This project will develop stability, time optimal, and minimum effort control theory of large scale hereditary systems. The principal investigator will focus on two broad areas: the quantitative behavior of each isolated system and the overall behavior of the large scale systems when the inter-connections are accounted for. The aim is to analyze the dynamics of large scale systems in terms of their subsystems and the properties of their interconnection. For the isolated system there are four aspects of the problem: stability, controllability when the controls are small, the form of optimal control when time and effort are minimum, and all the construction of optimal feedback controls. Proposed results may include: If each subsystem is controllable and the interaction "nice" then the large scale system is controllable. If some subsystem is not controllable the large scale system can still be controllable if some external control impact is brought to bear. The implications to the control of large organizations like global economics will be studied. Optimal control strategies will be pursued.
