Abstract
Solving high-dimensional optimal control problems in real-time is an important but challenging problem, with applications to multiagent path planning problems, which have drawn increased attention given the growing popularity of drones in recent years. In this paper, we propose a novel neural network method called SympOCnet that applies the symplectic network to solve high-dimensional optimal control problems with state constraints. We present several numerical results on path planning problems in two- and three-dimensional spaces. Specifically, we demonstrate that our SympOCnet can solve a problem with more than 500 dimensions in 1.5 hours on a single GPU, which shows the effectiveness and efficiency of SympOCnet. The proposed method is scalable and has the potential to solve truly high-dimensional path planning problems in real-time.
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