Optimal Control Design of Large Scale Systems with Uncertainty

In this paper, model reduction techniques are used to design optimal control strategies with low sensitivity to model uncertainty. Two sources of uncertainty are investigated; parameter variation and time delay. To obtain reduced order models, two techniques are considered; aggregation and singular perturbation. Performance sensitivity is reduced by adding a sensitivity measure to the performance index that represents the cost to be minimized. 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 doubled. Therefore, developing a reduced order model and using it in the design procedure will alleviate the problem of large dimensions. The design is completed based on the reduced order model. Then, such design is used to obtain an approximate design for the full order system.