Optimal Trajectories for Quadratic Variational Processes Via Invariant Imbedding

摘要

An improved derivation of the initial-value problems of invariant imbedding for a quadratic variational problem is provided. Although typical approaches lead to characterizing the optimizers as solutions of Euler differential equations subject to certain boundary conditions, numerical solution of such problems is far from routine. When optimizers are described as solutions of initial-value problems, however, there are inherent computational advantages. The transformation does not require the use of Euler equations, dynamic programming, or the Pontryagin principle; only ordinary differential equations are employed. The Cauchy problem provides a one-sweep integration procedure. Various extensions are indicated. (Author)