Fixed-Time Optimal-Power Thrust Control in Distributed Electric Cycloidal Propulsion Using Hybrid Residual Neural Networks

Distributed electric propulsion enabled cycloidal rotors offer enhanced maneuverability and sustainability for aerial and marine platforms through independent blade-level actuation. However, their over-actuated and nonlinear nature offers significant challenges in achieving accurate thrust control and vectoring alongside power-optimal operation. Additionally, a purely model-based optimal controller may yield inaccurate performance predictions due to the complex cycloidal rotor geometry, modeling uncertainties, and unsteady aerodynamic effects. To mitigate modeling limitations, the cycloidal rotor performance is evaluated using a hybrid approach by integrating a physics-based aerodynamic model with a residual neural network to predict the discrepancies in thrust and power. To address the control and optimization problem, the present article develops an optimal-power fixed-time control framework that integrates thrust tracking and energy minimization within a unified architecture. By exploiting the null space of the thrust Jacobian, the proposed approach achieves power optimization without compromising thrust feasibility. Moreover, the fixed-time control law guaranties convergence of the thrust vector to its desired value and convergence of the control inputs to their optimal values within a time bound. A Lyapunov-based analysis is employed to establish fixed-time stability and to derive an explicit bound on the settling time. Numerical results reflect that the proposed hybrid model outperforms the physics-based model in predicting thrust and power. Additional numerical simulations validate the theoretical results, demonstrating uniform thrust convergence, bounded control rates, dynamic thrust tracking with blade activation–deactivation and synchronization, and convergence to a constrained power-optimal solution. Compared with existing methods, the proposed approach achieves an approximately 22% improvement in thrust tracking performance and improves efficiency by$1.42% - 8.58 %$with optimal power consumption.