Fabio Pasqualetti

Attack Detection and Identification in Cyber-Physical Systems

Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial control processes, and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. In this paper: (i) we propose a mathematical framework for cyber-physical systems, attacks, and monitors; (ii) we characterize fundamental monitoring limitations from system-theoretic and graph-theoretic perspectives; and (ii) we design centralized and distributed attack detection and identification monitors. Finally, we validate our findings through compelling examples.

Consensus Computation in Unreliable Networks: A System Theoretic Approach

This paper addresses the problem of ensuring trustworthy computation in a linear consensus network. A solution to this problem is relevant for several tasks in multi-agent systems including motion coordination, clock synchronization, and cooperative estimation. In a linear consensus network, we allow for the presence of misbehaving agents, whose behavior deviate from the nominal consensus evolution. We model misbehaviors as unknown and unmeasurable inputs affecting the network, and we cast the misbehavior detection and identification problem into an unknown-input system theoretic framework. We consider two extreme cases of misbehaving agents, namely faulty (non-colluding) and malicious (Byzantine) agents. First, we characterize the set of inputs that allow misbehaving agents to affect the consensus network while remaining undetected and/or unidentified from certain observing agents. Second, we provide worst-case bounds for the number of concurrent faulty or malicious agents that can be detected and identified. Precisely, the consensus network needs to be 2k+1 (resp. k+1) connected for k malicious (resp. faulty) agents to be generically detectable and identifiable by every well behaving agent. Third, we quantify the effect of undetectable inputs on the final consensus value. Fourth, we design three algorithms to detect and identify misbehaving agents. The first and the second algorithm apply fault detection techniques, and affords complete detection and identification if global knowledge of the network is available to each agent, at a high computational cost. The third algorithm is designed to exploit the presence in the network of weakly interconnected subparts, and provides local detection and identification of misbehaving agents whose behavior deviates more than a threshold, which is quantified in terms of the interconnection structure.

Controllability Metrics, Limitations and Algorithms for Complex Networks

This paper studies the problem of controlling complex networks, i.e., the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem, 1) we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, 2) we derive bounds based on the system dynamics (network topology and weights) to characterize the tradeoff between the control energy and the number of control nodes, and 3) we propose an open-loop control strategy with performance guarantees. In our strategy, we select control nodes by relying on network partitioning, and we design the control input by leveraging optimal and distributed control techniques. Our findings show several control limitations and properties. For instance, for Schur stable and symmetric networks: 1) if the number of control nodes is constant, then the control energy increases exponentially with the number of network nodes; 2) if the number of control nodes is a fixed fraction of the network nodes, then certain networks can be controlled with constant energy independently of the network dimension; and 3) clustered networks may be easier to control because, for sufficiently many control nodes, the control energy depends only on the controllability properties of the clusters and on their coupling strength. We validate our results with examples from power networks, social networks and epidemics spreading.

Controllability of structural brain networks

Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behaviour. However, fundamental principles constraining these dynamic network processes have remained elusive. Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. Our results suggest that densely connected areas, particularly in the default mode system, facilitate the movement of the brain to many easily reachable states. Weakly connected areas, particularly in cognitive control systems, facilitate the movement of the brain to difficult-to-reach states. Areas located on the boundary between network communities, particularly in attentional control systems, facilitate the integration or segregation of diverse cognitive systems. Our results suggest that structural network differences between cognitive circuits dictate their distinct roles in controlling trajectories of brain network function.

Cyber-physical attacks in power networks: Models, fundamental limitations and monitor design

Future power networks will be characterized by safe and reliable functionality against physical and cyber attacks. This paper proposes a unified framework and advanced monitoring procedures to detect and identify network components malfunction or measurements corruption caused by an omniscient adversary. We model a power system under cyber-physical attack as a linear time-invariant descriptor system with unknown inputs. Our attack model generalizes the prototypical stealth, (dynamic) false-data injection and replay attacks. We characterize the fundamental limitations of both static and dynamic procedures for attack detection and identification. Additionally, we design provably-correct (dynamic) detection and identification procedures based on tools from geometric control theory. Finally, we illustrate the effectiveness of our method through a comparison with existing (static) detection algorithms, and through a numerical study.

On Cooperative Patrolling: Optimal Trajectories, Complexity Analysis, and Approximation Algorithms

The subject of this paper is the patrolling of an environment with the aid of a team of autonomous agents. We consider both the design of open-loop trajectories with optimal properties and of distributed control laws converging to optimal trajectories. As performance criteria, the refresh time and the latency are considered, i.e., respectively, time gap between any two visits of the same region and the time necessary to inform every agent about an event occurred in the environment. We associate a graph with the environment, and we study separately the case of a chain, tree, and cyclic graph. For the case of chain graph, we first describe a minimum refresh time and latency team trajectory and propose a polynomial time algorithm for its computation. Then, we describe a distributed procedure that steers the robots toward an optimal trajectory. For the case of tree graph, a polynomial time algorithm is developed for the minimum refresh time problem, under the technical assumption of a constant number of robots involved in the patrolling task. Finally, we show that the design of a minimum refresh time trajectory for a cyclic graph is NP-hard, and we develop a constant factor approximation algorithm.

Control-Theoretic Methods for Cyberphysical Security: Geometric Principles for Optimal Cross-Layer Resilient Control Systems

Cyberphysical systems integrate physical processes, computational resources, and communication capabilities. Cyberphysical systems have permeated modern society, becoming prevalent in many domains, including energy production, health care, and telecommunications. Examples of cyberphysical systems include sensor networks, industrial automation systems, and critical infrastructures such as transportation networks, power generation and distribution networks, water and gas distribution networks, and advanced manufacturing systems. The integration of cybertechnologies with physical processes increases system efficiencies and, at the same time, introduces vulnerabilities that undermine the reliability of critical infrastructures. As recently highlighted by the Maroochy water breach in March 2000 [1], multiple recent power blackouts in Brazil [2], the SQL Slammer worm attack on the Davis-Besse nuclear plant in January 2003 [3], the StuxNet computer worm in June 2010 [4], and various industrial security incidents [5], cyberphysical systems are prone to failures and attacks on their physical infrastructure and cyberattacks on their data management and communication layer [6], [7].

Optimally controlling the human connectome: the role of network topology

To meet ongoing cognitive demands, the human brain must seamlessly transition from one brain state to another, in the process drawing on different cognitive systems. How does the brain’s network of anatomical connections help facilitate such transitions? Which features of this network contribute to making one transition easy and another transition difficult? Here, we address these questions using network control theory. We calculate the optimal input signals to drive the brain to and from states dominated by different cognitive systems. The input signals allow us to assess the contributions made by different brain regions. We show that such contributions, which we measure as energy, are correlated with regions’ weighted degrees. We also show that the network communicability, a measure of direct and indirect connectedness between brain regions, predicts the extent to which brain regions compensate when input to another region is suppressed. Finally, we identify optimal states in which the brain should start (and finish) in order to minimize transition energy. We show that the optimal target states display high activity in hub regions, implicating the brain’s rich club. Furthermore, when rich club organization is destroyed, the energy cost associated with state transitions increases significantly, demonstrating that it is the richness of brain regions that makes them ideal targets.

Stimulation-Based Control of Dynamic Brain Networks

The ability to modulate brain states using targeted stimulation is increasingly being employed to treat neurological disorders and to enhance human performance. Despite the growing interest in brain stimulation as a form of neuromodulation, much remains unknown about the network-level impact of these focal perturbations. To study the system wide impact of regional stimulation, we employ a data-driven computational model of nonlinear brain dynamics to systematically explore the effects of targeted stimulation. Validating predictions from network control theory, we uncover the relationship between regional controllability and the focal versus global impact of stimulation, and we relate these findings to differences in the underlying network architecture. Finally, by mapping brain regions to cognitive systems, we observe that the default mode system imparts large global change despite being highly constrained by structural connectivity. This work forms an important step towards the development of personalized stimulation protocols for medical treatment or performance enhancement.

Cooperative Patrolling via Weighted Tours: Performance Analysis and Distributed Algorithms

This paper focuses on the problem of patrolling an environment with a team of autonomous agents. Given a set of strategically important locations (viewpoints) with different priorities, our patrolling strategy consists of 1) constructing a tour through the viewpoints, and 2) driving the robots along the tour in a coordinated way. As performance criteria, we consider the weighted refresh time, i.e., the longest time interval between any two visits of a viewpoint, weighted by the viewpoints priority. We consider the design of both optimal trajectories and distributed control laws for the robots to converge to optimal trajectories. First, we propose a patrolling strategy and we characterize its performance as a function of the environment and the viewpoints priorities. Second, we restrict our attention to the problem of patrolling a nonintersecting tour, and we describe a team trajectory with minimum weighted refresh time. Third, for the tour patrolling problem and for two distinct communication scenarios, namely the Passing and the Neighbor-Broadcast communication models, we develop distributed algorithms to steer the robots toward a minimum weighted refresh time team trajectory. Finally, we show the effectiveness and robustness of our control algorithms via simulations and experiments.