Abstract
A family of first-order algorithms for solving unconstrained nonlinear optimal control problems is presented. This method is based on the invariant imbedding and the successive approximations. The followings are considered to be the advantage of this method:
(a) the algorithms are simple;
(b) the choice of the initial approximation in this method is not so sensitive as in the second-order algorithms;
(c) it is not required in these computations to find appropriate parameters in contrast with the case of gradient methods.
Using the fixed point theorem, this paper explains the sufficient conditions for L1-convergence of the proposed algorithms.
