A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive control of a class of system of systems for which the overall objective function is the sum of convex quadratic cost functions of (locally) constrained linear subsystems that are coupled through a set of (global) linear constraints on the subsystems coordination parameters. The proposed control algorithm is based on parametrization and splitting of the underlying optimization problem into one global coordination problem and a set of local optimization problems pertaining to individual subsystems. The local optimization problems are solved offline, via parametric optimization, while the coordination problem is solved online. The properties of the local parametric solutions are utilized to solve the coordination problem very efficiently. In particular, it is shown that, for a fixed number of coupling constraints, the coordination problem can be solved with a linear-time algorithm in a finite number of iterations if all subsystems have one-dimensional coordination parameters.