Reverse engineering the brain holds the promise to overhaul the quality of life of human beings and vastly benefit mankind. Further advances towards this goal will lead to the reversal of cognitive decline, the creation of pioneering neural prostheses, the establishments of novel treatments for neurological disorders, and the development of human augmentation methods. This dissertation presents a cross-disciplinary approach to the study of the structure-function relationship in neural systems. Specifically, we study the brain as a dynamical system that obeys network-wide principles, and address three foundational challenges by using mathematically grounded methods that lie at the intersection of control theory, network science, and neuroscience.

First, through the application of control and graph-theoretic paradigms, we investigate how the spatial organization of anatomical brain network components governs and constrains its complex dynamical behaviors. The first chapters are dedicated to the study of structural brain networks – that is, empirically reconstructed large-scale networks that describe the interconnection scheme between different brain regions. We rigorously reveal that brain state transitions can be controlled by a single region, and that structural brain networks possess distinct controllability profiles with respect to random networks of the same size.

Second, we address the modeling and analysis of neural activity synchronization across different brain areas – which can be described by functional brain networks. To do so, we juxtapose a bottom-up approach and a top-down approach. In the former, we utilize data-driven dynamical models to reveal that the synchronization of brain network dynamics is resilient to data heterogeneity, thus supporting the utilization of large heterogeneous repositories of brain recordings. In the latter, we abstract rhythmic activity of a neural system as the output of a network of diffusively coupled oscillators, and derive prescriptive conditions for the emergence of cluster synchronization. Such a phenomenon emerges when different groups of synchronized components coexist in a network, and regulates the functional interactions among network components.

Third and final, we build upon our previous findings and take aim at the tantalizing idea of controlling the synchronization of brain dynamics through minimally invasive local interventions. We derive a method to optimally intervene on the structural network parameters to achieve desired cluster-synchronized trajectories and, thus, prescribed functional interactions. Additionally, we show that our synchronization-based framework is robust to mismatches in network parameters, and validate it using a realistic neurovascular model to simulate neural activity and functional connectivity in the human brain.

Crowdsourcing is an emerging method for efficient task distribution and completion. With multiple tasks at hand, it is considerably faster to divide these tasks to multiple operators than to queue them all onto one person. A single human agent can arguably only finish one problem at any single point in time, assuming the tasks do not overlap in their description. This method is useful for real-world applications as many complex systems with a variety of tasks could be solved more efficiently. Due to pulling agents from a randomized crowd; however, we are faced with the problem of the quality of the work of each agent utilized. Efficiency will always go up the more tasks we distribute to a random crowd, but the performance or success rate may go down depending on the quality of the crowd. We then consider the question, how do we optimize various users from a crowd? In this paper, we focus on a single exogenous human factor, fatigue, and the expertise of the agents to approximate the probability of an erroneous decision from the agents. We study various fatigue models, using the Three-Process Model to compare with our model. We will also present a simplified model to predict fatigue and approximate our agents' performance due to task load and compare with current models. Considering these fatigue models, performance values of agents will be calculated to maximize our success rate depending on their task allocation. The expertise of these agents are also important in analyzing the quality of their work. We model the expertise coefficient of our agents in two fashions: a single constant value throughout the system and a dynamic value based on the drift diffusion model in optimal decision making. The studies regarding a dynamic expertise coefficient are to be completed in detail during future works. We then provide an optimal control approach using dynamic linear systems. Our model is optimized by Pontryagin's Maximum Principle from optimal control theory, allowing for analysis as a continuous function. In this thesis, the models of study are also extended into the discrete time model where we provide a new optimal policy. At the end of our thesis, we will provide an analysis of our performance model and present its success rate due to optimal task allocation.

Modern dynamical systems are large and inevitably comprise dierent subsystems

that are often integrated with cyber (computation and communication) components. The

applications of these systems are far reaching, ranging from power and water networks, to

telecommunication and transportation systems etc. Recently, researchers and hackers have

shown that these systems are vulnerable to attacks targeting their physical infrastructure

or the signals exchanged between the physical and cyber layers. Given the interconnected

nature of dynamical systems, and the fact that each subsystem usually has only partial

knowledge or measurements of other interconnected units, the security question arises as

to whether sophisticated attackers can hide their action to the individual subsystems while

inducing system-wide critical perturbations.

This thesis addresses problems concerning security of interconnected systems that

are subject to random (stochastic) disturbances. Our contribution is twofold. First, we

investigate whether, and to what extent, coordination among different subsystems and

knowledge of the global system dynamics is necessary to detect attacks in interconnected systems. We consider centralized and decentralized detectors, which dier primarily in

their knowledge of the system model, and characterize the performance of the two detectors

and show that, depending on the system and attack parameters, each of the detectors can

outperform the other. Hence, it may be possible for the decentralized detector to outperform

its centralized counterpart, despite having less information about the system dynamics. We

provide an explanation for this counter-intuitive result and illustrate our results through

simulations. Second, we study an attack design problem for interconnected systems where

the attacker compromises a subsystem at each time, based on a pre-computed probabilistic

rule. The goal of the attacker is to degrade the system performance, which is measured based

on a quadratic function of the system state, while remaining undetected from a centralized

detector. We show that selectively compromising dierent subsystems over time increases

the severity of the attacks with respect to compromising a fixed subsystem at each time.

We study another related security problem for network systems, where changes

in the statistical properties of an input driving certain network nodes has to be detected

by remotely located sensors. To detect the changes, we associate a maximum-a-posteriori

detector for a given set of sensors, and study its detection performance as function of the

network topology, and the graphical distance between the input and sensor locations. We

derive conditions under which the detection performance obtained when sensors are located

on a network cut is not worse (resp. not better) than the performance obtained by measuring

all nodes of the subnetwork induced by the cut and not containing the input nodes. Our

results provide insights into the sensor placement from a detection-theoretic point of view.

Network systems model natural and engineered processes composed of groups of physical components that interact with the environment, and that are coupled with each other by means of an intricate communication network. Network systems have been widely adopted to model and understand many complex physical processes, ranging from stock markets in economics, transportation networks in engineering, to evolutionary processes in biology. A fundamental property of these systems is their robustness to contingencies, that is, the capability of operating effectively despite external perturbations, such as accidental component failures, malicious targeted attacks, or external disturbances. In this dissertation, we address four engineering problems concerning robustness in network systems.

First, we study robustness in highway transportation systems where travelers follow routing suggestions provided by modern navigation apps (such as GoogleMaps, Waze, Inrix, etc.). Navigation apps provide minimum-time routing directions to the travelers based on global and instantaneous congestion information, thus transforming the way users behave and impacting the aggregate system behavior. We propose and analyze new models to capture the routing decisions of app-informed travelers that are inspired from selection and learning mechanisms in biology. Our analysis and techniques are rigorous, and can be applied to any traffic network topology, independently of its size or interconnection patterns. Our findings demonstrate that among numerous favorable benefits, routing apps can introduce new undesirable congestion phenomena, and that appropriate information design will be necessary to ensure the robustness of modern traffic infrastructures. Second, we propose a set of robust control algorithms to optimize the operation of the signalized traffic intersections in an urban traffic network in order to guarantee system-level optimality. Our methods are computationally-tractable, outperform state-of-the-art intersection control policies, and are effective to reduce congestion in major cities, as demonstrated by our simulations for Manhattan, NY. Third, with a focus on networks with linear dynamics, we develop theories and tools to study the robustness of a network against changes in the the communication links. Our methods include both rigorous algebraic conditions and tractable numerical algorithms, and ultimately relate the robustness of a system to the graph-theoretical properties of the underlying network interconnection. Fourth, with an application focus to robotics, we tackle the problem of ensuring robust navigation despite maliciously-compromised localization sensors. Our methods rely on the nonlinear notion of zero dynamics, and unveil fundamental limitations for attack detection. More generally, our results demonstrate for the first time that the choice of inputs adopted for control affects the security of a dynamical system.

The traditional approach for the control of dynamical systems relies on the availability of a model describing the system to be controlled. Typically, a model is derived from first principles; however the feasibility of this strategy is threatened as the scope of controller design is expanding to increasingly complex domains. Alternatively, data can be used to identify a system's model when this is unavailable and challenging to derive from first principles. A pipeline for control design then becomes a two-step process: (i) use data to identify a model of the system, (ii) synthesize a controller for the identified model. Recently, there has been a growing interest in exploring control strategies for unmodelled systems that directly leverage data in one-step approach, with the expectation that this will improve the efficiency and performance of the overall process. The interest for this direct approach to data-driven control was a consequence of the streak of successes of machine learning for tasks such as classification, image generation and token prediction. Such a remarkable progress by the machine learning community came at the price of formality: in fact, a true understanding of the drawbacks and limitations of this modeling approach is missing. While failures might pose a minor risk in some consumer applications, these become unacceptable and potentially life-threatening in control applications. The challenge for modern data-driven control is therefore to capitalize on these advancements while grounding any result in a formal framework, where performance metrics, robustness concerns and system-theoretic properties are all first-class citizens.

This thesis introduces a comprehensive approach for designing controllers from data. Specifically, it formalizes a methodology that yields closed-form and robust solutions for a variety of control problems. Traditional control problems are re-examined through a data-driven lens, from establishing a system's observability, to designing optimal controllers for network systems. In practical terms, given a desired control objective and (possibly) noisy data from the system, the desired control action can be determined by feeding the data directly into the proposed expression, bypassing system identification. The result of this approach is a straightforward controller design technique with formally characterizable robustness bounds.

Global Navigation Satellite System (GNSS) is widely adopted in most applications requiring autonomous navigation, as it provides accurate measurements of a robot's position with limited hardware and computation requirements. Yet, recent studies and real world incidents have demonstrated that GNSS readings can be easily corrupted, for instance, by jamming the receiver unit or spoofing the transmitted measurements via unauthorized GNSS transmissions. In the presence of attacks, success of autonomous navigation is not guaranteed in most scenarios. In this paper we put forth the idea of planning a robot's trajectory and exploiting additional sensors to account and limit the effect of attacks against autonomous robots. In particular, we consider a robot equipped with a GNSS sensor and a Radio Signal Strength Indicator (RSSI) antenna, which provides the robot with an estimate of its distance to a radio station. We consider an attacker capable of arbitrarily spoofing the GNSS measurements and altering the robot's input commands. We analytically characterize the class of undetectable attacks, that is, the attack signals that alter the robot's nominal trajectory and that produce GNSS and RSSI measurements compatible with the robot's nominal trajectory. We quantify the largest perturbation induced by an undetectable attack, and we show how the robot's nominal trajectory should be designed to guarantee secure navigation in the presence of attacks. We illustrate our results through several numerical examples and experiments.