Linear Quadratic Performance Criteria for Cascade Control

In this paper we consider the problem of linear quadratic regulator (LQR) performance for cascade control structures of series coupled systems. The necessary and sufficient condition for the linear quadratic performance of a cascade control structure to achieve the same performance as any given centralized LQR is obtained. The cascade problem could be seen as a special case of the network control problem with a special network structure. The results presented show that decentralized control is possible with some natural fundamental limitations in this particular case. Also, a constructive proof is given for the inverse LQR problem that can be used to calculate the decentralized LQR from a given centralized one.