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Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem…
We present a minimal quasistatic 1D model describing the kinematics of the transition from static friction to stick-slip motion of a linear elastic block on a rigid plane. We show how the kinematics of both the precursors to frictional…
The unstable top-equilibrium point of a simple pendulum turns stable when its pivot point is given a fast and strong enough vertical vibration. Known as the Kapitza oscillator, it has four symmetrically spaced points of equilibrium in…
This paper studies the problem of passive grasp stability under an external disturbance, that is, the ability of a grasp to resist a disturbance through passive responses at the contacts. To obtain physically consistent results, such a…
The classical Hertzian contact model establishes a monotonic correlation between contact force and area. Here, we showed that the interplay between local friction and structural instability can deliberately lead to unconventional contact…
This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite-time horizon. We use stochastic control barrier functions as a means to quantify the probability that a system exits a given safe region of…
Pulse stabilization of cycles with Prediction-Based Control including noise and stochastic stabilization of maps with multiple equilibrium points is analyzed for continuous but, generally, non-smooth maps. Sufficient conditions of global…
This paper examines the details of an inelastic collision when a bullet shoots a block vertically upward from below. With the assumption of constant interaction force between them, we obtain quantities of interest including the displacement…
A focused acoustic standing wave creates a Hookean potential well for a small sphere and can levitate it stably against gravity. Exposing the trapped sphere to a second transverse traveling sound wave imposes an additional acoustical force…
The motion of several plates in an inviscid and incompressible fluid is studied numerically using a vortex sheet model. Two to four plates are initially placed in-line, separated by a specified distance, and actuated in the vertical…
This paper deals with the development of a handling-oriented stiffness control strategy using multichamber suspensions. Indeed, being this technology capable of stiffness variability, it is particularly indicated for improving the vehicle…
We investigate the dynamics of a dimer bouncing on a vertically oscillated plate. The dimer, composed of two spheres rigidly connected by a light rod, exhibits several modes depending on initial and driving conditions. The first excited…
Recent literature indicates that attractive interactions between particles of a dense liquid play a secondary role in determining its bulk mechanical properties. Here we show that, in contrast with their apparent unimportance to the bulk…
In this paper we study the finite-horizon optimal covariance steering problem for a continuous-time linear stochastic system subject to both additive and multiplicative noise. The noise can be continuous or it may contain jumps. Additive…
A theoretical analysis about the influence of the Hertz elastic contact on a three body chain collision is presented. In spite of the elastic character of the collision, the final velocity of each particle depends on the particular…
When facing a task of balancing a dynamic system near an unstable equilibrium, humans often adopt intermittent control strategy: instead of continuously controlling the system, they repeatedly switch the control on and off. Paradigmatic…
In this article, we focus on the global stabilizability problem for a class of second order uncertain stochastic control systems, where both the drift term and the diffusion term are nonlinear functions of the state variables and the…
We investigate the impact of noise on a two-dimensional simple paradigmatic piecewise-smooth dynamical system. For that purpose we consider the motion of a particle subjected to dry friction and coloured noise. The finite correlation time…
The planar inverted pendulum with a vibrating pivot point in the presence of an additional horizontal force field is studied. The horizontal force is not assumed to be small or rapidly oscillating. We assume that the pivot point of the…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…