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In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based dissipativity estimation of nonlinear systems. The interplay between the underlying assumptions of these methods and their sample complexity is investigated. It is shown that methods based on delta-covering result in an intractable trade-off between sample complexity and robustness. A new method is proposed to quantify the robustness of machine learning-based dissipativity estimation. It is shown that this method achieves a more tractable trade-off between robustness and sample complexity. Several numerical case studies demonstrate the results., Comment: Preprint of conference manuscript, currently under review

Laser-based surgical ablation relies heavily on surgeon involvement, restricting precision to the limits of human error. The interaction between laser and tissue is governed by various laser parameters that control the laser irradiance on the tissue, including the laser power, distance, spot size, orientation, and exposure time. This complex interaction lends itself to robotic automation, allowing the surgeon to focus on high-level tasks, such as choosing the region and method of ablation, while the lower-level ablation plan can be handled autonomously. This paper describes a sampling-based model predictive control (MPC) scheme to plan ablation sequences for arbitrary tissue volumes. Using a steady-state point ablation model to simulate a single laser-tissue interaction, a random search technique explores the reachable state space while preserving sensitive tissue regions. The sampled MPC strategy provides an ablation sequence that accounts for parameter uncertainty without violating constraints, such as avoiding critical nerve bundles or blood vessels., Comment: 7 pages, 6 figures, submitted to IEEE ICRA 2025

Robot-assisted ultrasound scanning promises to advance autonomous and accessible medical imaging. However, ensuring patient safety and compliant human-robot interaction (HRI) during probe contact poses a significant challenge. Most existing systems either have high mechanical stiffness or are compliant but lack sufficient force and precision. This paper presents a novel single-degree-of-freedom end-effector for safe and accurate robotic ultrasound imaging, using a quasi-direct drive actuator to achieve both passive mechanical compliance and precise active force regulation, even during motion. The end-effector demonstrates an effective force control bandwidth of 100 Hz and can apply forces ranging from 2.5N to 15N. To validate the end-effector's performance, we developed a novel ex vivo actuating platform, enabling compliance testing of the end-effector on simulated abdominal breathing and sudden patient movements. Experiments demonstrate that the end-effector can maintain consistent probe contact during simulated respiratory motion at 2.5N, 5N, 10N, and 15N, with an average force tracking RMS error of 0.83N compared to 4.70N on a UR3e robot arm using conventional force control. This system represents the first compliant ultrasound end-effector tested on a tissue platform simulating dynamic movement. The proposed solution provides a novel approach for designing and evaluating compliant robotic ultrasound systems, advancing the path for more compliant and patient-friendly robotic ultrasound systems in clinical settings.

In a seminal paper, Epstein introduced the theory of what are now called Epstein surfaces, which construct surfaces in $\mathbb{H}^3$ associated to a conformal metric on a domain in $\hat{\mathbb{C}}$. More recently, these surfaces have been used by Krasnov-Schlenker to define the W-volume and renormalized volume associated with a convex co-compact hyperbolic 3-manifold. In this paper we consider Epstein surfaces, W-volume and renormalized volume in two main parts. In the first, we develop an alternate construction of Epstein surfaces using the Osgood-Stowe differential, a generalization of the Schwarzian derivative. Krasnov-Schlenker showed that the metric and shape operator of a surface in hyperbolic space is naturally dual to a conformal metric and shape operator on a projective structure via the hyperbolic Gauss map. We show that this projective shape operator can be derived from the Osgood-Stowe differential. This approach allows us to give a comprehensive and self-contained development of Epstein surfaces, W-volume, and renormalized volume. In the second part, we use the theory developed in the first to prove a number of new results including a generalization of Epstein's univalence criterion, a variational formula for W-volume in terms of the Osgood-Stowe differential, and a use of W-volume to relate the length of the bending lamination of the convex core to the norm of the Schwarzian derivative of the associated univalent map on the conformal boundary., Comment: Sections 9.2 and 9.3 supersede arxiv:2201.08926

This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from an operator-theoretic perspective, and the well-known open-loop dissipativity conditions for closed-loop/network stability are extended to the stochastic case. Criteria are derived to identify dissipative nonlinear systems with stochastic input delays, and this result is used to find delay-distribution-dependent linear matrix inequality conditions for stochastic dissipativity of a linear system with input delays of a known probability distribution. A numerical experiment demonstrates the utility of the resulting criteria for robust plant analysis and controller design, highlighting significantly reduced conservatism compared to deterministic methods., Comment: Preprint, version 2

We bound the derivative of complex length of a geodesic under variation of the projective structure on a closed surface in terms of the norm of the Schwarzian in a neighborhood of the geodesic. One application is to cone-manifold deformations of acylindrical hyperbolic 3-manifolds., Comment: 25 pages, 1 figure

TheL2-gain characterizes a dynamical system's input-output properties, but can be difficult to determine for nonlinear systems. Previous work designed a nonconvex optimization problem to simultaneously search for a continuous piecewise affine (CPA) storage function and an upper bound on the small-signal L2-gain of a dynamical system over a triangulated region about the origin. This work improves upon those results by establishing a tighter upper-bound on a system's gain using a convex optimization problem. By reformulating the relationship between the Hamilton-Jacobi inequality and L2-gain as a linear matrix inequality and then developing novel LMI error bounds for a triangulation, tighter gain bounds are derived and computed more efficiently. Additionally, a combined quadratic and CPA storage function is considered to expand the nonlinear systems this optimization problem is applicable to. Numerical results demonstrate the tighter upper bound on a dynamical system's gain.

Imitation learning enables the synthesis of controllers for complex objectives and highly uncertain plant models. However, methods to provide stability guarantees to imitation learned controllers often rely on large amounts of data and/or known plant models. In this paper, we explore an input-output (IO) stability approach to dissipative imitation learning, which achieves stability with sparse data sets and with little known about the plant model. A closed-loop stable dynamic output feedback controller is learned using expert data, a coarse IO plant model, and a new constraint to enforce dissipativity on the learned controller. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to successfully learn the controller. This new imitation learning method is applied to two unknown plants and compared to traditionally learned dynamic output feedback controller and neural network controller. With little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance.

This paper provides a method to analyze the small-signal L2 gain of control-affine nonlinear systems on compact sets via iterative semi-definite programs. First, a continuous piecewise affine storage function and the corresponding upper bound on the L2 gain are found on a bounded, compact set's triangulation. Then, to ensure that the state does not escape this set, a barrier function is found that is robust to small-signal inputs. Small-signal L2 stability then holds inside each sublevel set of the barrier function inside the set where the storage function was found. The bound on the inputs is also found while searching for a barrier function. The method's effectiveness is shown in a numerical example.

The moduli space of Anosov representations of a surface group in a semisimple group, which is an open set in the character variety, admits many more natural functions than the regular functions. We will study in particular length functions and, correlation functions. Our main result is a formula that computes the Poisson bracket of those functions using some combinatorial devices called {\em ghost polygons} and {\em ghost bracket} encoded in a formal algebra called {\em ghost algebra} related in some cases to the swapping algebra introduced by the second author. As a consequence of our main theorem, we show that the set of those functions -- length and correlation -- is stable under the Poisson bracket. We give two applications: firstly in the presence of positivity we prove the convexity of length functions, generalising a result of Kerckhoff in Teichm\"uller space, secondly we exhibit subalgebras of commuting functions. An important tool is the study of {\em uniformly hyperbolic bundles} which is a generalisation of Anosov representations beyond periodicity., Comment: 60 pages, 7 figures. This new version details the structure of the paper, which is now cut into parts with a detailed introduction

Topological subsystem codes in three spatial dimensions allow for quantum error correction with no time overhead, even in the presence of measurement noise. The physical origins of this single-shot property remain elusive, in part due to the scarcity of known models. To address this challenge, we provide a systematic construction of a class of topological subsystem codes in three dimensions built from abelian quantum double models in one fewer dimension. Our construction not only generalizes the recently introduced subsystem toric code [Kubica and Vasmer, Nat. Commun. 13, 6272 (2022)] but also provides a new perspective on several aspects of the original model, including the origin of the Gauss law for gauge flux, and boundary conditions for the code family. We then numerically study the performance of the first few codes in this class against phenomenological noise to verify their single-shot property. Lastly, we discuss Hamiltonians naturally associated with these codes, and argue that they may be gapless., Comment: v3 - Published version