Optimal control design of large scale system with parameter uncertainty

Abstract

In this thesis, a model order reduction technique is used to design optimal control strategies with low sensitivity to model uncertainty. The source of uncertainty encountered here is called parameter variation and an aggregation methodology is used to obtain the reduced order model. Performance sensitivity of the system is reduced by adding a sensitivity measure to the performance index that represents the cost to be minimized. The sensitivity measure is defined as the variable given by the partial derivative of the state with respect to the uncertain parameter evaluated at the nominal value. This results in an augmented model that includes the new sensitivity variable, which has the same size as the state vector of the original system. As a result, the order of the dynamic constraint of the optimization procedure will be twice that of the original plant. Therefore, developing a reduced order model and using it in the design procedure will alleviate the problem of larger dimensions. The design is completed based on the reduced order model. Then, such a design is used to obtain the approximate design for the full-order system. Numerical examples are presented to illustrate the effectiveness of the approximated design in reducing the performance sensitivity of the full-order system.