Optimal deterministic guidance for bounded-thrust spacecrafts

Neighboring optimal control for fixed-time multi-burn orbital transfers

“…As is well known, it is impossible to construct the NOG unless the JC holds along the nominal extremal [4] since the gain matrices are unbounded if the JC is violated. This result was actually obtained by Kelley [2], Kornhauser et al [29], Chuang et al [5], Pontani et al [33,34], and many others who minimize the AMP to construct the NOG. As a matter of fact, given every infinitesimal deviation from the nominal state, the JC, once satisfied, guarantees that there exists a neighboring extremal trajectory passing through the deviated state.…”

“…[32]. As far as the author knows, a few scholars, including Chuang et al [5] and Kornhauser et al [29], have made efforts on developing the NOG for low-thrust multi-burn orbital transfer problems. In the work [5] by Chuang et al, without taking into account the feedback on thrust-on times, the second variation on each burn arc was minimized such that the neighboring optimal feedbacks on thrust direction and thrust off-times were obtained.…”

“…In the work [5] by Chuang et al, without taking into account the feedback on thrust-on times, the second variation on each burn arc was minimized such that the neighboring optimal feedbacks on thrust direction and thrust off-times were obtained. Considering both endpoints are fixed, Kornhauser and Lion [29] developed an AMP for bounded-thrust optimal orbital transfer problems. Then, through minimizing this AMP, the linear feedback forms of thrust direction and switching times were derived.…”

“…Therefore, the existence of neighboring extremals is a prerequisite to establish the NOG. Once the optimal control function exhibits a bang-bang behavior, it is however not clear what conditions have to be satisfied in order to guarantee the existence of neighboring extremals [29].…”

Successive Convexification for 6-DoF Powered Descent Guidance with Compound State-Triggered Constraints

“…However, these methods were not incorporated into the Apollo flight code since the polynomial-based guidance methods in use at the time were deemed sufficiently optimal, and were far simpler to design and implement [5]. After the Apollo program, research continued in search of analytical solutions to the 3-degree-of-freedom (DoF) landing problem [6,7,8,9].…”