Comparative Sensitivity of Optimal Control Systems

Mathematical models of dynamic systems, such as aircraft, are always approximate. In addition, the parameters in the model may be inaccurate and change with operating conditions. Clearly, sensitivity to such parameter variations is highly undesirable and, traditionally, negative feedback has been used to reduce such sensitivity. Optimal controls are usually computed as functions of time and a particular initial state and initial time; this is an open-loop solution. If the dependence on the particular initial state and time is eliminated, one obtains the optimal control as a function of the current state and time - a feedback solution. The feedback solution has the advantage that it automatically corrects errors and tends to counter disturbances. Is it also less sensitive. In what precise state should the sensitivity be measured. This report summarizes known results, mostly due to the author, on the sensitivity comparison of open-loop and closed-loop optimal control systems. (Author)