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We propose a neural network approach that yields approximate solutions for highdimensional optimal control problems and demonstrate its effectiveness using examples from multiagent path finding. Our approach yields controls in a feedback form, where the policy function is given by a neural network (NN). Specifically, we fuse the HamiltonJacobiBellman (HJB) and Pontryagin Maximum Principle (PMP) approaches by parameterizing the value function with an NN. Our approach enables us to obtain approximately optimal controls in realtime without having to solve an optimization problem. Once the policy function is trained, generating a control at a given spacetime location takes milliseconds; in contrast,more »Free, publiclyaccessible full text available July 1, 2023

A normalizing flow is an invertible mapping between an arbitrary probability distribution and a standard normal distribution; it can be used for density estimation and statistical inference. Computing the flow follows the change of variables formula and thus requires invertibility of the mapping and an efficient way to compute the determinant of its Jacobian. To satisfy these requirements, normalizing flows typically consist of carefully chosen components. Continuous normalizing flows (CNFs) are mappings obtained by solving a neural ordinary differential equation (ODE). The neural ODE's dynamics can be chosen almost arbitrarily while ensuring invertibility. Moreover, the logdeterminant of the flow's Jacobianmore »

We propose a neural network approach for solving highdimensional optimal control problems. In particular, we focus on multiagent control problems with obstacle and collision avoidance. These problems immediately become highdimensional, even for moderate phasespace dimensions per agent. Our approach fuses the Pontryagin Maximum Principle and HamiltonJacobiBellman (HJB) approaches and parameterizes the value function with a neural network. Our approach yields controls in a feedback form for quick calculation and robustness to moderate disturbances to the system. We train our model using the objective function and optimality conditions of the control problem. Therefore, our training algorithm neither involves a data generationmore »