Hybrid Energy-Aware Reward Shaping: A Unified Lightweight Physics-Guided Methodology for Policy Optimization

Deep reinforcement learning excels in continuous control but often requires extensive exploration, while physics-based models demand complete equations and suffer cubic complexity. This study proposes Hybrid Energy-Aware Reward Shaping (H-EARS), unifying potential-based reward shaping with energy-aware action regularization. H-EARS constrains action magnitude while balancing task-specific and energy-based potentials via functional decomposition, achieving linear complexity O(n) by capturing dominant energy components without full dynamics. We establish a theoretical foundation including: (1) functional independence for separate task/energy optimization; (2) energy-based convergence acceleration; (3) convergence guarantees under function approximation; and (4) approximate potential error bounds. Lyapunov stability connections are analyzed as heuristic guides. Experiments across baselines show improved convergence, stability, and energy efficiency. Vehicle simulations validate applicability in safety-critical domains under extreme conditions. Results confirm that integrating lightweight physics priors enhances model-free RL without complete system models, enabling transfer from lab research to industrial applications.