Related papers: A Neural Network Approach for High-Dimensional Opt…
We propose a neural network approach for solving high-dimensional optimal control problems. In particular, we focus on multi-agent control problems with obstacle and collision avoidance. These problems immediately become high-dimensional,…
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…
This paper first introduces a method to approximate the value function of high-dimensional optimal control by neural networks. Based on the established relationship between Pontryagin's maximum principle (PMP) and the value function of the…
The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…
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…
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…
Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional…
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 consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage…
We study the problem of generating control laws for systems with unknown dynamics. Our approach is to represent the controller and the value function with neural networks, and to train them using loss functions adapted from the…
The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently developed policy…
We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…
We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…
We address finding the semi-global solutions to optimal feedback control and the Hamilton--Jacobi--Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal control law can be implemented in real-time with minimum…
We propose a physics-informed neural network policy iteration (PINN-PI) framework for solving stochastic optimal control problems governed by second-order Hamilton--Jacobi--Bellman (HJB) equations. At each iteration, a neural network is…
To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that…
Neural network approaches that parameterize value functions have succeeded in approximating high-dimensional optimal feedback controllers when the Hamiltonian admits explicit formulas. However, many practical problems, such as the space…
This paper addresses the model-free nonlinear optimal problem with generalized cost functional, and a data-based reinforcement learning technique is developed. It is known that the nonlinear optimal control problem relies on the solution of…
The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal…
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…