Multi-time-scale online joint optimization control of driving strategy and energy management for diesel-battery hybrid trains

The joint optimization of driving strategy and energy management is crucial for the energy efficiency of diesel-battery hybrid trains. This paper proposes a multi-time-scale hierarchical joint optimization (MTHJO) architecture driven by a combined convex programming (CP) and proportional-integral dimension-reduced dynamic programming (PI-DRDP) control strategy. At the long-time-scale planning layer, the CP method employs techniques such as convex approximations, variable equivalence substitutions, and convex relaxation to transform the non-convex joint problem into the convex model, thereby rapidly generating optimal reference trajectories and extracting dual variables. At the short-time-scale control layer, the PI-DRDP method optimizes traction force and power split. It applies the Pontryagin minimum principle to reduce the state space dimension from 3 to 1, thereby lowering the computational burden. To further accelerate computation, this method maps the extracted dual variables to initial feedforward costates and uses a proportional-integral (PI) controller to adaptively adjust them online, thereby avoiding iterative boundary-value solutions. Simulations and hardware-in-the-loop tests validate the strategy. Compared to a rule-based baseline, model predictive control, and reinforcement learning, it achieves fuel savings of up to 50.65%, 7.28%, and 7.95%, respectively. The maximum fuel gap from the offline global optimum is only 1.85%. Planning computation takes under 5 s, and control executes in milliseconds, ensuring real-time operation. This strategy exhibits robustness to operational disturbances and ensures safe train operation under extreme conditions with communication delays and positioning errors.