Related papers: Hamilton-Jacobi Based Policy-Iteration via Deep Op…
There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…
Mixed optimal stopping and stochastic control problems define variational inequalities with non-linear Hamilton-Jacobi-Bellman (HJB) operators, whose numerical solution is notoriously difficult and lack of reliable benchmarks. We first use…
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…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
We address the problem of combined stochastic and impulse control for a market maker operating in a limit order book. The problem is formulated as a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose an implicit…
The performance of deep neural networks (DNN) is very sensitive to the particular choice of hyper-parameters. To make it worse, the shape of the learning curve can be significantly affected when a technique like batchnorm is used. As a…
This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…
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 construct and compare three operator learning architectures, DeepONet, Fourier Neural Operator, and Wavelet Neural Operator, in order to learn the operator mapping a time-dependent applied current to the transmembrane potential of the…
We propose a class of numerical schemes for nonlocal HJB variational inequalities (HJBVIs) with monotone drivers. The solution and free boundary of the HJBVI are constructed from a sequence of penalized equations, for which a continuous…
We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve…
This paper presents a learning-based optimal control framework for safety-critical systems with parametric uncertainties, addressing both time-triggered and self-triggered controller implementations. First, we develop a robust control…
We propose and analyze a randomization scheme for a general class of impulse control problems. The solution to this randomized problem is characterized as the fixed point of a compound operator which consists of a regularized nonlocal…
In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We…
We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the…
We present a method for collisionless multi-agent path planning using the Hamilton-Jacobi-Bellman equation. Because the method is rooted in optimal control theory and partial differential equations, it avoids the need for hierarchical…
We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and…
It is well known that time dependent Hamilton-Jacobi-Isaacs partial differential equations (HJ PDE), play an important role in analyzing continuous dynamic games and control theory problems. An important tool for such problems when they…
The paper studies a system of first order Hamilton-Jacobi equations with discontinuous coefficients, arising from a model of deterministic optimal debt management in infinite time horizon, with exponential discount and currency devaluation.…