# From boundary lines to boundary surfaces for dynamic programming with final state constraints

IFAC PAPERSONLINE（2023）

摘要

This article addresses the generalization of the boundary lines method for Dynamic Programming, called here boundary surface. This method can be applied on any system with 2 states as long as there are border constraints (initial or final). The method has been applied to two different problems. The first one is a simplified convex acceleration problem with final constraints on speed and position. The second problem is the energy minimization of a parallel hybrid electric vehicle along a trip in a non linear and non convex formulation. Results show a non negligible accuracy improvement despite the increase in calculation time. This can yield more accurate optimal results than those found by any possible mesh grids on an average computer for a reasonable calculation time. Copyright (c) 2023 The Authors.

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关键词

Dynamic Programming (DP),Boundary Lines (BL),Boundary Surface (BdS),Optimal Control Problem ( OCP),Energy Management Strategy (EMS)

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