Distributed Control of Large Scale Interconnected Systems with Boundary Conditions-Shift Operator vs. Interconnection Graph

Different modeling and control strategies for distributed systems described by partial differential equations, where the involved signals depend not only on a temporal but also on one or more spatial variables, are investigated. When applying an array of actuator/sensor pairs, a spatial discretization is induced and - assuming spatial invariance - the system can be modeled as an interconnection of identical subsystems together with boundary conditions. While centralized control methods quickly turn impractical for such systems due to the high number of input and output channels, low-complexity synthesis techniques based on either a spatial shift operator or on interconnection graphs offer a solution for this problem at the cost of some conservatism. In order to compare the methods with respect to performance and complexity in terms of computation and implementation, the simple model of the temperature distribution in a thin rod with two different boundary conditions is used. Three types of distributed controllers are compared to an optimal centralized output feedback controller, obtained using standard H
_∞
-loopshaping.