Related papers: Geometry of non-holonomic diffusion
We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokker-Planck equation for the probability density function of…
This paper studies hamiltonization of nonholonomic systems using geometric tools. By making use of symmetries and suitable first integrals of the system, we explicitly define a global 2-form for which the gauge transformed nonholonomic…
We demonstrate the phenomenon of stochastic resonance (SR) for discrete-time dynamical systems. We investigate various systems that are not necessarily bistable, but do have two well defined states, switching between which is aided by…
We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
This paper discusses dynamical systems for disk-covering and sphere-packing problems. We present facility location functions from geometric optimization and characterize their differentiable properties. We design and analyze a collection of…
We address the risk bounded trajectory optimization problem of stochastic nonlinear robotic systems. More precisely, we consider the motion planning problem in which the robot has stochastic nonlinear dynamics and uncertain initial…
We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1-$d$ map models whose slope is everywhere 1 (therefore the Lyapunov exponent is zero) but with random quenched discontinuities and quasi-periodic…
We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…
We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph…
We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…
Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study…
We investigate the high dimensional Hamiltonian chaotic dynamics in $N$ coupled area-preserving maps. We show the existence of an enhanced trapping regime caused by trajectories performing a random walk {\em inside} the area corresponding…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
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…
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a…
A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation…
The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. This…