A Method for Reducing the Sensitivity of Optimal Nonlinear Systems to Parameter Uncertainty

Mathematical relationships are derived and used to establish a procedure for reshaping the optimal solution so as to reduce the statistical uncertainty in the terminal conditions of the system due to system parameter uncertainties of known statistical properties. The procedure introduces the use of an augmented performance index which contains a scalar measure of the system sensitivity partial derivatives. A nonlinear multiparameter optimal-rocket-trajectory problem was solved by using an algorithm based on the method of steepest descent to illustrate the procedure.