Performance index sensitivity of optimal control systems

This correspondence analyzes the performance index sensitivity to small parameter variations of the optimal control problem with initial and final target manifolds, free end time, and where a terminal penalty appears in the performance index. An expression is derived to relate the variations of the performance index, the trajectory, the final time, and the parameters. This expression generalizes to the free end time case the result obtained by Kokotovic et al. [1] for fixed time problem without terminal penalty.