Second-order and Second-variation Methods for Determining Optimal Control: A Comparative Study using Differential Dynamic Programming†

†Communicated by Professor J. H. Westcott.

Abstract

Second-variation methods for computing optimal control exhibit more rapid convergence than first-variation methods but at the exponse of vastly increased computing effort.

In this paper two second-order algorithms for determining optimal control are derived using the notion of differential dynamic programming, which is also used to re-derive the well known second-variation method. This unified treatment allows the differences between the three algorithms to be studied in detail.

It is shown that the second-order algorithms are more accurate than the second-variation method and, moreover, that one of these algorithms is simpler to implement.

Notes

†Communicated by Professor J. H. Westcott.

Additional information

Notes on contributors

D. H. JACOBSON‡

‡Present address: Computation Laboratory, Harvard University, Cambridge, Massachusetts, 02138, U.S.A.