Related papers: Universal differential equations for optimal contr…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…
We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…
In this paper we propose a new methodology for decision-making under uncertainty using recent advancements in the areas of nonlinear stochastic optimal control theory, applied mathematics, and machine learning. Grounded on the fundamental…
Solving real-world optimal control problems are challenging tasks, as the complex, high-dimensional system dynamics are usually unrevealed to the decision maker. It is thus hard to find the optimal control actions numerically. To deal with…
In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the…
Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets.…
In this article, a well-known mathematical model of cancer immunotherapy is discussed and used to represent therapeutic protocols for cancer treatment. The optimal control problem is formulated based on the Pontryagin maximum principle to…
In this work, we investigate an indirect approach for the numerical solution of optimal control problems via neural networks. A customized neural network is constructed, where optimal state, co-state and control trajectories are…
We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…
We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are…
In this paper, we consider a class of stochastic control problems for stochastic differential equations with random coefficients. The control domain need not to be convex but the control process is not allowed to enter in diffusion term.…
In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear…
An optimal control problem for a model of tumor growth is studied. In a given subdomain, it is required to minimize the density of tumor cells, while the drug concentration in tissue is limited by given minimal and maximal values. Based on…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…