The Powered Explicit Guidance is a successful algorithm with many practical applications. However, there are areas of improvement that can be made. As can be seen, there are many approximations made which reduce the optimality of PEG. There is also no way to completely constrain the final po- sition with the original implementation; however, Fill’s improvements should allow for this. In addition, while PEG is able to combine multiple thrust arcs, such as a constant thrust arc followed by a constant acceleration arc, there is no computation of optimal bang-bang switching times for the throttle command between maximum and minimum thrust levels. In fact, PEG was derived assuming that the thrust profile is a known function of time.

-- An Investigation of Fuel Optimal Descent, Jeremy Ryan Rea, 2009

Having worked on guidance algorithms for on-orbit maneuvers and soft landings on the Moon, I'll add that PEG is useful in the boost stage of rockets (high thrust long burn times) but not as useful when it comes to precise maneuvering (maybe high thrust, possibly very low burn times (10-30 seconds)). Coworkers have disagreed with me on that by correctly pointing out that Orion uses PEG for all of its maneuvering.

In my experience, one of the main issues with PEG is that it targets a Cartesian state with an open-loop time to go: matching the orbital energy is important for transfers (e.g. trans-lunar injections, probably also for lunar orbit injections) but may increase the cost of cleanup maneuvers. In fact, if the Cartesian state is achieved at the wrong epoch, then the orbit may be completely different. Hence, one approach is to use a orbital element targeting scheme (Ruggiero, Q-Law, etc.) to meet the orbital parameters with high accuracy and have the true anomaly as a free parameter. This ensure correct orbital insertion and allows mission designers to then perform clean-up maneuvers to fix specific orbital elements.

The other issue with PEG is that it requires very good knowledge of the acceleration of the vehicle throughout the burn. In turn, this means low-noise inertial measurement units (and low noise aggregation (random walk is small)), and those can be prohibitively expensive (several million dollars each). That's why a common scheme used on non-governmental missions is to have a cheaper IMU and two cut-off thresholds: (noisy) acceleration and max burn time.

The Powered Explicit Guidance is a successful algorithm with many practical applications. However, there are areas of improvement that can be made. As can be seen, there are many approximations made which reduce the optimality of PEG. There is also no way to completely constrain the final po- sition with the original implementation; however, Fill’s improvements should allow for this. In addition, while PEG is able to combine multiple thrust arcs, such as a constant thrust arc followed by a constant acceleration arc, there is no computation of optimal bang-bang switching times for the throttle command between maximum and minimum thrust levels. In fact, PEG was derived assuming that the thrust profile is a known function of time.

-- An Investigation of Fuel Optimal Descent, Jeremy Ryan Rea, 2009 [1]

Having worked on guidance algorithms for on-orbit maneuvers and soft landings on the Moon, I'll add that PEG is useful in the boost stage of rockets (high thrust long burn times) but not as useful when it comes to precise maneuvering (maybe high thrust, possibly very low burn times (10-30 seconds)). Coworkers have disagreed with me on that by correctly pointing out that Orion uses PEG for all of its maneuvering.

In my experience, one of the main issues with PEG is that it targets a Cartesian state with an open-loop time to go: matching the orbital energy is important for transfers (e.g. trans-lunar injections, probably also for lunar orbit injections) but may increase the cost of cleanup maneuvers. In fact, if the Cartesian state is achieved at the wrong epoch, then the orbit may be completely different. Hence, one approach is to use an orbital element targeting scheme (Ruggiero, Q-Law, etc.) to meet the orbital parameters with high accuracy and have the true anomaly as a free parameter. This ensures correct orbital insertion and allows mission designers to then perform clean-up maneuvers to fix specific orbital elements.

The other issue with PEG is that it requires very good knowledge of the acceleration of the vehicle throughout the burn. In turn, this means low-noise inertial measurement units (and low noise aggregation (random walk is small)), and those can be prohibitively expensive (several million dollars each). That's why a common scheme used on non-governmental missions is to have a cheaper IMU and two cut-off thresholds: (noisy) acceleration and max burn time. Then, mission designers simply upload a $\Delta v$ (velocity change) to achieve and an orientation the vehicle should have throughout the burn.