Efficient dynamic programming implementations of Newton's method for unconstrained optimal control problems

摘要: Naive implementations of Newton's method for unconstrainedN-stage discrete-time optimal control problems with Bolza objective functions tend to increase in cost likeN 3 asN increases. However, if the inherent recursive structure problem is properly exploited, computing a Newton step will only linearly withN. The efficient implementation scheme proposed here similar Mayne's DDP (differential dynamic programming) but produces exactly, even when dynamical equations are nonlinear. also related Riccati treatment linear, two-point boundary-value that characterize solutions. For problems, programming approach and substitution differ an interesting way; however, these differences essentially vanish continuous-time limit.