Related papers: Weak Dynamic Programming for Generalized State Con…
We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…
Within the framework of viscosity solution, we study the relationship between the maximum principle (MP) in [9] and the dynamic programming principle (DPP) in [10] for a fully coupled forward-backward stochastic controlled system (FBSCS)…
In this paper, we propose an original approach to stochastic control problems. We consider a weak formulation that is written as an optimization (minimization) problem on the space of probability measures. We then introduce a penalized…
We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to…
We formulate a path-dependent stochastic optimal control problem under general conditions, for which weprove rigorously the dynamic programming principle and that the value function is the unique Crandall-Lions viscosity solution of the…
We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, called measure-valued martingales (MVMs). We establish the…
We propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument which is based only on the subadditive structure of maximal subsolutions (solutions of the "metric problem"). This permits us to give…
We study optimal control problems governed by abstract infinite dimensional stochastic differential equations using the dynamic programming approach. In the first part, we prove Lipschitz continuity, semiconcavity and semiconvexity of the…
In this paper, we consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in [10.11], we can investigate the…
This paper is concerned with the stochastic recursive optimal control problem with mixed delay. The connection between Pontryagin's maximum principle and Bellman's dynamic programming principle is discussed. Without containing any…
We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In particular, we establish a maximum principle (MP) for control…
Discrete time control systems whose dynamics and observations are described by stochastic equations are common in engineering, operations research, health care, and economics. For example, stochastic filtering problems are usually defined…
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
Weak KAM theory for discount Hamilton-Jacobi equations and corresponding discount Lagrangian/Hamiltonian dynamics is developed. Then it is applied to error estimates for viscosity solutions in the vanishing discount process. The main…
We discuss a class of debt management problems in a stochastic environment model. We propose a model for the debt-to-GDP (Gross Domestic Product) ratio where the government interventions via fiscal policies affect the public debt and the…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…