Related papers: Reverse-engineering invariant manifolds with asymp…
In this paper, we address the problem of stabilizing a system around a desired manifold determined by virtual nonlinear nonholonomic constraints. Virtual constraints are relationships imposed on a control system that are rendered invariant…
Spectral submanifolds (SSMs) have recently been shown to provide exact and unique reduced-order models for nonlinear unforced mechanical vibrations. Here we extend these results to periodically or quasiperiodically forced mechanical…
A hyper-redundant robotic arm is a manipulator with many degrees of freedom, capable of executing tasks in cluttered environments where robotic arms with fewer degrees of freedom are unable to operate. This paper introduces a new method for…
Stabilizing thermodynamically unstable phases in many-body systems, such as suppressing pathological neuronal synchronization in Parkinson's disease or maintaining magnetic order across broad temperature ranges, remains a persistent…
We give a procedure for "reverse engineering" a closed, simply connected, Riemannian manifold with bounded local geometry from a sparse chain complex over $\mathbb{Z}$. Applying this procedure to chain complexes obtained by "lifting"…
Exploring the design and control strategies of soft robots through simulation is highly attractive due to its cost-effectiveness. Although many existing models (e.g., finite element analysis) are effective for simulating soft robotic…
When intelligent spacecraft or space robots perform tasks in a complex environment, the controllable variables are usually not directly available and have to be inferred from high-dimensional observable variables, such as outputs of neural…
Inspired by the vertebrate branch of the animal kingdom, articulated soft robots are robotic systems embedding elastic elements into a classic rigid (skeleton-like) structure. Leveraging on their bodies elasticity, soft robots promise to…
Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data,…
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\bH^n$. The graphs are considered as subsets of $\bH^{n+1}$ and carry the induced metric. For such…
Evolution in time-varying environments naturally leads to adaptable biological systems that can easily switch functionalities. Advances in the synthesis of environmentally-responsive materials therefore open up the possibility of creating a…
We return to the subject of stability of infinite time asymptotics of kinetic equations. We found a model which is simpler than those studied previously and which shows unstable behavior corresponding to our arguments to appear elsewhere,…
This paper is motivated by the problem of asymptotically stabilizing invariant sets in the state space of control systems by means of output feedback. The sets considered are smooth embedded in submanifolds and the class of system is…
We revisit Vasy's method for showing meromorphy of the resolvent for (even) asymptotically hyperbolic manifolds. It provides an effective definition of resonances in that setting by identifying them with poles of inverses of a family of…
We introduce a numerical scheme to approximate a quasi-linear hyperbolic system which models the movement of cells under the influence of chemotaxis. Since we expect to find solutions which contain vacuum parts, we propose an upwinding…
A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a…
Continuum soft robots are mechanical systems entirely made of continuously deformable elements. This design solution aims to bring robots closer to invertebrate animals and soft appendices of vertebrate animals (e.g., an elephant's trunk, a…
An impulsive feedback-adaptive control is developed in order to drive trajectories of a dynamical system towards an invariant manifold with fixed and spaced impulsive controls. The approach requires the explicit knowledge of the set of…
In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…
We show that the mass of an asymptotically hyperbolic manifold with a noncompact boundary can be evaluated via the Ricci tensor and the second fundamental form by using purely coordinates. The method is analog to Miao-Tam's approach to the…