Pontryagin’s Minimum Principle (PMP)를 이용한 하이브리드 전기차의 주행 제어 최적화
김남욱, 임원식, 오창은, 변상민, 차석원
Abstract
김남욱, 임원식, 오창은, 변상민, 차석원
Abstract
Several optimal control ideas for Hybrid Electric Vehicles (HEVs) were proposed in the literature. The representative optimal concept based on the bellman’s optimality, Dynamic Programming, guarantees a global optimal solution which could be obtained from an optimal field. In this paper, we suggest the Pontryagin’s minimum principle as an optimal control concept, in which the principle produces necessary conditions that the optimal control trajectory must satisfy. From a static model, the optimal results solved from PMP show that the results are really close to the results solved from DP, which should be supposed to be a global optimal solution. The differences between the results solved from PMP and the results solved from DP are only under 1 %. By the optimal control concept, PMP, we could build a real-time optimal controller because the technique is fundamentally based on an instantaneous optimal concept, which means that the control idea based on PMP is very useful if we have an intelligent model to approximate the costate in real-time driving.
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Several optimal control ideas for Hybrid Electric Vehicles (HEVs) were proposed in the literature. The representative optimal concept based on the bellman’s optimality, Dynamic Programming, guarantees a global optimal solution which could be obtained from an optimal field. In this paper, we suggest the Pontryagin’s minimum principle as an optimal control concept, in which the principle produces necessary conditions that the optimal control trajectory must satisfy. From a static model, the optimal results solved from PMP show that the results are really close to the results solved from DP, which should be supposed to be a global optimal solution. The differences between the results solved from PMP and the results solved from DP are only under 1 %. By the optimal control concept, PMP, we could build a real-time optimal controller because the technique is fundamentally based on an instantaneous optimal concept, which means that the control idea based on PMP is very useful if we have an intelligent model to approximate the costate in real-time driving.
Key concepts: Optimal control, Pontryagin's minimum principle, Maximum principle, Dynamic programming, Mathematical optimization, Trajectory, Mathematics, Control theory (sociology)