Optimal Design Of Complex Systems With Low Sensitivity To Time Delay

Abstract

In this dissertation, two optimal control strategies are investigated for a large-scale decentralized system in order to optimize and study the system. The main objective of the optimization and analysis is to reduce the effect of time delay on the system. This can be accomplished by adding the sensitivity function to the optimal control design and inserting it into the performance index function. In this way, the effect of the time delay can be reduced. The first strategy is to create a nearly optimal composite control by using the singular perturbation method as a reduction method. The singular perturbation utilizes the separation of slow and fast dynamic systems and decomposing full-order systems into reduced-order slow and fast subsystems to reduce the complexity of the large-scale system and simplify the problem. Then, after solving each subsystem individually, the optimal solution for the nearly optimal composite control can be obtained by combining the solutions of the subsystems. The Stackelberg game strategy is applied to the reduced order model and then implemented in order to optimize the performance index function. This is the second strategy. The design can be completed successfully based on the reduced-order model, which allow for the attainment of optimal results. It is shown through the use of numerical examples how well the design performs and how successfully it alleviates the impact of the sensitivity.