We propose the study of robustness measures for signal detection in non-stationary noise using differential geometric tools in conjunction with empirical distribution analysis. Our approach shows that the gradient can be viewed as a random variable and therefore used to generate sample densities allowing one to draw conclusions regarding the robustness. As an example, one can apply the geometric methodology to the detection of time varying deterministic signals in imperfectly known dependent nonstationary Gaussian noise. We also compare stationary to non-stationary noise and prove that robustness is barely reduced by admitting non-stationarity. In addition, we show that robustness decreases with larger sample sizes, but there is a convergence in this decrease for sample sizes greater than 14. We then move on to compare the effect on robustness for signal detection between non-Gaussian tail effects and residual dependency. The work focuses on robustness as applied to tail effects for the noise distribution, affecting discrete-time detection of signals in independent non-stationary noise. This approach makes use of the extension to the generalized Gaussian case allowing the comparison in robustness between the Gaussian and Laplacian PDF. The obtained results are contrasted with the influence of dependency on robustness for a fixed tail category and draws consequences on residual dependency versus tail uncertainty.

Cable robots are a type of robotic manipulator that has recently attracted interest for large workspace manipulation tasks. Cable robots are relatively simple in form, with multiple cables attached to a mobile platform or end-effector. The end-effector is manipulated by motors that can extend or retract the cables. Cable robots have many desirable characteristics, including low inertial properties, high payload-to-weight ratios, potentially vast workspaces, transportability, ease of disassembly/reassembly, reconfigurability and economical construction and maintenance. However, relatively few analytical tools are available for analyzing and designing these manipulators. This thesis focuses on expanding the existing theoretical framework for the design and analysis of cable robots in two areas: disturbance robustness and workspace generation. Underconstrained cable robots cannot resist arbitrary external disturbances acting on the end-effector. Thus a disturbance robustness measure for general underconstrained single-body and multi-body cable robots is presented. This measure captures the robustness of the manipulator to both static and impulsive disturbances. Additionally, a wrench-based method of analyzing cable robots has been developed and is used to formulate a method of generating the Wrench-Feasible Workspace of cable robots. This workspace consists of the set of all poses of the manipulator where a specified set of wrenches (force/moment combinations) can be exerted. For many applications the Wrench-Feasible Workspace constitutes the set of all usable poses. The concepts of robustness and workspace generation are then combined to introduce a new workspace: the Specified Robustness Workspace. This workspace consists of the set of all poses of the manipulator that meet or exceed a specified robustness value.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Caterina Scoglio / Critical infrastructures are repeatedly attacked by external triggers causing tremendous amount of damages. Any infrastructure can be studied using the powerful theory of complex networks. A complex network is composed of extremely large number of different elements that exchange commodities providing significant services. The main functions of complex networks can be damaged by different types of attacks and failures that degrade the network performance. These attacks and failures are considered as disturbing dynamics, such as the spread of viruses in computer networks, the spread of epidemics in social networks, and the cascading failures in power grids. Depending on the network structure and the attack strength, every network differently suffers damages and performance degradation. Hence, quantifying the robustness of complex networks becomes an essential task. In this dissertation, new metrics are introduced to measure the robustness of technological and social networks with respect to the spread of epidemics, and the robustness of power grids with respect to cascading failures. First, we introduce a new metric called the Viral Conductance ($VC_{SIS}$) to assess the robustness of networks with respect to the spread of epidemics that are modeled through the susceptible/infected/susceptible ($SIS$) epidemic approach. In contrast to assessing the robustness of networks based on a classical metric, the epidemic threshold, the new metric integrates the fraction of infected nodes at steady state for all possible effective infection strengths. Through examples, $VC_{SIS}$ provides more insights about the robustness of networks than the epidemic threshold. In addition, both the paradoxical robustness of Barab\'si-Albert preferential attachment networks and the effect of the topology on the steady state infection are studied, to show the importance of quantifying the robustness of networks. Second, a new metric $VC_$ is introduced to assess the robustness of networks with respect to the spread of susceptible/infected/recovered ($SIR$) epidemics. To compute $VC_$, we propose a novel individual-based approach to model the spread of $SIR$ epidemics in networks, which captures the infection size for a given effective infection rate. Thus, $VC_$ quantitatively integrates the infection strength with the corresponding infection size. To optimize the $VC_$ metric, a new mitigation strategy is proposed, based on a temporary reduction of contacts in social networks. The social contact network is modeled as a weighted graph that describes the frequency of contacts among the individuals. Thus, we consider the spread of an epidemic as a dynamical system, and the total number of infection cases as the state of the system, while the weight reduction in the social network is the controller variable leading to slow/reduce the spread of epidemics. Using optimal control theory, the obtained solution represents an optimal adaptive weighted network defined over a finite time interval. Moreover, given the high complexity of the optimization problem, we propose two heuristics to find the near optimal solutions by reducing the contacts among the individuals in a decentralized way. Finally, the cascading failures that can take place in power grids and have recently caused several blackouts are studied. We propose a new metric to assess the robustness of the power grid with respect to the cascading failures. The power grid topology is modeled as a network, which consists of nodes and links representing power substations and transmission lines, respectively. We also propose an optimal islanding strategy to protect the power grid when a cascading failure event takes place in the grid. The robustness metrics are numerically evaluated using real and synthetic networks to quantify their robustness with respect to disturbing dynamics. We show that the proposed metrics outperform the classical metrics in quantifying the robustness of networks and the efficiency of the mitigation strategies. In summary, our work advances the network science field in assessing the robustness of complex networks with respect to various disturbing dynamics.