arXiv subjects

Justin Ruths

Publications and source records attributed to Justin Ruths.

At least 19 recordsLinked to original sources

arXiv2025

Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks

Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the exponential scaling often associated with analyses over high-dimensional spaces. This paper presents automated methods for constructing functional decompositions used to form set-based over-approximations of nonlinear functions, with particular focus on the hybrid zonotope set representation. To demonstrate these methods, we construct a hybrid zonotope set that over-approximates the input-output graph of a long short-term memory neural network, and use functional decomposition to represent a discrete hybrid automaton via a hybrid zonotope.

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arXiv2023

zonoLAB: A MATLAB toolbox for set-based control systems analysis using hybrid zonotopes

This paper introduces zonoLAB, a MATLAB-based toolbox for set-based control system analysis using the hybrid zonotope set representation. Hybrid zonotopes have proven to be an expressive set representation that can exactly represent the reachable sets of mixed-logical dynamical systems and tightly approximate the reachable sets of nonlinear dynamic systems. Moreover, hybrid zonotopes can exactly represent the continuous piecewise linear control laws associated with model predictive control and the input-output mappings of neural networks with piecewise linear activation functions. The hybrid zonotope set representation is also highly exploitable, where efficient methods developed for mixed-integer linear programming can be directly used for set operation and analysis. The zonoLAB toolbox is designed to make these capabilities accessible to the dynamic systems and controls community, with functionality spanning fundamental operations with hybrid zonotope, constrained zonotope, and zonotope set representations, powerful set analysis tools, and general-purpose algorithms for reachability analysis of open- and closed-loop systems.

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arXiv2023

Convex Optimization-based Policy Adaptation to Compensate for Distributional Shifts

Many real-world systems often involve physical components or operating environments with highly nonlinear and uncertain dynamics. A number of different control algorithms can be used to design optimal controllers for such systems, assuming a reasonably high-fidelity model of the actual system. However, the assumptions made on the stochastic dynamics of the model when designing the optimal controller may no longer be valid when the system is deployed in the real-world. The problem addressed by this paper is the following: Suppose we obtain an optimal trajectory by solving a control problem in the training environment, how do we ensure that the real-world system trajectory tracks this optimal trajectory with minimal amount of error in a deployment environment. In other words, we want to learn how we can adapt an optimal trained policy to distribution shifts in the environment. Distribution shifts are problematic in safety-critical systems, where a trained policy may lead to unsafe outcomes during deployment. We show that this problem can be cast as a nonlinear optimization problem that could be solved using heuristic method such as particle swarm optimization (PSO). However, if we instead consider a convex relaxation of this problem, we can learn policies that track the optimal trajectory with much better error performance, and faster computation times. We demonstrate the efficacy of our approach on tracking an optimal path using a Dubin's car model, and collision avoidance using both a linear and nonlinear model for adaptive cruise control.

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arXiv2023

Hybrid Zonotopes Exactly Represent ReLU Neural Networks

We show that hybrid zonotopes offer an equivalent representation of feed-forward fully connected neural networks with ReLU activation functions. Our approach demonstrates that the complexity of binary variables is equal to the total number of neurons in the network and hence grows linearly in the size of the network. We demonstrate the utility of the hybrid zonotope formulation through three case studies including nonlinear function approximation, MPC closed-loop reachability and verification, and robustness of classification on the MNIST dataset.

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arXiv2021

Generalized Outer Bounds on the Finite Geometric Sum of Ellipsoids

General results on convex bodies are reviewed and used to derive an exact closed-form parametric formula for the boundary of the geometric (Minkowski) sum of $k$ ellipsoids in $n$-dimensional Euclidean space. Previously this was done through iterative algorithms in which each new ellipsoid was added to an ellipsoid approximation of the sum of the previous ellipsoids. Here we provide one shot formulas to add $k$ ellipsoids directly with no intermediate approximations required. This allows us to observe a new degree of freedom in the family of ellipsoidal bounds on the geometric sum. We demonstrate an application of these tools to compute the reachable set of a discrete-time dynamical system.

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arXiv2021

Finite sample guarantees for quantile estimation: An application to detector threshold tuning

In threshold-based anomaly detection, we want to tune the threshold of a detector to achieve an acceptable false alarm rate. However, tuning the threshold is often a non-trivial task due to unknown detector output distributions. A detector threshold that provides an acceptable false alarm rate is equivalent to a specific quantile of the detector output distribution. Therefore, we use quantile estimators based on order statistics to estimate the detector threshold. The estimation of quantiles from sample data has a more than a century long tradition and we provide three different distribution-free finite sample guarantees for a class of quantile estimators. The first is based on the Dworetzky-Kiefer-Wolfowitz inequality, the second utilizes the Vysochanskij-Petunin inequality, and the third is based on exact confidence intervals for a beta distribution. These guarantees are then compared and used in the detector threshold tuning problem. We use both simulated data as well as data obtained from an experimental setup with the Temperature Control Lab to validate the guarantees provided.

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arXiv2021

Anomaly Detection Under Multiplicative Noise Model Uncertainty

State estimators are crucial components of anomaly detectors that are used to monitor cyber-physical systems. Many frequently-used state estimators are susceptible to model risk as they rely critically on the availability of an accurate state-space model. Modeling errors make it more difficult to distinguish whether deviations from expected behavior are due to anomalies or simply a lack of knowledge about the system dynamics. In this research, we account for model uncertainty through a multiplicative noise framework. Specifically, we propose to use the multiplicative noise LQG based compensator in this setting to hedge against the model uncertainty risk. The size of the residual from the estimator can then be compared against a threshold to detect anomalies. Finally, the proposed detector is validated using numerical simulations. Extension of state-of-the-art anomaly detection in cyber-physical systems to handle model uncertainty represents the main novel contribution of the present work.

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arXiv2021

Performance Bounds for Neural Network Estimators: Applications in Fault Detection

We exploit recent results in quantifying the robustness of neural networks to input variations to construct and tune a model-based anomaly detector, where the data-driven estimator model is provided by an autoregressive neural network. In tuning, we specifically provide upper bounds on the rate of false alarms expected under normal operation. To accomplish this, we provide a theory extension to allow for the propagation of multiple confidence ellipsoids through a neural network. The ellipsoid that bounds the output of the neural network under the input variation informs the sensitivity - and thus the threshold tuning - of the detector. We demonstrate this approach on a linear and nonlinear dynamical system.

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arXiv2020

Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimization

Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness of feedback systems involving neural networks. In this paper, we propose a convex program, in the form of a Linear Matrix Inequality (LMI), to certify incremental quadratic constraints on the map of neural networks over a region of interest. These certificates can capture several useful properties such as (local) Lipschitz continuity, one-sided Lipschitz continuity, invertibility, and contraction. We illustrate the utility of our approach in two different settings. First, we develop a semidefinite program to compute guaranteed and sharp upper bounds on the local Lipschitz constant of neural networks and illustrate the results on random networks as well as networks trained on MNIST. Second, we consider a linear time-invariant system in feedback with an approximate model predictive controller parameterized by a neural network. We then turn the stability analysis into a semidefinite feasibility program and estimate an ellipsoidal invariant set for the closed-loop system.

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arXiv2020

Higher-Order Moment-Based Anomaly Detection

The identification of anomalies is a critical component of operating complex, and possibly large-scale and geo-graphically distributed cyber-physical systems. While designing anomaly detectors, it is common to assume Gaussian noise models to maintain tractability; however, this assumption can lead to the actual false alarm rate being significantly higher than expected. Here we design a distributionally robust threshold of detection using finite and fixed higher-order moments of the detection measure data such that it guarantees the actual false alarm rate to be upper bounded by the desired one. Further, we bound the states reachable through the action of a stealthy attack and identify the trade-off between this impact of attacks that cannot be detected and the worst-case false alarm rate. Through numerical experiments, we illustrate how knowledge of higher-order moments results in a tightened threshold, thereby restricting an attacker's potential impact.

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arXiv2020

Generalized Outer Bounds on the Finite Geometric Sum of Ellipsoids

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arXiv2019

Co-design for Security and Performance: LMI Tools

We present a convex optimization to reduce the impact of sensor falsification attacks in linear time invariant systems controlled by observer-based feedback. We accomplish this by finding optimal observer and controller gain matrices that minimize the size of the reachable set of attack-induced states. To avoid trivial solutions, we integrate a covariance-based $\|H\|_2$ closed-loop performance constraint, for which we develop a novel linearization for this typically nonlinear, non-convex problem. We demonstrate the effectiveness of this linear matrix inequality framework through a numerical case study.

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arXiv2019

Distributionally Robust Tuning of Anomaly Detectors in Cyber-Physical Systems with Stealthy Attacks

Designing resilient control strategies for mitigating stealthy attacks is a crucial task in emerging cyber-physical systems. In the design of anomaly detectors, it is common to assume Gaussian noise models to maintain tractability; however, this assumption can lead the actual false alarm rate to be significantly higher than expected. We propose a distributionally robust anomaly detector for noise distributions in moment-based ambiguity sets. We design a detection threshold that guarantees that the actual false alarm rate is upper bounded by the desired one by using generalized Chebyshev inequalities. Furthermore, we highlight an important trade-off between the worst-case false alarm rate and the potential impact of a stealthy attacker by efficiently computing an outer ellipsoidal bound for the attack-reachable states corresponding to the distributionally robust detector threshold. We illustrate this trade-off with a numerical example and compare the proposed approach with a traditional chi-squared detector.

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arXiv2019

Community Detection via Katz and Eigenvector Centrality

The computational demands of community detection algorithms such as Louvain and spectral optimization can be prohibitive for large networks. Eigenvector centrality and Katz centrality are two network statistics commonly used to describe the relative importance of nodes; and their calculation can be closely approximated on large networks by scalable iterative methods. In this paper, we present and leverage a surprising relationship between Katz centrality and eigenvector centrality to detect communities. Beyond the computational gains, we demonstrate that our approach identifies communities that are as good or better than conventional methods.

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arXiv2019

Generalized chi-squared detector for LTI systems with non-Gaussian noise

Previously, we derived exact relationships between the properties of a linear time-invariant control system and properties of an anomaly detector that quantified the impact an attacker can have on the system if that attacker aims to remain stealthy to the detector. A necessary first step in this process is to be able to precisely tune the detector to a desired level of performance (false alarm rate) under normal operation, typically through the selection of a threshold parameter. To-date efforts have only considered Gaussian noises. Here we generalize the approach to tune a chi-squared anomaly detector for noises with non-Gaussian distributions. Our method leverages a Gaussian Mixture Model to represent the arbitrary noise distributions, which preserves analytic tractability and provides an informative interpretation in terms of a collection of chi-squared detectors and multiple Gaussian disturbances.

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arXiv2019

Filtering Approaches for Dealing with Noise in Anomaly Detection

The leading workhorse of anomaly (and attack) detection in the literature has been residual-based detectors, where the residual is the discrepancy between the observed output provided by the sensors (inclusive of any tampering along the way) and the estimated output provided by an observer. These techniques calculate some statistic of the residual and apply a threshold to determine whether or not to raise an alarm. To date, these methods have not leveraged the frequency content of the residual signal in making the detection problem easier, specifically dealing with the case of (e.g., measurement) noise. Here we demonstrate some opportunities to combine filtering to enhance the performance of residual-based detectors. We also demonstrate how filtering can provide a compelling alternative to residual-based methods when paired with a robust observer. In this process, we consider the class of attacks that are stealthy, or undetectable, by such filtered detection methods and the impact they can have on the system.

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arXiv2018

Security Metrics of Networked Control Systems under Sensor Attacks (extended preprint)

As more attention is paid to security in the context of control systems and as attacks occur to real control systems throughout the world, it has become clear that some of the most nefarious attacks are those that evade detection. The term stealthy has come to encompass a variety of techniques that attackers can employ to avoid being detected. In this manuscript, for a class of perturbed linear time-invariant systems, we propose two security metrics to quantify the potential impact that stealthy attacks could have on the system dynamics by tampering with sensor measurements. We provide analysis mathematical tools (in terms of linear matrix inequalities) to quantify these metrics for given system dynamics, control structure, system monitor, and set of sensors being attacked. Then, we provide synthesis tools (in terms of semidefinite programs) to redesign controllers and monitors such that the impact of stealthy attacks is minimized and the required attack-free system performance is guaranteed.

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arXiv2017

Synchronization in Networks of Diffusively Coupled Nonlinear Systems: Robustness Against Time-Delays

In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and the network topology, there always exists a unimodal region in the parameter space (coupling strength versus time-delay), such that if they belong to this region, the systems synchronize. Moreover, we show how this unimodal region scales with the network topology, which, in turn, provides useful insights on how to design the network topology to maximize robustness against time-delays. The results are illustrated by extensive simulation experiments of time-delayed coupled Hindmarsh-Rose neural chaotic oscillators.

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