Sensitivity of the Performance of Optimal Linear Control Systems to Parameter Variations†

Abstract

The sensitivity of the index of performance to parameter variations in optimal control systems is examined in this paper. It is shown, in the case of linear optimal systems with quadratic performance criteria, that the value of the performance index, after the system parameters have deviated from a nominal set of values, is still given by a symmetric positive definite quadratic form of the initial state. The matrix of this quadratic form is governed by a special case of the matrix Riccati equation. It is shown also, that similar results hold for the performance index sensitivity function. Because the sensitivity problem closely parallels the original optimization problem, the computational techniques used in the design of the optimal system may be reapplied in the sensitivity analysis.