On the comparison of the sensitivities of open-loop and closed-loop optimal control systems

This paper derives, via Pontryagin´s minimum principle, the invariance of the sensitivity of cost for optimal systems with respect to open-loop and closed-loop control law implementation when system parameters undergo small variations. The result obtained here is more general than that of Pagurek[1] and somewhat easier to apply than that of Witsenhausen.[2] The cost of the sensitivity vector is simply related to the gradient of the Hamiltonian function.