Related papers: Set Invariance with Probability One for Controlled…
Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time $T_1$ by adding noise to the data, (ii) estimate its score function, and (iii)…
Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs…
In this paper, we show that under mild controllability assumptions a time-invariant Control Barrier Function (CBF) can be constructed based on predictions with a finite horizon. As a starting point, we require only a known subset of a…
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…
This paper presents novel theoretical results to guarantee multi-agent set invariance using Matrix Control Barrier Functions in sampled-data systems. More specifically, the paper presents conditions under which heterogeneous control-affine…
We consider the problem of safety verification and safety-aware controller synthesis for systems with sector bounded nonlinearities. We aim to keep the states of the system within a given safe set under potential actuator and sensor…
We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…
Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…
The problem of domain aiming control is formulated for controlled stochastic nonlinear systems. This issue involves regularity of the solution to the resulting closed-loop stochastic system. To begin with, an extended existence and…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
In this work we show that one can solve a finite horizon non-Markovian impulse control problem with control dependant dynamics. This dynamic satisfies certain functional Lipschitz conditions and is path dependent in such a way that the…
In the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…
Uncertainties influencing the dynamical systems pose a significant challenge in estimating the achievable performance of a controller aiming to control such uncertain systems. When the uncertainties are of stochastic nature, obtaining hard…
A new class of control problems is discussed - homeostasis control. Homeostasis control problems can be considered as control problems with a given target set, in particular, as a problem of stabilizing the values of some target function,…
We introduce a general methodology for quantitative model checking and control synthesis with supermartingale certificates. We show that every specification that is invariant to time shifts admits a stochastic invariant that bounds its…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
In N.V. Krylov, Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies, Electron. J. Probab., 4(2), 1999, it is proved under standard assumptions that the value functions of…
In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…
We study the problem of optimally managing an inventory with unknown demand trend. Our formulation leads to a stochastic control problem under partial observation, in which a Brownian motion with non-observable drift can be singularly…
In this paper, we consider the problem of simultaneously testing many two-sided hypotheses when rejections of null hypotheses are accompanied by claims of the direction of the alternative. The fundamental goal is to construct methods that…