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Typical plug-in hybrid electric buses (PHEBs) with fast-charged Lithium titanate battery, which might be fulfill about 70 percent distance of a representative city-bus-route, have been adopted in many Chinese cities. Considering that the detailed information of the driving cycle could be deduced with the historical driving data and online estimation methods, there might be an opportunity for applying the dynamic programming (DP)-based global optimal energy management strategy for these PHEBs. But the road-slopes or the variable loads might induce transient fluctuations of the driving resistance in a given driving cycle. Meantime, the single-shaft parallel configuration, with Automatic Mechanical Transmission (AMT), might constrain the implementability of the optimal energy distribution from DP-based strategy. Therefore, in this paper a novel correctional DP algorithm is brought forward to balance the optimization of the fuel economy and the drivability. Simulation results demonstrate that, integrated with the correctional logic of the AMT gear-shifting, the proposed energy management strategy can guarantee the engine and the electric machine (EM) work in the high-efficiency area with the optimal energy distribution, while keeping the drivability in the variation of the road-slope and loads. The proposed method might give a technical solution to these typical PHEB with a lower cost system configuration of the powertrain in China.Index Terms-plug-in hybrid electric bus; single-shaft parallel hybrid powertrain; energy management strategy; dynamic programming; drivability

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The adaptive synchronized problem of the four-dimensional (4D) Lü hyperchaotic system performed by Elabbasy et al. (Chaos Solitons Fractals 30:1133-1142 with uncertain parameters by applying the single control input is addressed in this article. Based on the Lyapunov theorem of stability, the single-input adaptive synchronization controllers associated with the adaptive update laws of system parameters are developed to make the states of two nearly identical 4D Lü hyperchaotic systems asymptotically synchronized. Numerical studies are presented to illustrate the effectiveness of the proposed chaotic synchronization schemes.

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