# On the use of frequency analysis tools to minimize the calculation complexity of Optimal Control Problems

IFAC-PapersOnLine（2022）

摘要

Transport domain is currently facing the challenge of reducing its CO2 emissions. To do so, hybrid electric vehicles have been developed. Having several power sources offer the possibility to reach an optimal use of power systems. This can be considered as Optimal Control Problem (OCP). Various methods exist to solve such problems. Since the 1960s and the Dynamic Programming (DP) developed by Bellman, it is possible to get the optimal solution for a constrained nonlinear system. This method is used to solve OCPs. However, the computational effort of DP is exponential and depends on the number of state and control variables. The present study used the frequency analysis tools Relative Gain Array and Column Diagonal Dominance Degree to dissociate states and control variables that are not linked and on the contrary pair those that are linked. This enables a larger Multi Input Multi Output (MIMO) DP to be built from a succession of smaller MIMO DP that will successively solve the OCP. Since there is sub optimality by not solving problems at the same time, a trade-of between accuracy and computational time has to be done. The methodology reduces the calculation complexity and memory, making it possible to use a better mesh-grid to recover lost optimality.

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关键词

Optimal Control Problem (OCP),Energy Management Strategy (EMS),Dynamic Programming (DP),Hybrid Electric Vehicle (HEV),Frequency tool analysis

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