Sensitivity of optimal control systems with bang-bang control.

The effects of small parameter variations on the performance index of optimal control systems with initial and final target manifolds, free end time, and bang-bang control are analyzed in this paper. A new approach to the sensitivity equation is presented. This approach takes into account the pulse-shaped variation produced by the parameter change on the bang-bang control. An expression, that relates the variations of the performance index, the trajectory, the final time, and the parameter, is derived. This expression extends to the class of optimal systems with bang-bang control, a result previously obtained by Courtin and Rootenberg (1971).