Related papers: Optimal response for stochastic differential equat…
We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times…
Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport…
We address the problem of discriminating with minimal error probability two given quantum operations. We show that the use of entangled input states generally improves the discrimination. For Pauli channels we provide a complete comparison…
We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality…
Assuming $A$ has maximal $L^p$-regularity, this paper investigates perturbations of $A$ by time-dependent operators $B$ that are unbounded and satisfy a critical $L^q$-integrability condition in time. We establish two main results. The…
A modification of the optimal fluctuation approach is applied to study the tails of the free energy distribution function P(F) for an elastic string in quenched disorder both in the regions of the universal behavior of P(F) and in the…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
This paper introduces a concept of a derivative of the optimal value function in linear programming (LP). Basically, it is the the worst case optimal value of an interval LP problem when the nominal data the data are inflated to intervals…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
We consider the problem of controlling the movement of multiple cooperating agents so as to minimize an uncertainty metric associated with a finite number of targets. In a one-dimensional mission space, we adopt an optimal control framework…
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…
We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
In this paper, we study parametric analysis of semidefinite optimization problems w.r.t. the perturbation of the objective function. We study the behavior of the optimal partition and optimal set mapping on a so-called nonlinearity…
In this manuscript, we investigate optimal control problems which arise in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems…
In spatio-temporal point pattern analysis, one of the main statistical objectives is to estimate the first-order intensity function, i.e., the expected number of points per unit area and unit time. This estimation is usually carried out…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
Neural operator approximations of the gain kernels in PDE backstepping has emerged as a viable method for implementing controllers in real time. With such an approach, one approximates the gain kernel, which maps the plant coefficient into…
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of…