Publications (41)
Invariant Forms in Hybrid and Impact Systems and a Taming of Zeno
William Clark, Anthony Bloch
Hybrid (and impact) systems are dynamical systems experiencing both continuous and discrete transitions. In this work, we derive necessary and sufficient conditions for when a give…
Continuous Direct Sparse Visual Odometry from RGB-D Images
Maani Ghaffari, William Clark, Anthony Bloch +2
This paper reports on a novel formulation and evaluation of visual odometry from RGB-D images. Assuming a static scene, the developed theoretical framework generalizes the widely u…
Optimal Control of Reduced Left-Invariant Hybrid Control Systems
William Clark, Maria Oprea
Optimal control is ubiquitous in many fields of engineering. A common technique to find candidate solutions is via Pontryagin's maximum principle. An unfortunate aspect of this met…
Demonstration of a Reconfigurable Entangled Radiofrequency-Photonic Sensor Network
Yi Xia, Wei Li, William Clark +3
Quantum metrology takes advantage of nonclassical resources such as entanglement to achieve a sensitivity level below the standard quantum limit. To date, almost all quantum-metrol…
A Path-Dependent Variational Framework for Incremental Information Gathering
William Clark, Maani Ghaffari
Information gathered along a path is inherently submodular; the incremental amount of information gained along a path decreases due to redundant observations. In addition to submod…
Stem Cell Transplantation As A Dynamical System: Are Clinical Outcomes Deterministic?
Amir A Toor, Jared D Kobulnicky, Salman Salman +14
Outcomes in stem cell transplantation (SCT) are modeled using probability theory. However the clinical course following SCT appears to demonstrate many characteristics of dynamical…
Optimality of Zeno Executions in Hybrid Systems
William Clark, Maria Oprea
A unique feature of hybrid dynamical systems (systems whose evolution is subject to both continuous- and discrete-time laws) is Zeno trajectories. Usually these trajectories are av…
Nonparametric Continuous Sensor Registration
William Clark, Maani Ghaffari, Anthony Bloch
This paper develops a new mathematical framework that enables nonparametric joint semantic and geometric representation of continuous functions using data. The joint embedding is m…
Delay effects on the discontinuous stabilization of the nonholonomic integrator and its generalizations
William Clark, Anthony Bloch
The nonholonomic integrator is a famous example in feedback design - although it is small-time locally controllable to the origin, no continuous feedback law exists. Therefore, any…
A New Dynamic Model of a Two-Wheeled Two-Flexible-Beam Inverted Pendulum Robot
Amin Mehrvarz, Mohammad Javad Khodaei, William Clark +1
Two-wheeled inverted pendulum robots are designed for self-balancing and they have remarkable advantages. In this paper, a new configuration and consequently dynamic model of one s…
Chromatic numbers with closed local modular constraints
Daniel Herden, Jonathan Meddaugh, Mark R. Sepanski +9
Generalizing the notion of odd-sum colorings, a -labeling of a graph is called a closed coloring with remainder if the closed neighborhood label sum of ea…
Adaptive Continuous Visual Odometry from RGB-D Images
Tzu-Yuan Lin, William Clark, Ryan M. Eustice +3
In this paper, we extend the recently developed continuous visual odometry framework for RGB-D cameras to an adaptive framework via online hyperparameter learning. We focus on the…
Repeater-enhanced distributed quantum sensing based on continuous-variable multipartite entanglement
Yi Xia, Quntao Zhuang, William Clark +1
Entanglement is a unique resource for quantum-enhanced applications. When employed in sensing, shared entanglement between distributed quantum sensors enables a substantial gain in…
Optimal Target Shape for LiDAR Pose Estimation
Jiunn-Kai Huang, William Clark, Jessy W. Grizzle
Targets are essential in problems such as object tracking in cluttered or textureless environments, camera (and multi-sensor) calibration tasks, and simultaneous localization and m…
A Dynamical Systems view of Feedback Synthesis
William Clark
Control theory and dynamical systems are closely intertwined fields. Pontryagin's maximum principal offers a strong connection by providing a constructive way to synthesize feedbac…
Deep Learning for Low-Latency, Quantum-Ready RF Sensing
Pranav Gokhale, Caitlin Carnahan, William Clark +2
Recent work has shown the promise of applying deep learning to enhance software processing of radio frequency (RF) signals. In parallel, hardware developments with quantum RF senso…
Optimal Control of Hybrid Systems with Submersive Resets
William Clark, Maria Oprea, Aden Shaw
Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the opti…
A Geometric Approach to Optimal Control of Hybrid and Impulsive Systems
William Clark, Maria Oprea, Andrew J. Graven
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory is applied to these systems and a hybrid…
Time-minimum control of quantum purity for 2-level Lindblad equations
William Clark, Anthony Bloch, Leonardo Colombo +1
We study time-minimum optimal control for a class of quantum two-dimensional dissipative systems whose dynamics are governed by the Lindblad equation and where control inputs acts…
The Interplay Between Symmetries and Impact Effects on Hybrid Mechanical Systems
William Clark, Leonardo Colombo, Anthony Bloch
Hybrid systems are dynamical systems with continuous-time and discrete-time components in their dynamics. When hybrid systems are defined on a principal bundle we are able to defin…
Optimal Control of Nonholonomic Systems via Magnetic Fields
Maria Oprea, Max Ruth, Dora Kassabova +1
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome…
Uncertainty propagation of stochastic hybrid systems: a case study for types of jump
Tejaswi K. C., William Clark, Taeyoung Lee
Stochastic hybrid systems are dynamic systems that undergo both random continuous-time flows and random discrete jumps. Depending on how randomness is introduced into the continuou…
The Bouncing Penny and Nonholonomic Impacts
William Clark, Anthony Bloch
The evolution of a Lagrangian mechanical system is variational. Likewise, when dealing with a hybrid Lagrangian system (a system with discontinuous impacts), the impacts can also b…
Poincaré-Bendixson Theorem for Hybrid Systems
William Clark, Anthony Bloch, Leonardo Colombo
The Poincaré-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such…
Dissipation-assisted stabilization of periodic orbits via actuated exterior impacts in hybrid mechanical systems with symmetry
William Clark, Leonardo Colombo, Anthony Bloch
Impulsive mechanical systems exhibit discontinuous jumps in their state, and when such jumps are triggered by spatial events, the geometry of the impact surface carries information…
Lie Algebraic Cost Function Design for Control on Lie Groups
Sangli Teng, William Clark, Anthony Bloch +2
This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and di…
A Generalized Metriplectic System via Free Energy and System~Identification via Bilevel Convex Optimization
Sangli Teng, Kaito Iwasaki, William Clark +4
This work generalizes the classical metriplectic formalism to model Hamiltonian systems with nonconservative dissipation. Classical metriplectic representations allow for the descr…
Existence of invariant volumes in nonholonomic systems subject to nonlinear constraints
William Clark, Anthony Bloch
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…
On the Evidence for Violation of the Equivalence Principle in Disk Galaxies
Corey Sargent, William Clark, Antonia Seifert +5
We examine the claimed observations of a gravitational external field effect (EFE) reported in Chae et al. We show that observations suggestive of the EFE can be interpreted withou…
Learning the Delay Using Neural Delay Differential Equations
Maria Oprea, Mark Walth, Robert Stephany +3
The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap bet…
Asymmetric Private Set Intersection with Applications to Contact Tracing and Private Vertical Federated Machine Learning
Nick Angelou, Ayoub Benaissa, Bogdan Cebere +9
We present a multi-language, cross-platform, open-source library for asymmetric private set intersection (PSI) and PSI-Cardinality (PSI-C). Our protocol combines traditional DDH-ba…
How do we walk? Using hybrid holonomy to approximate non-holonomic systems
Maria Oprea, William Clark
Why do we move forward when we walk? Our legs undergo periodic motion and thus possess no net change in position; however, our bodies do possess a net change in position and we are…
A New Framework for Registration of Semantic Point Clouds from Stereo and RGB-D Cameras
Ray Zhang, Tzu-Yuan Lin, Chien Erh Lin +5
This paper reports on a novel nonparametric rigid point cloud registration framework that jointly integrates geometric and semantic measurements such as color or semantic labels in…
Orientation Control of the Bouncing Ball
William Clark, Dora Kassabova
Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous…
An Error-State Model Predictive Control on Connected Matrix Lie Groups for Legged Robot Control
Sangli Teng, Dianhao Chen, William Clark +1
This paper reports on a new error-state Model Predictive Control (MPC) approach to connected matrix Lie groups for robot control. The linearized tracking error dynamics and the lin…
Optimal Control of Quantum Purity for Systems
William Clark, Anthony Bloch, Leonardo Colombo +1
The objective of this work is to study time-minimum and energy-minimum global optimal control for dissipative open quantum systems whose dynamics is governed by the Lindblad equati…
Chromatic numbers with open and nonzero local modular constraints
Daniel Herden, Jonathan Meddaugh, Mark R. Sepanski +9
In this paper, we explore chromatic numbers subject to various local modular constraints. For fixed , we consider proper integer colorings of a graph for which the closed an…
Secret key distillation across a quantum wiretap channel under restricted eavesdropping
Ziwen Pan, Kaushik P. Seshadreesan, William Clark +4
The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assu…
Density of Gabor Systems Via the Short Time Fourier Transform
Andrew Ahn, William Clark, Shahaf Nitzan +1
We apply a new approach to the study of the density of Gabor systems, and obtain a simple and straightforward proof of Ramanathan and Steger's well known result regarding the densi…
Fully Relativistic Derivation of the Thermal Sunyaev-Zel'dovich Effect
BalÅ¡a TerziÄ, Geoffrey A. Krafft, William Clark +3
We present the first fully and inherently relativistic derivation of the thermal Sunyaev-Zel'dovich effect. This work uses the formalism historically used to compute radiation spec…
Symplectic Geometry in Hybrid and Impulsive Optimal Control
William Clark, Maria Oprea
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid…