The purpose of this course is to develop theoretical and applied skills in optimization and control for spacecraft guidance.
This video introduces boundary value problems that arise in optimal control. It explores some simple cases that can be solved analytically, and a strategy known as the shooting method for solving more difficult problems.
This video introduces the minimum time double integrator problem. This problem has been studied in most texts, and it provides an opportunity for us to apply the optimality conditions. We will show that the solution is non-singular, bang-bang, has at most one switch, and is fully characterized by a feedback control law. We will also look at other ways to solve the problem in preparation for more difficult problems.
This video analyzes the terminal descent phase of a lunar descent. It follows the work of Meditch originally published in 1964. We show that singular arcs cannot occur and expect, based on intuition, that the optimal thrust is off-bang. See Meditch for a full analysis.
This video takes a closer look at singularity in minimum time control. It specifically looks at the rendezvous of multiple spacecraft in LEO with motion described by the CWH equations. We see that singular solutions cannot occur when only two vehicles are involved, and we see that singular solutions must occur when more than two vehicles are involved. It is also seen the importance of controllability in the analysis.