Related papers: Optimal Paths for Spatially Extended Metastable Sy…
Recent advances in active noise control have enabled the development of hearables with spatial selectivity, which actively suppress undesired noise while preserving desired sound from specific directions. In this work, we propose an…
In physics, there is a scalar function called the action which behaves like a cost function. When minimized, it yields the "path of least action" which represents the path a physical system will take through space and time. This function is…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We consider the problem of finding a control policy for a Markov Decision Process (MDP) to maximize the probability of reaching some states while avoiding some other states. This problem is motivated by applications in robotics, where such…
This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…
We study the collective motion of self-propelled particles affected by the spatial-dependent noise based on the Vicsek rules. Only the particles inside the special region will affected by noise. The consideration of the spatial-dependent…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows…
Navigating toward a known target in a noisy environment is a fundamental problem shared across biological, physical, and engineered systems. Although optimal strategies are often framed in terms of continuous, fine-grained feedback, we show…
Agreement of the probability current with the resolving paths requires a simplified forward equation for the (unique) Ito paths. Their increments are the most probable rather than expected ones, in accordance with an existing extremum…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
This paper deals with the optimal path placement for a manipulator based on energy consumption. It proposes a methodology to determine the optimal location of a given test path within the workspace of a manipulator with minimal electric…
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
At present, the problem to steer a non-Markovian process with minimum energy between specified end-point marginal distributions remains unsolved. Herein, we consider the special case for a non-Markovian process y(t) which, however, assumes…
A popular approach for predicting the future of dynamical systems involves mapping them into a lower-dimensional "latent space" where prediction is easier. We show that the information-theoretically optimal approach uses different mappings…
We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…
Dissipation in quantum many-body systems provides a more general and experimentally realistic perspective on particle transport than closed quantum systems. In this work, we determine the maximal speed of macroscopic particle transport in…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…