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<p>This paper investigates the design of a robust optimal tracking control law for a quadrotor unmanned aerial vehicle (UAV). The quadrotor is considered an underactuated system subjected to external disturbances. Mathematically, it is modeled by translational and rotational dynamic equations that are strongly coupled through a rotation matrix. Moreover, the quadrotor is well known as a highly nonlinear system. Consequently, it is difficult, and in many cases impossible, to obtain a closed-form solution to the Hamilton–Jacobi–Bellman (HJB) equation by purely analytical means. To overcome this challenge, a control strategy that combines an optimal backstepping-based Reinforcement Learning (RL) controller with an extended state observer (ESO) is proposed. The ESO is designed to accurately estimate and compensate for external disturbances. Based on the backstepping technique and RL theory, an optimal backstepping-based RL controller is developed for both the translational and rotational subsystems to learn the optimal solution of the HJB equations. The stability of the overall quadrotor system is established by means of Lyapunov stability analysis. Finally, numerical simulations are conducted to verify the effectiveness of the proposed controller.</p>

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Robust Optimal Backstepping Control for Quadrotor UAVs via Reinforcement Learning

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Truong Minh Ngo,
  • Gia Khiem Dinh,
  • Phuong Nam Dao

摘要

This paper investigates the design of a robust optimal tracking control law for a quadrotor unmanned aerial vehicle (UAV). The quadrotor is considered an underactuated system subjected to external disturbances. Mathematically, it is modeled by translational and rotational dynamic equations that are strongly coupled through a rotation matrix. Moreover, the quadrotor is well known as a highly nonlinear system. Consequently, it is difficult, and in many cases impossible, to obtain a closed-form solution to the Hamilton–Jacobi–Bellman (HJB) equation by purely analytical means. To overcome this challenge, a control strategy that combines an optimal backstepping-based Reinforcement Learning (RL) controller with an extended state observer (ESO) is proposed. The ESO is designed to accurately estimate and compensate for external disturbances. Based on the backstepping technique and RL theory, an optimal backstepping-based RL controller is developed for both the translational and rotational subsystems to learn the optimal solution of the HJB equations. The stability of the overall quadrotor system is established by means of Lyapunov stability analysis. Finally, numerical simulations are conducted to verify the effectiveness of the proposed controller.