arXiv subjects

Linda Bushnell

Publications and source records attributed to Linda Bushnell.

35 records · Page 2Linked to original sources

arXiv2019

Secure Control under Partial Observability with Temporal Logic Constraints

This paper studies the synthesis of control policies for an agent that has to satisfy a temporal logic specification in a partially observable environment, in the presence of an adversary. The interaction of the agent (defender) with the adversary is modeled as a partially observable stochastic game. The search for policies is limited to over the space of finite state controllers, which leads to a tractable approach to determine policies. The goal is to generate a defender policy to maximize satisfaction of a given temporal logic specification under any adversary policy. We relate the satisfaction of the specification in terms of reaching (a subset of) recurrent states of a Markov chain. We then present a procedure to determine a set of defender and adversary finite state controllers of given sizes that will satisfy the temporal logic specification. We illustrate our approach with an example.

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arXiv2019

Shape of the Cloak: Formal Analysis of Clock Skew-Based Intrusion Detection System in Controller Area Networks

This paper presents a new masquerade attack called the cloaking attack and provides formal analyses for clock skew-based Intrusion Detection Systems (IDSs) that detect masquerade attacks in the Controller Area Network (CAN) in automobiles. In the cloaking attack, the adversary manipulates the message inter-transmission times of spoofed messages by adding delays so as to emulate a desired clock skew and avoid detection. In order to predict and characterize the impact of the cloaking attack in terms of the attack success probability on a given CAN bus and IDS, we develop formal models for two clock skew-based IDSs, i.e., the state-of-the-art (SOTA) IDS and its adaptation to the widely used Network Time Protocol (NTP), using parameters of the attacker, the detector, and the hardware platform. To the best of our knowledge, this is the first paper that provides formal analyses of clock skew-based IDSs in automotive CAN. We implement the cloaking attack on two hardware testbeds, a prototype and a real vehicle (the University of Washington (UW) EcoCAR), and demonstrate its effectiveness against both the SOTA and NTP-based IDSs. We validate our formal analyses through extensive experiments for different messages, IDS settings, and vehicles. By comparing each predicted attack success probability curve against its experimental curve, we find that the average prediction error is within 3.0% for the SOTA IDS and 5.7% for the NTP-based IDS.

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arXiv2019

On the Structure and Computation of Random Walk Times in Finite Graphs

We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the convergence of Markov processes, as well as applications in control, machine learning, and social sciences. In this paper, we investigate the computational structure of the random walk times as a function of the set of target nodes, and find that the commute, hitting, and cover times all exhibit submodular structure, even in non-stationary random walks. We provide a unifying proof of this structure by considering each of these times as special cases of stopping times. We generalize our framework to walks in which the transition probabilities and target sets are jointly chosen to minimize the travel times, leading to polynomial-time approximation algorithms for choosing target sets. Our results are validated through numerical study.

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arXiv2018

A Game Theoretic Approach for Dynamic Information Flow Tracking to Detect Multi-Stage Advanced Persistent Threats

Advanced Persistent Threats (APTs) infiltrate cyber systems and compromise specifically targeted data and/or resources through a sequence of stealthy attacks consisting of multiple stages. Dynamic information flow tracking has been proposed to detect APTs. In this paper, we develop a dynamic information flow tracking game for resource-efficient detection of APTs via multi-stage dynamic games. The game evolves on an information flow graph, whose nodes are processes and objects (e.g. file, network endpoints) in the system and the edges capture the interaction between different processes and objects. Each stage of the game has pre-specified targets which are characterized by a set of nodes of the graph and the goal of the APT is to evade detection and reach a target node of that stage. The goal of the defender is to maximize the detection probability while minimizing performance overhead on the system. The resource costs of the players are different and the information structure is asymmetric resulting in a nonzero-sum imperfect information game. We first calculate the best responses of the players and characterize the set of Nash equilibria for single stage attacks. Subsequently, we provide a polynomial-time algorithm to compute a correlated equilibrium for the multi-stage attack case. Finally, we experiment our model and algorithms on real-world nation state attack data obtained from Refinable Attack Investigation system.

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arXiv2018

Cloaking the Clock: Emulating Clock Skew in Controller Area Networks

Automobiles are equipped with Electronic Control Units (ECU) that communicate via in-vehicle network protocol standards such as Controller Area Network (CAN). These protocols are designed under the assumption that separating in-vehicle communications from external networks is sufficient for protection against cyber attacks. This assumption, however, has been shown to be invalid by recent attacks in which adversaries were able to infiltrate the in-vehicle network. Motivated by these attacks, intrusion detection systems (IDSs) have been proposed for in-vehicle networks that attempt to detect attacks by making use of device fingerprinting using properties such as clock skew of an ECU. In this paper, we propose the cloaking attack, an intelligent masquerade attack in which an adversary modifies the timing of transmitted messages in order to match the clock skew of a targeted ECU. The attack leverages the fact that, while the clock skew is a physical property of each ECU that cannot be changed by the adversary, the estimation of the clock skew by other ECUs is based on network traffic, which, being a cyber component only, can be modified by an adversary. We implement the proposed cloaking attack and test it on two IDSs, namely, the current state-of-the-art IDS and a new IDS that we develop based on the widely-used Network Time Protocol (NTP). We implement the cloaking attack on two hardware testbeds, a prototype and a real connected vehicle, and show that it can always deceive both IDSs. We also introduce a new metric called the Maximum Slackness Index to quantify the effectiveness of the cloaking attack even when the adversary is unable to precisely match the clock skew of the targeted ECU.

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arXiv2018

Controlled Islanding via Weak Submodularity

Cascading failures typically occur following a large disturbance in power systems, such as tripping of a generating unit or a transmission line. Such failures can propagate and destabilize the entire power system, potentially leading to widespread outages. One approach to mitigate impending cascading failures is through controlled islanding, in which a set of transmission lines is deliberately tripped to partition the unstable system into several disjoint, internally stable islands. Selecting such a set of transmission lines is inherently a combinatorial optimization problem. Current approaches address this problem in two steps: first classify coherent generators into groups and then separate generator groups into different islands with minimal load-generation imbalance. These methods, however, are based on computationally expensive heuristics that do not provide optimality guarantees. In this paper, we propose a novel approach to controlled islanding based on weak submodularity. Our formulation jointly captures the minimal generator non-coherency and minimal load-generation imbalance in one objective function. We relax the problem to a formulation with bounded submodularity ratio and a matroid constraint, and propose an approximation algorithm which achieves a provable optimality bound on non-coherency and load-generation imbalance. The proposed framework is tested on IEEE 39-bus and 118-bus power systems.

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arXiv2017

Distributed Observers Design for Leader-Following Control of Multi-Agent Networks (Extended Version)

This paper is concerned with a leader-follower problem for a multi-agent system with a switching interconnection topology. Distributed observers are designed for the second-order follower-agents, under the common assumption that the velocity of the active leader cannot be measured in real time. Some dynamic neighbor-based rules, consisting of distributed controllers and observers for the autonomous agents, are developed to keep updating the information of the leader. With the help of an explicitly constructed common Lyapunov function (CLF), it is proved that each agent can follow the active leader. Moreover, the tracking error is estimated even in a noisy environment. Finally, a numerical example is given for illustration.

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arXiv2017

Minimal Input Selection for Robust Control

This paper studies the problem of selecting a minimum-size set of input nodes to guarantee stability of a networked system in the presence of uncertainties and time delays. Current approaches to input selection in networked dynamical systems focus on nominal systems with known parameter values in the absence of delays. We derive sufficient conditions for existence of a stabilizing controller for an uncertain system that are based on a subset of system modes lying within the controllability subspace induced by the set of inputs. We then formulate the minimum input selection problem and prove that it is equivalent to a discrete optimization problem with bounded submodularity ratio, leading to polynomial-time algorithms with provable optimality bounds. We show that our approach is applicable to different types of uncertainties, including additive and multiplicative uncertainties in the system matrices as well as uncertain time delays. We demonstrate our approach in a numerical case study on the IEEE 39-bus test power system.

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arXiv2017

Maximizing the Smallest Eigenvalue of a Symmetric Matrix: A Submodular Optimization Approach

This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input nodes in order to guarantee consensus of networks with negative edges as well as maximizing the convergence rate of distributed systems. We develop a submodular optimization approach to maximizing the smallest eigenvalue by first proving that positivity of the eigenvalues of a submatrix can be characterized using the probability distribution of the quadratic form induced by the submatrix. We then exploit that connection to prove that positive-definiteness of a submatrix can be expressed as a constraint on a submodular function. We prove that our approach results in polynomial-time algorithms with provable bounds on the size of the submatrix. We also present generalizations to non-symmetric matrices, alternative sufficient conditions for the smallest eigenvalue to exceed a desired bound that are valid for Laplacian matrices, and a numerical evaluation.

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arXiv2017

Combinatorial Algorithms for Control of Biological Regulatory Networks

Biological processes, including cell differentiation, organism development, and disease progression, can be interpreted as attractors (fixed points or limit cycles) of an underlying networked dynamical system. In this paper, we study the problem of computing a minimum-size subset of control nodes that can be used to steer a given biological network towards a desired attractor, when the networked system has Boolean dynamics. We first prove that this problem cannot be approximated to any nontrivial factor unless P=NP. We then formulate a sufficient condition and prove that the sufficient condition is equivalent to a target set selection problem, which can be solved using integer linear programming. Furthermore, we show that structural properties of biological networks can be exploited to reduce the computational complexity. We prove that when the network nodes have threshold dynamics and certain topological structures, such as block cactus topology and hierarchical organization, the input selection problem can be solved or approximated in polynomial time. For networks with nested canalyzing dynamics, we propose polynomial-time algorithms that are within a polylogarithmic bound of the global optimum. We validate our approach through numerical study on real-world gene regulatory networks.

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arXiv2016

Adaptive Mitigation of Multi-Virus Propagation: A Passivity-Based Approach

Malware propagation poses a growing threat to networked systems such as computer networks and cyber-physical systems. Current approaches to defending against malware propagation are based on patching or filtering susceptible nodes at a fixed rate. When the propagation dynamics are unknown or uncertain, however, the static rate that is chosen may be either insufficient to remove all viruses or too high, incurring additional performance cost. In this paper, we formulate adaptive strategies for mitigating multiple malware epidemics when the propagation rate is unknown, using patching and filtering-based defense mechanisms. In order to identify conditions for ensuring that all viruses are asymptotically removed, we show that the malware propagation, patching, and filtering processes can be modeled as coupled passive dynamical systems. We prove that the patching rate required to remove all viruses is bounded above by the passivity index of the coupled system, and formulate the problem of selecting the minimum-cost mitigation strategy. Our results are evaluated through numerical study.

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arXiv2016

Submodularity in Input Node Selection for Networked Systems

Networked systems are systems of interconnected components, in which the dynamics of each component are influenced by the behavior of neighboring components. Examples of networked systems include biological networks, critical infrastructures such as power grids, transportation systems, and the Internet, and social networks. The growing importance of such systems has led to an interest in control of networks to ensure performance, stability, robustness, and resilience. A widely-studied method for controlling networked systems is to directly control a subset of input nodes, which then steer the remaining nodes to their desired states. This article presents submodular optimization approaches for input node selection in networked systems. Submodularity is a property of set functions that enables the development of computationally tractable algorithms with provable optimality bounds. For a variety of physically relevant systems, the physical dynamics have submodular structures that can be exploited to develop efficient input selection algorithms. This article will describe these structures and the resulting algorithms, as well as discuss open problems.

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arXiv2015

Global Practical Node and Edge Synchronization in Kuramoto Networks: A Submodular Optimization Framework

Synchronization underlies phenomena including memory and perception in the brain, coordinated motion of animal flocks, and stability of the power grid. These synchronization phenomena are often modeled through networks of phase-coupled oscillating nodes. Heterogeneity in the node dynamics, however, may prevent such networks from achieving the required level of synchronization. In order to guarantee synchronization, external inputs can be used to pin a subset of nodes to a reference frequency, while the remaining nodes are steered toward synchronization via local coupling. In this paper, we present a submodular optimization framework for selecting a set of nodes to act as external inputs in order to achieve synchronization from almost any initial network state. We derive threshold-based sufficient conditions for synchronization, and then prove that these conditions are equivalent to connectivity of a class of augmented network graphs. Based on this connection, we map the sufficient conditions for synchronization to constraints on submodular functions, leading to efficient algorithms with provable optimality bounds for selecting input nodes. We illustrate our approach via numerical studies of synchronization in networks from power systems, wireless networks, and neuronal networks.

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arXiv2014

Input Selection for Performance and Controllability of Structured Linear Descriptor Systems

A common approach to controlling complex networks is to directly control a subset of input nodes, which then controls the remaining nodes via network interactions. While techniques have been proposed for selecting input nodes based on either performance metrics or controllability, a unifying approach based on joint consideration of performance and controllability is an open problem. In this paper, we develop a submodular optimization framework for selecting input nodes based on joint performance and controllability in structured linear descriptor systems. We develop our framework for arbitrary linear descriptor systems. In developing our framework, we first prove that selecting a minimum-size set of input nodes for controllability is a matroid intersection problem that can be solved in polynomial-time in the network size. We then prove that input selection to maximize a performance metric with controllability as a constraint is equivalent to maximizing a monotone submodular function with two matroid basis constraints, and derive efficient approximation algorithms with provable optimality bounds for input selection. Finally, we present a graph controllability index metric, which characterizes the largest controllable subgraph of a given complex network, and prove its submodular structure, leading to input selection algorithms that trade-off performance and controllability. We provide improved optimality guarantees for known systems such as strongly connected networks, consensus networks, networks of double integrators, and networks where all system parameters (e.g., link weights) are chosen independently and at random.

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arXiv2013

A Passivity Framework for Modeling and Mitigating Wormhole Attacks on Networked Control Systems

Networked control systems consist of distributed sensors and actuators that communicate via a wireless network. The use of an open wireless medium and unattended deployment leaves these systems vulnerable to intelligent adversaries whose goal is to disrupt the system performance. In this paper, we study the wormhole attack on a networked control system, in which an adversary establishes a link between two distant regions of the network by using either high-gain antennas, as in the out-of-band wormhole, or colluding network nodes as in the in-band wormhole. Wormholes allow the adversary to violate the timing constraints of real-time control systems by delaying or dropping packets, and cannot be detected using cryptographic mechanisms alone. We study the impact of the wormhole attack on the network flows and delays and introduce a passivity-based control-theoretic framework for modeling the wormhole attack. We develop this framework for both the in-band and out-of-band wormhole attacks as well as complex, hereto-unreported wormhole attacks consisting of arbitrary combinations of in-and out-of band wormholes. We integrate existing mitigation strategies into our framework, and analyze the throughput, delay, and stability properties of the overall system. Through simulation study, we show that, by selectively dropping control packets, the wormhole attack can cause disturbances in the physical plant of a networked control system, and demonstrate that appropriate selection of detection parameters mitigates the disturbances due to the wormhole while satisfying the delay constraints of the physical system.

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arXiv2013

Minimizing Convergence Error in Multi-Agent Systems via Leader Selection: A Supermodular Optimization Approach

In a leader-follower multi-agent system (MAS), the leader agents act as control inputs and influence the states of the remaining follower agents. The rate at which the follower agents converge to their desired states, as well as the errors in the follower agent states prior to convergence, are determined by the choice of leader agents. In this paper, we study leader selection in order to minimize convergence errors experienced by the follower agents, which we define as a norm of the distance between the follower agents' intermediate states and the convex hull of the leader agent states. By introducing a novel connection to random walks on the network graph, we show that the convergence error has an inherent supermodular structure as a function of the leader set. Supermodularity enables development of efficient discrete optimization algorithms that directly approximate the optimal leader set, provide provable performance guarantees, and do not rely on continuous relaxations. We formulate two leader selection problems within the supermodular optimization framework, namely, the problem of selecting a fixed number of leader agents in order to minimize the convergence error, as well as the problem of selecting the minimum-size set of leader agents to achieve a given bound on the convergence error. We introduce algorithms for approximating the optimal solution to both problems in static networks, dynamic networks with known topology distributions, and dynamic networks with unknown and unpredictable topology distributions. Our approach is shown to provide significantly lower convergence errors than existing random and degree-based leader selection methods in a numerical study.

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arXiv2012

A Supermodular Optimization Framework for Leader Selection under Link Noise in Linear Multi-Agent Systems

In many applications of multi-agent systems (MAS), a set of leader agents acts as a control input to the remaining follower agents. In this paper, we introduce an analytical approach to selecting leader agents in order to minimize the total mean-square error of the follower agent states from their desired value in steady-state in the presence of noisy communication links. We show that the problem of choosing leaders in order to minimize this error can be solved using supermodular optimization techniques, leading to efficient algorithms that are within a provable bound of the optimum. We formulate two leader selection problems within our framework, namely the problem of choosing a fixed number of leaders to minimize the error, as well as the problem of choosing the minimum number of leaders to achieve a tolerated level of error. We study both leader selection criteria for different scenarios, including MAS with static topologies, topologies experiencing random link or node failures, switching topologies, and topologies that vary arbitrarily in time due to node mobility. In addition to providing provable bounds for all these cases, simulation results demonstrate that our approach outperforms other leader selection methods, such as node degree-based and random selection methods, and provides comparable performance to current state of the art algorithms.

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