Power-based supervisory control theory of hybrid systems and its application to the analysis of financial crisis

Abstract

The authors study how n local supervisors with individual control objectives can achieve a common goal by modular control based on power in a hybrid system framework. Each local supervisor is an observer designed with its own objective for an approximated finite state machine of a hybrid plant based on the l-complete approximation scheme of Moor et al. in 2002. We present the notion of power observability of the common control objective and show that, if the common specification is controllable and power observable with respect to an approximated model, then n local supervisors can achieve the control objective of the hybrid plant. Then, we apply the proposed power-based modular control theory to the analysis of the financial crisis occurred in 2008. The power observability explains how the deregulation policies leading to the crisis could be pursued. While the small elite group of politicians and bankers could set the policies with inordinate power based on full information, most public people were ignorant and unconcerned about the policies, and hence did not oppose them