More Like this

1. Existence of invariant volumes in nonholonomic systems subject to nonlinear constraints

   Clark, W; Bloch, A (June 2024, Journal of geometric mechanics)

   We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if and only if a certain 1-form is exact and a certain function vanishes (this function automatically vanishes for linear constraints). Moreover, this result can be extended to geodesic flows for arbitrary metric connections and the sufficient condition manifests as integrability of the torsion. As a consequence, volume-preservation of a nonholonomic system is closely related to the torsion of the nonholonomic connection. Examples of nonlinear/affine/linear constraints are considered. 

   more » « less
2. Perfectly Undetectable Reflection and Scaling False Data Injection Attacks via Affine Transformation on Mobile Robot Trajectory Tracking Control

   https://doi.org/10.1109/TRO.2025.3626620  

   Ueda, Jun; Kwon, Hyukbin (October 2025, IEEE Transactions on Robotics)

   With the increasing integration of cyber-physical systems (CPS) into critical applications, ensuring their resilience against cyberattacks is paramount. A particularly concerning threat is the vulnerability of CPS to deceptive attacks that degrade system performance while remaining undetected. This article investigates perfectly undetectable false data injection attacks (FDIAs) targeting the trajectory tracking control of a nonholonomic mobile robot. The proposed attack method utilizes affine transformations of intercepted signals, exploiting weaknesses inherent in the partially linear dynamic properties and symmetry of the nonlinear plant. The feasibility and potential impact of these attacks are validated through experiments using a Turtlebot 3 platform, highlighting the urgent need for sophisticated detection mechanisms and resilient control strategies to safeguard CPS against such threats. Furthermore, a novel approach for detection of these attacks called the state monitoring signature function (SMSF) is introduced. An example SMSF, a carefully designed function resilient to FDIA, is shown to be able to detect the presence of an FDIA through signatures based on system states. 

   more » « less
3. Output-only identification of self-excited systems using discrete-time Lur'e models with application to a gas-turbine combustor

   https://doi.org/10.1080/00207179.2022.2137702  

   Paredes, Juan A.; Yang, Yulong; Bernstein, Dennis S. (November 2022, International Journal of Control)

   A self-excited system is a nonlinear system with the property that a constant input yields a bounded, nonconvergent response. Nonlinear identification of self-excited systems is considered using a Lur'e model structure, where a linear model is connected in feedback with a nonlinear feedback function. To facilitate identification, the nonlinear feedback function is assumed to be continuous and piecewise affine (CPA). The present paper uses least-squares optimization to estimate the coefficients of the linear dynamics and the slope vector of the CPA nonlinearity, as well as mixed-integer optimization to estimate the order of the linear dynamics and the breakpoints of the CPA function. The proposed identification technique requires only output data, and thus no measurement of the constant input is required. This technique is illustrated on a diverse collection of low-dimensional numerical examples as well as data from a gas-turbine combustor. 

   more » « less
4. Persistence landscapes of affine fractals

   https://doi.org/10.1515/dema-2022-0015  

   Catanzaro, Michael J.; Przybylski, Lee; Weber, Eric S. (January 2022, Demonstratio Mathematica)

   Abstract We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes, which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations. 

   more » « less
5. Template-based piecewise affine regression

   https://doi.org/10.1017/cbp.2024.3  

   Berger, Guillaume O; Sankaranarayanan, Sriram (January 2024, Research Directions: Cyber-Physical Systems)

   Abstract We study the problem of fitting a piecewise affine (PWA) function to input–output data. Our algorithm divides the input domain into finitely many regions whose shapes are specified by a user-provided template and such that the input–output data in each region are fit by an affine function within a user-provided error tolerance. We first prove that this problem is NP-hard. Then, we present a top-down algorithmic approach for solving the problem. The algorithm considers subsets of the data points in a systematic manner, trying to fit an affine function for each subset using linear regression. If regression fails on a subset, the algorithm extracts a minimal set of points from the subset (an unsatisfiable core) that is responsible for the failure. The identified core is then used to split the current subset into smaller ones. By combining this top-down scheme with a set-covering algorithm, we derive an overall approach that provides optimal PWA models for a given error tolerance, where optimality refers to minimizing the number of pieces of the PWA model. We demonstrate our approach on three numerical examples that include PWA approximations of a widely used nonlinear insulin–glucose regulation model and a double inverted pendulum with soft contacts. 

   more » « less