Bi-Level Multiobjective Convex Co-Design Optimization of Hybrid VTOL Power and Energy Management Systems

Hybrid vertical take-off and landing aircraft are essential enablers of urban air mobility, and their performance critically depends on the coordinated matching between power system hardware parameters and the energy management strategy. Conventional sequential design–then–control approaches often neglect the strong coupling between physical components and control decisions, preventing the system from achieving global optimality. To address this issue, this study proposes a bi-level collaborative design optimization framework that integrates multi-objective particle swarm optimization with convex optimization. In the outer level, the multi-objective particle swarm optimization algorithm explores the hardware design space of the battery, electric motor, and rotor to balance multiple conflicting objectives, including endurance, total mass, system cost, and hover power. In the inner level, a convex-relaxed energy management model is formulated to obtain the fuel-optimal control strategy corresponding to each hardware candidate. Experimental results demonstrate that, compared with the decoupled design approach, the proposed bi-level collaborative design optimization framework leverages hardware–software synergy to reduce total system cost by 29.7%, propulsion-system mass by 8.8%, hover power by 5.2%, and mission fuel consumption by 13.7%, while maintaining required flight performance. These results confirm the effectiveness, superiority, and robustness of collaborative optimization for highly coupled electrified aerospace systems.