arXiv subjects

Michelle S. Chong

Publications and source records attributed to Michelle S. Chong.

At least 19 recordsLinked to original sources

arXiv2026

Periodic fixed-points and their algebraic characteristics in discrete-time Lur'e feedback systems

We study the problem of identifying nontrivial, i.e., nonzero, periodic fixed-points in discrete-time Lur'e feedback systems. Using the circulant matrix constructed from the transfer function of the linear subsystem, whether stable or unstable, we introduce an algebraic framework that allows us to determine when such fixed-points exist. This framework yields a sector bound defined by two vectors, whose slopes correspond to the maximum and minimum positive singular values of the circulant matrix. Assuming that the nonlinear feedback function is memoryless, we show that a necessary condition for the existence of nontrivial $P$-periodic fixed-points is that the intersection of the continuous completion of the nonlinear feedback function with that sector bound contains at least one point other than the origin. Our characterization provides a unified condition valid for all periods $P$, and further enables us to derive upper bounds on the amplitudes of admissible periodic fixed-points with bounded feedback functions. In particular, for relay feedback systems with passive feedback functions, we derive both upper and lower bounds for the amplitudes of such periodic fixed-points.

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arXiv2026

Secure Set-based State Estimation for Safety-Critical Applications under Adversarial Attacks on Sensors

Set-based state estimation provides guaranteed state inclusion certificates that are crucial for the safety verification of dynamical systems. However, when system sensors are subject to cyberattacks, maintaining both safety and security guarantees becomes a fundamental challenge. Existing point-based secure state estimation methods cannot adequately address this challenge because they cannot provide state inclusion certificates. This paper introduces a novel approach that simultaneously ensures safety guarantees through guaranteed state inclusion and security guarantees against sensor attacks, without imposing conservative restrictions on system operation. We propose a Secure Set-based State Estimation (S3E) algorithm that maintains the true system state within the estimated set under sensor attacks, provided the initialization set contains the initial state and the system remains observable from the uncompromised sensor subset. The algorithm provides the estimated set as a collection of constrained zonotopes (agreement sets), which can be used as robust certificates to verify whether the system adheres to safety constraints. Furthermore, we demonstrate that the estimated set remains unaffected by attack signals of sufficiently large magnitude and also establish sufficient conditions for attack detection, identification, and filtering. This compels the attacker to inject only signals of small magnitudes to evade detection, thus preserving the accuracy of the estimated set. To address the computational complexity of the algorithm, we offer several strategies for complexity-performance tradeoffs. The efficacy of the proposed algorithm is illustrated through several examples, including its application to a three-story building model.

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arXiv2026

Confidentiality of Linear Control Systems with Quadratic Output Under Sensor Attacks [Extended Version]

We study the state estimation problem for linear control systems with quadratic outputs which are locally unobservable at the equilibrium. We show that, despite this inherent lack of observability, an adversary with sensor read and write capability can induce observability by injecting an appropriate signal into the measurement channel. Taking the role of an adversary, we characterize when an injected signal can or cannot induce observability and, in the successful case, construct an observer that achieves local exponential convergence of state estimates to the true states of the system. A simulation study demonstrates our results.

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arXiv2026

Secure estimator design for Lur'e-type systems with nonuniformly and synchronously sampled measurements under attacks [extended version]

Motivated by the need for real-time health monitoring of power distribution grids, we propose a secure state estimator design for continuous time Lur'e type systems with non-uniformly and synchronously sampled outputs which have potentially been maliciously corrupted. The secure state estimator provides state estimates with accuracy independent of the sensor attack, when less than half of the sensors are under attack and when all inter-sample times are upper bounded. We show convergence of the state estimation error under an impulsive system framework and provide an upper bound on the estimation error that is independent of the attack signals. The stability conditions are formulated as linear matrix inequalities, which can be used to design the observer parameters. We demonstrate the capabilities of the proposed secure state estimator on a low-voltage power distribution grid.

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arXiv2026

Data-driven Reachable Set Estimation with Tunable Adversarial and Wasserstein Distributional Guarantees

We study finite horizon reachable set estimation for unknown discrete-time dynamical systems using only sampled state trajectories. Rather than treating scenario optimization as a black-box tool, we show how it can be tailored to reachable set estimation, where one must learn a family of sets based on whole trajectories, while preserving probabilistic guarantees on future trajectory inclusion for the entire horizon. To this end, we formulate a relaxed scenario program with slack variables that yields a tunable trade-off between reachable set size and out-of-sample trajectory inclusion over the horizon, thereby reducing sensitivity to outliers. Leveraging the recent results in adversarially robust scenario optimization, we then extend this formulation to account for bounded adversarial perturbations of the observed trajectories and derive a posteriori probabilistic guarantees on future trajectory inclusion. When probability distribution shifts in the Wasserstein distance occur, we obtain an explicit bound on how gracefully the theoretical probabilistic guarantees degrade. For different geometries, i.e., $p$-norm balls, ellipsoids, and zonotopes, we derive tractable convex reformulations and corroborate our theoretical results in simulation.

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arXiv2026

Data-Driven Nonconvex Reachability Analysis using Exact Set Propagation

This paper studies deterministic data-driven reachability analysis for dynamical systems with unknown dynamics and nonconvex reachable sets. Existing deterministic data-driven approaches typically employ zonotopic set representations, for which the multiplication between a zonotopic model set and a zonotopic state set cannot be represented algebraically exactly, thereby necessitating over-approximation steps in reachable-set propagation. To remove this structural source of conservatism, we introduce constrained polynomial matrix zonotopes (CPMZs) to represent data-consistent model sets, and show that the multiplication between a CPMZ model set and a constrained polynomial zonotope (CPZ) state set admits an algebraically exact CPZ representation. This property enables set propagation entirely within the CPZ representation, thereby avoiding propagation-induced over-approximation and even retaining the ability to represent nonconvex reachable sets. Moreover, we develop set-theoretic results that enable the intersection of data-consistent model sets as new data become available, yielding the proposed online refinement scheme that progressively tightens the data-consistent model set and, in turn, the resulting reachable set. Beyond linear systems, we extend the proposed framework to polynomial dynamics and develop additional set-theoretic results that enable both model-based and data-driven reachability analysis within the same algebraic representation. By deriving algebraically exact CPZ representations for monomials and their compositions, reachable-set propagation can be carried out directly at the set level without resorting to interval arithmetic or relaxation-based bounding techniques. Numerical examples for both linear and polynomial systems demonstrate a significant reduction in conservatism compared to state-of-the-art deterministic data-driven reachability methods.

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arXiv2026

Unimodal self-oscillations and their sign-symmetry for discrete-time relay feedback systems with dead zone

This paper characterizes self-oscillations in discrete-time linear time-invariant (LTI) relay feedback systems with nonnegative dead zone. Specifically, we aim to establish existence criteria for unimodal self-oscillations, defined as periodic solutions where the output exhibits a single-peaked period. Assuming that the linear part of system is stable, with a strictly monotonically decreasing impulse response on its infinite support, we propose a novel analytical framework based on the theory of total positivity to address this problem. We demonstrate that unimodal self-oscillations subject to mild variation-based constraints exist only if the number of positive and negative values of the system's loop gain coincides within a given strictly positive period, i.e., the self-oscillation is sign-symmetric. Building upon these findings, we derive conditions for the existence of such self-oscillations, establish tight bounds on their periods, and address the question of their uniqueness.

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arXiv2025

Data-Driven Nonconvex Reachability Analysis using Exact Multiplication

This paper addresses a fundamental challenge in data-driven reachability analysis: accurately representing and propagating non-convex reachable sets. We propose a novel approach using constrained polynomial zonotopes to describe reachable sets for unknown LTI systems. Unlike constrained zonotopes commonly used in existing literature, constrained polynomial zonotopes are closed under multiplication with constrained matrix zonotopes. We leverage this property to develop an exact multiplication method that preserves the non-convex geometry of reachable sets without resorting to approximations. We demonstrate that our approach provides tighter over-approximations of reachable sets for LTI systems compared to conventional methods.

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arXiv2025

Self-sustained oscillations in discrete-time relay feedback systems

We study the problem of determining self-sustained oscillations in discrete-time linear time-invariant relay feedback systems. Concretely, we are interested in predicting when such a system admits unimodal oscillations, i.e., when the output has a single-peaked period. Under the assumption that the linear system is stable and has an impulse response that is strictly monotonically decreasing on its infinite support, we take a novel approach in using the framework of total positivity to address our main question. It is shown that unimodal self-oscillations can only exist if the number of positive and negative elements in a period coincides. Based on this result, we derive conditions for the existence of such oscillations, determine bounds on their periods, and address the question of uniqueness.

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arXiv2025

Modified Control Barrier Function for Quadratic Program Based Control Design via Sum-of-Squares Programming

We consider a nonlinear control affine system controlled by inputs generated by a quadratic program (QP) induced by a control barrier functions (CBF). Specifically, we slightly modify the condition satisfied by CBFs and study how the modification can positively impact the closed loop behavior of the system. We show that, QP-based controllers designed using the modified CBF condition preserves the desired properties of QP-based controllers using standard CBF conditions. Furthermore, using the generalized S-procedure for polynomial functions, we formulate the design of the modified CBFs as a Sum-Of-Squares (SOS) program, which can be solved efficiently. Via a numerical example, the proposed CBF design is shown to have superior performance over the standard CBF widely used in existing literature.

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arXiv2025

Secondary Safety Control for Systems with Sector Bounded Nonlinearities [Extended Version]

We consider the problem of safety verification and safety-aware controller synthesis for systems with sector bounded nonlinearities. We aim to keep the states of the system within a given safe set under potential actuator and sensor attacks. Specifically, we adopt the setup that a controller has already been designed to stabilize the plant. Using invariant sets and barrier certificate theory, we first give sufficient conditions to verify the safety of the closed-loop system under attacks. Furthermore, by using a subset of sensors that are assumed to be free of attacks, we provide a synthesis method for a secondary controller that enhances the safety of the system. The sufficient conditions to verify safety are derived using Lyapunov-based tools and the S-procedure. Using the projection lemma, the conditions are then formulated as linear matrix inequality (LMI) problems which can be solved efficiently. Lastly, our theoretical results are illustrated through numerical simulations.

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arXiv2025

Nonconvex Obstacle Avoidance using Efficient Sampling-Based Distance Functions

We consider nonconvex obstacle avoidance where a robot described by nonlinear dynamics and a nonconvex shape has to avoid nonconvex obstacles. Obstacle avoidance is a fundamental problem in robotics and well studied in control. However, existing solutions are computationally expensive (e.g., model predictive controllers), neglect nonlinear dynamics (e.g., graph-based planners), use diffeomorphic transformations into convex domains (e.g., for star shapes), or are conservative due to convex overapproximations. The key challenge here is that the computation of the distance between the shapes of the robot and the obstacles is a nonconvex problem. We propose efficient computation of this distance via sampling-based distance functions. We quantify the sampling error and show that, for certain systems, such sampling-based distance functions are valid nonsmooth control barrier functions. We also study how to deal with disturbances on the robot dynamics in our setting. Finally, we illustrate our method on a robot navigation task involving an omnidirectional robot and nonconvex obstacles. We also analyze performance and computational efficiency of our controller as a function of the number of samples.

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arXiv2023

Data-Driven Identification of Attack-free Sensors in Networked Control Systems

This paper proposes a data-driven framework to identify the attack-free sensors in a networked control system when some of the sensors are corrupted by an adversary. An operator with access to offline input-output attack-free trajectories of the plant is considered. Then, a data-driven algorithm is proposed to identify the attack-free sensors when the plant is controlled online. We also provide necessary conditions, based on the properties of the plant, under which the algorithm is feasible. An extension of the algorithm is presented to identify the sensors completely online against certain classes of attacks. The efficacy of our algorithm is depicted through numerical examples.

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arXiv2023

Reachable set-based dynamic quantization for the remote state estimation of linear systems

We employ reachability analysis in designing dynamic quantization schemes for the remote state estimation of linear systems over a finite date rate communication channel. The quantization region is dynamically updated at each transmission instant, with an approximated reachable set of the linear system. We propose a set-based method using zonotopes and compare it to a norm-based method in dynamically updating the quantization region. For both methods, we guarantee that the quantization error is bounded and consequently, the remote state reconstruction error is also bounded. To the best of our knowledge, the set-based method using zonotopes has no precedent in the literature and admits a larger class of linear systems and communication channels, where the set-based method allows for a longer inter-transmission time and lower bit rate. Finally, we corroborate our theoretical guarantees with a numerical example.

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arXiv2023

Safety monitoring under stealthy sensor injection attacks using reachable sets

Stealthy sensor injection attacks are serious threats for industrial plants as they can compromise the plant's integrity without being detected by traditional fault detectors. In this manuscript, we study the possibility of revealing the presence of such attacks by monitoring only the control input. This approach consists in computing an ellipsoidal bound of the input reachable set. When the control input does not belong to this set, this means that a stealthy sensor injection attack is driving the plant to critical states. The problem of finding this ellipsoidal bound is posed as a convex optimization problem (convex cost with Linear Matrix Inequalities constraints). Our monitoring approach is tested in simulation.

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arXiv2023

Secondary Controller Design for the Safety of Nonlinear Systems via Sum-of-Squares Programming

We consider the problem of ensuring the safety of nonlinear control systems under adversarial signals. Using Lyapunov based reachability analysis, we first give sufficient conditions to assess safety, i.e., to guarantee that the states of the control system, when starting from a given initial set, always remain in a prescribed safe set. We consider polynomial systems with semi-algebraic safe sets. Using the S-procedure for polynomial functions, safety conditions can be formulated as a Sum-Of-Squares (SOS) programme, which can be solved efficiently. When safety cannot be guaranteed, we provide tools via SOS to synthesize polynomial controllers that enforce safety of the closed loop system. The theoretical results are illustrated through numerical simulations.

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arXiv2022

Plug-and-Play Secondary Control for Safety of LTI Systems under Attacks

We consider the problem of controller design for linear time-invariant cyber-physical systems (CPSs) controlled via networks. Specifically, we adopt the set-up that a controller has already been designed to stabilize the plant. However, the closed loop system may be subject to actuator and sensor attacks. We first perform a reachability analysis to see the effect of potential attacks. To further ensure the safety of the states of the system, we choose a subset of sensors that can be locally secured and made free of attacks. Using these limited resources, an extra controller is designed to enhance the safety of the new closed loop. The safety of the system will be characterized by the notion of safe sets. Lyapunov based analysis will be used to derive sufficient conditions that ensure the states always stay in the safe set. The conditions will then be stated as convex optimization problems which can be solved efficiently. Lastly, our theoretical results are illustrated through numerical simulations.

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arXiv2022

Resilient Set-based State Estimation for Linear Time-Invariant Systems Using Zonotopes

This paper considers the problem of set-based state estimation for linear time-invariant (LTI) systems under time-varying sensor attacks. Provided that the LTI system is stable and observable via every single sensor and that at least one sensor is uncompromised, we guarantee that the true state is always contained in the estimated set. We use zonotopes to represent these sets for computational efficiency. However, we show that intelligently designed stealthy attacks may cause exponential growth in the algorithm's worst-case complexity. We present several strategies to handle this complexity issue and illustrate our resilient zonotope-based state estimation algorithm on a rotating target system.

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