A control strategy for two-level systems with optimization in the feedback loop

In this paper the case of a linear decentralized large scale system (LSS) which consists of N linear subsystems S₁,S₂ ,...,S_N in lower hierarchical level, interconnected through a common linear subsystem S₀, in a higher hierarchical level, is considered. The N subsystems are not connected to each other, thus leading to a matrix A having a block arrow structure (BAS). The continuous state space model and controlling algorithm of such a system is presented. We describe the optimization of the feedback gain using a gradient type algorithm for the adaptation of the gain in the constrained space of the SAS feedback gains. Thus a near optimal solution is obtained, which keeps all the BAS appealing characteristics and is closer to the optimal solution than any other previous approach