Dual-loop voltage control of electric vehicle DWPT systems based on robust right coprime factorization and deep Q-networks

This paper proposes an adaptive robust voltage-control framework for dynamic wireless power transfer (DWPT) systems, explicitly targeting the problem of voltage stabilization under time-varying and uncertain load resistance typical in vehicular charging scenarios. The proposed architecture adopts a dual-loop structure: an inner loop that enforces provable stability via operator-theoretic robust right coprime factorization, and an outer loop that provides high-precision tracking through a data-driven deep reinforcement learning policy. In the inner-loop design, the receiver-side BUCK converter within an LCC-S DWPT topology is modeled in operator form and decomposed into right coprime factors. A controlled operator representation that accounts for unknown disturbances is formulated, and nonlinear control operators are synthesized based on the Bézout identity together with Lipschitz-type conditions. This design ensures bounded-input–bounded-output (BIBO) stability of the inner closed loop and limits the influence of model perturbations induced by abrupt load changes and coupling variations. In the outer-loop design, a Deep Q-Network (DQN) is trained to implement the tracking operator: a carefully constructed reward function drives the agent to learn duty-cycle adjustment policies that minimize voltage tracking error, eliminate steady-state bias, and improve transient response across a wide operating envelope. The combined scheme also incorporates practical considerations such as measurement noise and actuation constraints. Extensive comparative simulations against standard industrial controllers—proportional–integral (PI), model predictive control (MPC), and active disturbance rejection control (ADRC)，which demonstrate that the proposed hybrid approach markedly enhances robustness under stochastic load-resistance variations, achieves faster settling times, and reduces steady-state deviation. Overall, this work provides a theoretically grounded yet practically viable solution for reliable voltage regulation in electric-vehicle DWPT systems.