A partial order approach to decentralized control of spatially invariant systems

In this paper, we consider a class of spatially distributed systems which have a special property known as spatial invariance. It is well-known that for such problems, the problem of designing decentralized controllers is hard. In this paper, we generalize some previously known results and show that for a certain class of problems, the control problem has a convex reformulation. We employ the notion of partially-ordered sets and the associated notion of incidence algebras to introduce a class of systems called poset causal systems. We show that poset causal systems are a fairly large class of systems that properly include some other classes of systems studied in the literature (namely cone-causal and funnel causal systems). Finally we show that the set of poset-causal controllers for poset-causal plants are amenable to a convex parameterization.