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    This study introduces an adaptive dynamic programming scheme for optimal control of nonlinear impulsive systems. The method provides a feedback solution for fuel-optimal spacecraft orbital maneuvers, even with actuator faults.

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    Area of Science:

    • Control Theory
    • Aerospace Engineering
    • Applied Mathematics

    Background:

    • Optimal control of nonlinear impulsive systems presents challenges due to free impulse instants and number of impulses.
    • Existing methods may lack efficiency for real-time applications or complex maneuvers.

    Purpose of the Study:

    • To develop an adaptive dynamic programming (ADP) scheme for optimal control of nonlinear impulsive systems.
    • To provide a feedback solution for fuel-optimal spacecraft orbital maneuvers with fixed final time.
    • To enable simultaneous path planning and control for impulsive actuators.

    Main Methods:

    • A learning algorithm tunes function approximator parameters offline for on-the-fly feedback control.
    • The ADP scheme is designed to handle single and multiple impulsive actuators with low online computational cost.
    • The controller is applied to spacecraft orbital maneuvers with a fixed final time.

    Main Results:

    • The proposed ADP scheme successfully generates feedback control for optimal impulsive systems.
    • Simultaneous path planning and control were achieved for spacecraft orbital maneuvers.
    • The scheme demonstrated robustness in scenarios with shorter final times, varied initial states, and actuator faults.

    Conclusions:

    • The adaptive dynamic programming scheme offers an effective approach for optimal control of nonlinear impulsive systems.
    • The developed controller is suitable for fuel-optimal spacecraft orbital maneuvers, providing real-time feedback.
    • The scheme's adaptability to various conditions highlights its potential for complex aerospace applications.