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

Structured preconditioning of conjugate gradients for path-graph network optimal control problems