Direct-sensitivity method of solving boundary-value problems in optimal control studies

A method of solving the 2-point boundary-value problem arising from Pontryagin´s principle is described. The technique is based on the use of sensitivity coefficients with respect to the initial-condition parameters and is shown to have rapid convergence. The method is applicable to multivariable systems with hard constraints on state or control variables. Several examples of applications are described in the paper. A modification of the method enables free-time or time-optimal problems to be treated, and examples of these are also described.