A Decomposition Result in Linear-Quadratic Coordinated Control?

Abstract: Scalability is a fundamental requirement in control design for large-scale systems. Typically, it needs to be considered explicitly at the expense of performance degradation and more complicated design procedures. In this paper, we present a class of large scale systems where scalability is an inherent property of the optimal centralized solution. More specifically, we study a coordination problem where a group of identical subsystems are required to satisfy an equality constraint on the sum of their inputs. We show that the problem can be completely decomposed in terms of the unconstrained problems associated with each subsystem. In particular, the computational effort required to obtain the optimal solution is independent of the number of subsystems and the only global information processing required to execute the optimal control law is a simple summation, which scales well when the number of subsystems grows large