Optimal Impulsive Control Using Adaptive Dynamic Programming and its Application in Spacecraft Rendezvous

Optimal control of nonlinear impulsive systems with free impulse instants and the number of impulses is investigated in this study. A scheme based on adaptive dynamic programming is developed, which leads to a feedback (approximate) solution to the defined optimal impulsive control problem. This is done by proposing a learning algorithm for tuning parameters of a function approximator, which, once tuned offline, provides feedback solution on-the-fly. The scheme is shown to handle single and multiple impulsive actuators with a small online computational burden. Afterward, the controller is applied to a challenging problem, namely, the orbital maneuver of spacecraft with the fixed final time using impulsive actuators. The objective is triggering the actuators in a fuel-optimal manner such that the spacecraft transfers to the desired orbit at a prescribed time. It was shown that the proposed scheme leads to simultaneous and feedback path planning and control for the maneuver. The potentials of the scheme are analyzed in different scenarios, including enforcing a shorter final time, selecting different initial states, and incorporating actuator faults.