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We consider a non-Markovian optimal stopping problem on finite horizon. We prove that the value process can be represented by means of a backward stochastic differential equation (BSDE), defined on an enlarged probability space, containing…
This paper studies optimal motion planning subject to motion and environment uncertainties. By modeling the system as a probabilistic labeled Markov decision process (PL-MDP), the control objective is to synthesize a finite-memory policy,…
IIn this paper, we study a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enter…
We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…
We derive the equations governing the protocols minimizing the heat released by a continuous-time Markov jump process on a one-dimensional countable state space during a transition between assigned initial and final probability…
This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs. Using an auxiliary function of maximum representation type, conditions are given to…
This paper is devoted to solving a time-inconsistent risk-sensitive control problem with parameter $\e$ and its limit case ($\e\rightarrow0^+$) for countable-stated Markov decision processes (MDPs for short). Since the cost functional is…
This paper studies a large number of homogeneous Markov decision processes where the transition probabilities and costs are coupled in the empirical distribution of states (also called mean-field). The state of each process is not known to…
In recent advances in finite-time thermodynamics, optimization of entropy production required for finite-time information processing is an important issue. In this work, we consider finite-time feedback processes in classical discrete…
This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching.…
In this paper, we concern with the ergodic linear-quadratic closed-loop optimal control problems, in which the state equation is the mean-field stochastic differential equation with periodic coefficients. We first study the asymptotic…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
We introduce the Lyapunov approach to optimal control problems of average risk-sensitive Markov control processes with general risk maps. Motivated by applications in particular to behavioral economics, we consider possibly non-convex risk…
We consider the constrained optimal control problem for the gradual-impulsive CTMDP model with the performance criteria being the expected total undiscounted costs (from the running cost and the cost from each time an impulse being…
This paper addresses the problem of steering the distribution of the state of a discrete-time linear system to a given target distribution while minimizing an entropy-regularized cost functional. This problem is called a maximum entropy…
We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture…
We study optimal Markovian couplings of Markov processes, where the optimality is understood in terms of minimization of concave transport costs between the time-marginal distributions of the coupled processes. We provide explicit…
This paper investigates the infinite horizon optimal control problem (OCP) for space applications characterized by nonlinear dynamics. The proposed approach divides the problem into a finite horizon OCP with a regularized terminal cost,…