  We formulate a general mathematical framework for self-tuning network control
architecture design. This problem involves jointly adapting the locations of
active sensors and actuators in the network and the feedback control policy to
all available information about the time-varying network state and dynamics to
optimize a performance criterion. We propose a general solution structure
analogous to the classical self-tuning regulator from adaptive control. We show
that a special case with full-state feedback can be solved in principle with
dynamic programming, and in the linear quadratic setting the optimal cost
functions and policies are piecewise quadratic and piecewise linear,
respectively. For large networks where exhaustive architecture search is
prohibitive, we describe a greedy heuristic for joint architecture-policy
design. We demonstrate in numerical experiments that self-tuning architectures
can provide dramatically improved performance over fixed architectures. Our
general formulation provides an extremely rich and challenging problem space
with opportunities to apply a wide variety of approximation methods from
stochastic control, system identification, reinforcement learning, and static
architecture design.
