Factored Output Feedback Controller Synthesis with Locality Constraints for Spatially-Invariant Systems

Abstract

We consider H2 output feedback controller synthesis with pre-specified constraints on spatial communication distance (locality) for spatially-invariant systems using two factored controller frameworks: the system-level parameterization and the input-output parameterization. In our main result, we show that in both frameworks, output feedback controller synthesis with locality constraints can be formulated as a convex problem in finitely many transfer function variables, admitting the use of standard numerical solution techniques. The number of decision variables in the optimal controller design problem scales linearly with the distance of allowed communication. We also show that the optimal controller design problems for the system-level and input-ouptput parameterizations are equivalent for the chosen system of interest. We present numerical examples to illustrate the tradeoff between communication sparsity and performance.