Related papers: A patchy Dynamic Programming scheme for a class of…
In this paper, we consider the functional It\^o calculus framework to find a path-dependent version of the Hamilton-Jacobi-Bellman equation for stochastic control problems that feature dynamics and running cost that depend on the path of…
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution…
We present an algorithm for a multi-agent path planning problem with pattern coordination based on dynamic programming and a Hamilton-Jacobi-Bellman equation. This falls broadly into the class of partial differential equation (PDE) based…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The…
This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, similar to that of the Pauli matrices, and…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value…
In this article, we study optimal feedback control synthesis of stochastic 2D Navier-Stokes equations perturbed Levy type noise with distributed stochastic control process acting on the state equation. We use the dynamic programming…
Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…
The Dynamic Programming approach allows to compute a feedback control for nonlinear problems, but suffers from the curse of dimensionality. The computation of the control relies on the resolution of a nonlinear PDE, the…
Stochastic optimal control problems governed by delay equations with delay in the control are usually more difficult to study than the the ones when the delay appears only in the state. This is particularly true when we look at the…
We discuss time-optimal control problems for two setups involving globally driven Rydberg atoms in the blockade limit by deriving the associated Hamilton-Jacobi-Bellman equations. From these equations, we extract the globally optimal…
We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential…
We study the numerical approximation of time-dependent, possibly degenerate, second-order Hamilton-Jacobi-Bellman equations in bounded domains with nonhomogeneous Dirichlet boundary conditions. It is well known that convergence towards the…
In this paper, we investigate the distributed optimal control problem for a kind of nonlinear multi-agent systems. In particular,both the state and the system dynamic structures of each agent are private and can only be shared among…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-based structures. In this paper, we establish the existence and…
This paper extends the considerations of the works [1, 2] regarding curse-of-dimensionality-free numerical approaches to solve certain types of Hamilton-Jacobi equations arising in optimal control problems, differential games and elsewhere.…