Optimized distributed control and topology design for hierarchically interconnected systems

A method to reduce the computational complexity for the simultaneous design of a communication topology and feedback control laws for large scale systems is proposed. In general, such combined procedures may be posed as Mixed-Integer Programs (MIPs), which suffer from high combinatorial complexity when the number of possible communication links grows large. Although some explicit solutions for MIP formulations exist, these are either based on very restrictive assumptions or yield an iterative LMI procedure, which is computationally expensive. The presented scheme tackles the problem by pre-analyzing the coupling structure of the plant and dividing it into hierarchically coupled, distinct groups (clusters). This enables one to decompose the global MIP into a set of smaller MIPs, which can then be solved independently. In contrast to existing approaches, a global LMI optimization has to be solved only once, not repeatedly.