Abstract
The performance index sensitivities to plant parameter variation (PS) in optimum-control systems of both open and closed loop types are compared with each other. First, comparison is made with regard to two specific systems, namely a first-order linear stationary plant with the quadratic form performance index and the time optimal control process of a self-adjoint system with bounded norm control. The coefficients of PS of the two types are evaluated numerically in the two processes and are found to be always equal in their magnitudes.
Next, treating the above comparision problem generally, the conclusions are obtained as follows: if the performance index variation is stationary with respect to the variation of control signal around the optimal one and the closed and open loop optimum-control laws are differentiable with respect to the state variables (closed loop case) and the controller parameters (open loop case), the PS of the two types always have same magnitude and therefore the closed loop configuration is siginificant merely when the plant has no parameter variation and is disturbed only by so-called outer disturbances.
