  A structured preconditioned conjugate gradient (PCG) solver is developed for
the Newton steps in second-order methods for a class of constrained network
optimal control problems. Of specific interest are problems with discrete-time
dynamics arising from the path-graph interconnection of $N$ heterogeneous
sub-systems. The computational complexity of each PGC step is shown to be
$O(NT)$, where $T$ is the length of the time horizon. The proposed
preconditioning involves a fixed number of block Jacobi iterations per PCG
step. A decreasing analytic bound on the effective conditioning is given in
terms of this number. The computations are decomposable across the spatial and
temporal dimensions of the optimal control problem, into sub-problems of size
independent of $N$ and $T$. Numerical results are provided for a
mass-spring-damper chain.
