Feedback coordinating control for a class of two-level descriptor systems

A Stackelberg optimization problem for two-level systems was formulated by M. Simaan (1977) in which it was assumed that there is a coordinator at the high level who exerts control on N subsystems at the low level. The authors consider a similar problem with two differences. The first one is that the subsystems are described by the equations of the form Ex˙=Ax+Bv+Cu, that is the descriptor systems. The second one is that the coordinator does not have a cost functional of its own, and the objective of the coordinator is to optimize N different cost functionals simultaneously by using one coordinating strategy. In contrast with the problem for state space systems, it is found that there exists a linear feedback coordinating strategy for the coordinator because of the first difference