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In this study, a multi-objective optimization method based on the Radau pseudospectral method is proposed for the energy management strategy in the hybrid energy storage system (HESS). In the proposed method, by approximating state and control variables in the system with global interpolating polynomials, the optimal control problem (OCP) is transformed into a nonlinear programming problem (NLP) and solved by a sparse nonlinear optimizer. Further, the Pareto solution set is obtained by taking the energy consumption of the HESS and the equivalent life of the battery as objective functions. Three solutions representing different tradeoffs were selected for comparative analysis: minimum system energy consumption (5819.60 kJ), with battery life 68368 cycles; maximum battery life (76227 cycles), with energy consumption 5865.68 kJ; and the balanced tradeoff optimal solution with battery life 72488 cycles and energy consumption 5841.96 kJ. The results showed that for every additional 5 kJ in system energy consumption, the battery Ah-throughput was reduced by 0.053 Ah and its equivalent life extended by 876 cycles. Further, compared with the single-cell energy source, the balanced tradeoff optimal solution increased the battery life by 29.92% and decreased the system energy consumption by 1.79%. Thus, this work provides a fast and stable multi-objective optimization method for the energy management strategy of HESS and lays the foundation for obtaining optimal system parameters. INDEX TERMS Energy management strategy, hybrid energy storage system, multi-objective optimization, Radau pseudospectral method.

For a seamless two-speed transmission specially equipped in electric vehicles, the global trajectory optimization problem of the overlapping shift process with multiple stages and complex path/point constraints is investigated in this article. The overlapping shift principle and the dynamic models in each phase are also demonstrated in detail. The parameters to evaluate the shift quality are analyzed and then introduced into the objective function and constraints, respectively. The jerks in process and at the key moments have been distinguished and selected as the path and point constraints, respectively. Moreover, considering the joint characteristics of the torque phase and the inertia phase, the trajectory optimization problems in the above two phases are summarized as a multi-stage global trajectory optimization problem. Then, Legendre pseudo-spectral method is used to transfer the multi-stage global trajectory optimization problem into a nonlinear programming problem for numerical solutions. Finally, the effectiveness and feasibility of the multi-stage global trajectory optimization method have been verified through the comparison of the optimal shift trajectories under different conditions with that obtained by the piecewise trajectory optimization method.