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In this work we provide explicit conditions on the existence of optimal feedback controls for stochastic processes with regime-switching. We use the compactification method which needs less regularity conditions on the coefficients of the…
We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum…
Continuous-discrete models with dynamics described by stochastic differential equations are used in a wide variety of applications. For these systems, the maximum a posteriori (MAP) state path can be defined as the curves around which lie…
Trajectory optimization and model predictive control are essential techniques underpinning advanced robotic applications, ranging from autonomous driving to full-body humanoid control. State-of-the-art algorithms have focused on data-driven…
This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node…
We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a…
We study the probability distribution and the escape rate in systems with delayed dissipation that comes from the coupling to a thermal bath. To logarithmic accuracy in the fluctuation intensity, the problem is reduced to a variational…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
Optimal transport theory, originally developed in the 18th century for civil engineering, has since become a powerful optimization framework across disciplines, from generative AI to cell biology. In physics, it has recently been shown to…
Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
This work extends the minimum-dissipation model of large-eddy simulation and symmetry-preserving discretization to account for active or passive scalar transport and complex physical mechanisms.This novel scalar-minimum-dissipation model…
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…
A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum…
Controlling the evolution of nonequilibrium systems to minimize dissipated heat or work is a key goal for designing nanodevices, both in nanotechnology and biology. Progress in computing optimal protocols has thus far been limited to either…
Small nonequelibrium systems driven by an external periodic protocol can be described by Markov processes with time-periodic transition rates. In general, current fluctuations in such small systems are large and may play a crucial role. We…
The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variation distance ambiguity on the conditional distribution of the controlled process. We formulate the stochastic…
We establish a collection of closed-loop guarantees and propose a scalable optimization algorithm for distributionally robust model predictive control (DRMPC) applied to linear systems, convex constraints, and quadratic costs. Via standard…