. Respondents are presented sets of profiles called choice sets, and asked to select the one they consider best. Sets with no dominating or dominated profiles are called Pareto Optimal sets. Information Per Profile (IPP) is used as an optimality criteria to compare designs with different numbers of profiles. For a 2^n experiment, the optimality of connected main effects plans based on two consecutive choice sets, Sl and Sl+1, has been examined in the literature. In this thesis we examine the IPP of both consecutive and non-consecutive choice sets and show that IPP can be maximized under certain conditions. We show that non-consecutive choice sets have higher IPP than consecutive choice sets for n ≥ 4. We also examine the optimality of connected first-order-interaction designs based on three choice sets and show that non-consecutive choice sets have higher IPP than consecutive choice sets under certain conditions. Further, we examine the D-, A- and E-optimality of consecutive and non-consecutive PO choice sets with maximum IPP. Finally, we consider 3^n choice experiments. We look for the optimal PO choice sets and examine their IPP, D-, A- and E-optimality, as well as comparing consecutive and non-consecutive choice sets. / Statistics

Graphical summaries are becoming important tools for evaluating designs. The need to compare designs in term of their prediction variance properties advanced this development. A recent graphical tool, the Fraction of Design Space plot, is useful to calculate the fraction of the design space where the scaled prediction variance (SPV) is less than or equal to a given value. In this dissertation we adapt FDS plots, to study three specific design problems: robustness to model assumptions, robustness to measurement error and design properties for generalized linear models (GLM). This dissertation presents a graphical method for examining design robustness related to the SPV values using FDS plots by comparing designs across a number of potential models in a pre-specified model space. Scaling the FDS curves by the G-optimal bounds of each model helps compare designs on the same model scale. FDS plots are also adapted for comparing designs under the GLM framework. Since parameter estimates need to be specified, robustness to parameter misspecification is incorporated into the plots. Binomial and Poisson examples are used to study several scenarios. The third section involves a special type of response surface designs, mixture experiments, and deals with adapting FDS plots for two types of measurement error which can appear due to inaccurate measurements of the individual mixture component amounts. The last part of the dissertation covers mixture experiments for the GLM case and examines prediction properties of mixture designs using the adapted FDS plots. / Ph. D.

This dissertation presents a class of utility accrual scheduling and synchronization algorithms for dynamic, single and multiprocessor real-time systems. Dynamic real-time systems operate in environments with run-time uncertainties including those on activity execution times and arrival behaviors. We consider the time/utility function (or TUF) timing model for specifying application time constraints, and the utility accrual (or UA) timeliness optimality criteria of satisfying lower bounds on accrued activity utility, and maximizing the total accrued utility. Efficient TUF/UA scheduling algorithms exist for single processors---e.g., the Resource-constrained Utility Accrual scheduling algorithm (RUA), and the Dependent Activity Scheduling Algorithm (DASA). However, they all use lock-based synchronization. To overcome shortcomings of lock-based (e.g., serialized object access, increased run-time overhead, deadlocks), we consider non-blocking synchronization including wait-free and lock-free synchronization. We present a buffer-optimal, scheduler-independent wait-free synchronization protocol (the first such), and develop wait-free versions of RUA and DASA. We also develop their lock-free versions, and upper bound their retries under the unimodal arbitrary arrival model. The tradeoff between wait-free, lock-free, and lock-based is fundamentally about their space and time costs. Wait-free sacrifices space efficiency in return for no additional time cost, as opposed to the blocking time of lock-based and the retry time of lock-free. We show that wait-free RUA/DASA outperform lock-based RUA/DASA when the object access times of both approaches are the same, e.g., when the shared data size is so large that the data copying process dominates the object access time of two approaches. We derive lower bounds on the maximum accrued utility that is possible with wait-free over lock-based. Further, we show that when maximum sojourn times under lock-free RUA/DASA is shorter than under lock-based, it is a necessary condition that the object access time of lock-free is shorter than that of lock-based. We also establish the maximum increase in activity utility that is possible under lock-free and lock-based. Multiprocessor TUF/UA scheduling has not been studied in the past. For step TUFs, periodic arrivals, and under-loads, we first present a non-quantum-based, optimal scheduling algorithm called Largest Local Remaining Execution time-tasks First (or LLREF) that yields the optimum total utility. We then develop another algorithm for non-step TUFs, arbitrary arrivals, and overloads, called the global Multiprocessor Utility Accrual scheduling algorithm (or gMUA). We show that gMUA lower bounds each activity's accrued utility, as well as the system-wide, total accrued utility. We consider lock-based, lock-free, and wait-free synchronization under LLREF and gMUA. We derive LLREF's and gMUA's minimum-required space cost for wait-free synchronization using our space-optimal wait-free algorithm, which also applies for multiprocessors. We also develop lock-free versions of LLREF and gMUA with bounded retries. While the tradeoff between wait-free LLREF/gMUA versus lock-based LLREF/gMUA is similar to that for the single processor case, that between lock-free LLREF/gMUA and lock-based LLREF/gMUA hinges on the cost of the lock-free retry, blocking time under lock-based, and the operating system overhead. / Ph. D.

Autonomous cyber-physical systems (CPSs) such as autonomous connected vehicles (ACVs), unmanned aerial vehicles (UAVs), critical infrastructure (CI), and the Internet of Things (IoT) will be essential to the functioning of our modern economies and societies. Therefore, maintaining the autonomy of CPSs as well as their stability, robustness, and security (SRS) in face of exogenous and disruptive events is a critical challenge. In particular, it is crucial for CPSs to be able to not only operate optimally in the vicinity of a normal state but to also be robust and secure so as to withstand potential failures, malfunctions, and intentional attacks. However, to evaluate and improve the SRS of CPSs one must overcome many technical challenges such as the unpredictable behavior of a CPS's cyber-physical environment, the vulnerability to various disruptive events, and the interdependency between CPSs. The primary goal of this dissertation is, thus, to develop novel foundational analytical tools, that weave together notions from machine learning, game theory, and control theory, in order to study, analyze, and optimize SRS of autonomous CPSs. Towards achieving this overarching goal, this dissertation led to several major contributions. First, a comprehensive control and learning framework was proposed to thwart cyber and physical attacks on ACV networks. This framework brings together new ideas from optimal control and reinforcement learning (RL) to derive a new optimal safe controller for ACVs in order to maximize the street traffic flow while minimizing the risk of accidents. Simulation results show that the proposed optimal safe controller outperforms the current state of the art controllers by maximizing the robustness of ACVs to physical attacks. Furthermore, using techniques from convex optimization and deep RL a joint trajectory and scheduling policy is proposed in UAV-assisted networks that aims at maintaining the freshness of ground node data at the UAV. The analytical and simulation results show that the proposed policy can outperform policies such discretized state RL and value-based methods in terms of maximizing the freshness of data. Second, in the IoT domain, a novel watermarking algorithm, based on long short term memory cells, is proposed for dynamic authentication of IoT signals. The proposed watermarking algorithm is coupled with a game-theoretic framework so as to enable efficient authentication in massive IoT systems. Simulation results show that using our approach, IoT messages can be transmitted from IoT devices with an almost 100% reliability. Next, a brainstorming generative adversarial network (BGAN) framework is proposed. It is shown that this framework can learn to generate real-looking data in a distributed fashion while preserving the privacy of agents (e.g. IoT devices, ACVs, etc). The analytical and simulation results show that the proposed BGAN architecture allows heterogeneous neural network designs for agents, works without reliance on a central controller, and has a lower communication over head compared to other state-of-the-art distributed architectures. Last, but not least, the SRS challenges of interdependent CI (ICI) are addressed. Novel game-theoretic frameworks are proposed that allow the ICI administrator to assign different protection levels on ICI components to maximizing the expected ICI security. The mixed-strategy Nash of the games are derived analytically. Simulation results coupled with theoretical analysis show that, using the proposed games, the administrator can maximize the security level in ICI components. In summary, this dissertation provided major contributions across the areas of CPSs, machine learning, game theory, and control theory with the goal of ensuring SRS across various domains such as autonomous vehicle networks, IoT systems, and ICIs. The proposed approaches provide the necessary fundamentals that can lay the foundations of SRS in CPSs and pave the way toward the practical deployment of autonomous CPSs and applications. / Doctor of Philosophy / In order to deliver innovative technological services to their residents, smart cities will rely on autonomous cyber-physical systems (CPSs) such as cars, drones, sensors, power grids, and other networks of digital devices. Maintaining stability, robustness, and security (SRS) of those smart city CPSs is essential for the functioning of our modern economies and societies. SRS can be defined as the ability of a CPS, such as an autonomous vehicular system, to operate without disruption in its quality of service. In order to guarantee SRS of CPSs one must overcome many technical challenges such as CPSs' vulnerability to various disruptive events such as natural disasters or cyber attacks, limited resources, scale, and interdependency. Such challenges must be considered for CPSs in order to design vehicles that are controlled autonomously and whose motion is robust against unpredictable events in their trajectory, to implement stable Internet of digital devices that work with a minimum communication delay, or to secure critical infrastructure to provide services such as electricity, gas, and water systems. The primary goal of this dissertation is, thus, to develop novel foundational analytical tools, that weave together notions from machine learning, game theory, and control theory, in order to study, analyze, and optimize SRS of autonomous CPSs which eventually will improve the quality of service provided by smart cities. To this end, various frameworks and effective algorithms are proposed in order to enhance the SRS of CPSs and pave the way toward the practical deployment of autonomous CPSs and applications. The results show that the developed solutions can enable a CPS to operate efficiently while maintaining its SRS. As such, the outcomes of this research can be used as a building block for the large deployment of smart city technologies that can be of immense benefit to tomorrow's societies.

Simulation, design, and control of dynamical systems play an important role in numerous scientific and industrial tasks. The need for detailed models leads to large-scale dynamical systems, posing tremendous computational difficulties when employed in numerical simulations. In order to overcome these challenges, we perform model reduction, replacing the large-scale dynamics with high-fidelity reduced representations. There exist a plethora of methods for reduced order modeling of linear systems, including the Iterative Rational Krylov Algorithm (IRKA), Balanced Truncation (BT), and Hankel Norm Approximation. However, these methods generally target stable systems and the approximation is performed over an infinite time horizon. If we are interested in a finite horizon reduced model, we utilize techniques such as Time-limited Balanced Truncation (TLBT) and Proper Orthogonal Decomposition (POD). In this dissertation we establish interpolation-based optimality conditions over a finite horizon and develop an algorithm, Finite Horizon IRKA (FHIRKA), that produces a locally optimal reduced model on a specified time-interval. Nonetheless, the quantities being interpolated and the interpolant are not the same as in the infinite horizon case. Numerical experiments comparing FHIRKA to other algorithms further support our theoretical results. Next, we discuss model reduction for nonlinear dynamical systems. For models with unstructured nonlinearities, POD is the method of choice. However, POD is input dependent and not optimal with respect to the output. Thus, we use operator splitting to integrate the best features of system theoretic approaches with trajectory based methods such as POD in order to mitigate the effect of the control inputs for the approximation of nonlinear dynamical systems. We reduce the linear terms with system theoretic methods and the nonlinear terms terms via POD. Evolving the linear and nonlinear terms separately yields the reduced operator splitting solution. We present an error analysis for this method, as well as numerical results that illustrate the effectiveness of our approach. While in this dissertation we only pursue the splitting of linear and nonlinear terms, this approach can be implemented with Quadratic Bilinear IRKA or Balanced Truncation for Quadratic Bilinear systems to further diminish the input dependence of the reduced order modeling. / Doctor of Philosophy / Simulation, design, and control of dynamical systems play an important role in numerous scientific and industrial tasks such as signal propagation in the nervous system, heat dissipation, electrical circuits and semiconductor devices, synthesis of interconnects, prediction of major weather events, spread of fires, fluid dynamics, machine learning, and many other applications. The need for detailed models leads to large-scale dynamical systems, posing tremendous computational difficulties when applied in numerical simulations. In order to overcome these challenges, we perform model reduction, replacing the large-scale dynamics with high-fidelity reduced representations. Reduced order modeling helps us to avoid the outstanding burden on computational resources. Numerous model reduction techniques exist for linear models over an infinite horizon. However, in practice we usually are interested in reducing a model over a specific time interval. In this dissertation, given a reduced order, we present a method that finds the best local approximation of a dynamical system over a finite horizon. We present both theoretical and numerical evidence that supports the proposed method. We also develop an algorithm that integrates operator splitting with model reduction to solve nonlinear models more efficiently while preserving a high level of accuracy.

本研究旨在建立廣義線性模式下之D-與A-最適設計(optimal designs)，並依不同處理結構(treatment structure)分成完全隨機設計(completely randomized design, CRD)與隨機集區設計(randomized block design, RBD)兩部分探討。 根據完全隨機設計所推導出之行列式的性質與理論結果，我們首先提出一個能快速大幅限縮尋找D-最適正合(exact)設計範圍的演算法。解析解的部分，則從將v個處理的變異數分為兩類出發，建立其D-最適近似(approximate)設計，並由此發現 (1) 各水準對應之樣本最適配置的上下界並非與水準間不同變異有關，而是與有多少處理之變異相同有關；(2) 即使是變異很大的處理，也必須分配觀察值，始能極大化行列式值。此意味著當v較大時，均分應不失為一有效率(efficient)的設計。至於正合設計，我們僅能得出某一處理特別大或特別小時的D-最適設計，並舉例說明求不出一般解的原因。 除此之外，我們亦求出當三個處理的變異數皆不同時之D-最適近似設計，以及v個處理皆不同時之A-最適近似設計。 至於最適隨機集區設計的建立，我們的重點放在v=2及v=3的情形，並假設集區樣本數(block size)為給定。當v=2時，各集區對應之行列式值不受其他集區的影響，故僅需依照完全隨機設計之所得，將各集區之行列式值分別最佳化，即可得出D-與A-最適設計。值得一提的是，若進一步假設各集區中兩處理變異的比例(>1)皆相同，且集區大小皆相同，則將各處理的「近似設計下最適總和」取最接近的整數，再均分給各集區，其結果未必為最適設計。當v=3時，即使只有2個集區，行列式也十分複雜，我們目前僅能證明當集區內各處理的變異相同時(不同集區之處理變異可不同)，均分給定之集區樣本數為D-最適設計。當集區內各處理的變異不全相同時，我們僅能先以2個集區為例，類比完全隨機設計的性質，舉例猜想當兩集區中處理之變異大小順序相同時，各處理最適樣本配置的多寡亦與變異大小呈反比。由於本研究對處理與集區兩者之效應假設為可加，因此可合理假設集區中處理之變異大小順序相同。 / The problem of finding D- and A-optimal designs for the zero- and one-way elimination of heterogeneity under generalized linear models is considered. Since GLM designs rely on the values of parameters to be estimated, our strategy is to employ the locally optimal designs. For the zero-way elimination model, a theorem-based algorithm is proposed to search for the D-optimal exact designs. A formula for the construction of D-optimal approximate design when values of unknown parameters are split into two, with respective sizes m and v-m, are derived. Analytic solutions provided to the exact counterpart, however, are restricted to the cases when m=1 and m=v-1. An example is given to explain the problem involved. On the other hand, the upper bound and lower bound of the optimal number of replicates per treatment are proved dependent on m, rather than the unknown parameters. These bounds imply that designs having as equal number of replications for each treatment as possible are efficient in D-optimality. In addition, a D-optimal approximate design when values of unknown parameters are divided into three groups is also obtained. A closed-form expression for an A-optimal approximate design for comparing arbitrary v treatments is given. For the one-way elimination model, our focus is on studying the D-optimal designs for v=2 and v=3 with each block size given. The D- and A-optimality for v=2 can be achieved by assigning units proportional to square root of the ratio of two variances, which is larger than 1, to the treatment with smaller variance in each block separately. For v=3, the structure of determinant is much more complicated even for two blocks, and we can only show that, when treatment variances are the same within a block, design having equal number of replicates as possible in each block is a D-optimal block design. Some numerical evidences conjecture that a design satisfying the condition that the number of replicates are inversely proportional to the treatment variances per block is better in terms of D-optimality, as long as the ordering of treatment variances are the same across blocks, which is reasonable for an additive model as we assume.