  We extend the regret analysis of the online distributed weighted dual
averaging (DWDA) algorithm [1] to the dynamic setting and provide the tightest
dynamic regret bound known to date with respect to the time horizon for a
distributed online convex optimization (OCO) algorithm. Our bound is linear in
the cumulative difference between consecutive optima and does not depend
explicitly on the time horizon. We use dynamic-online DWDA (D-ODWDA) and
formulate a performance-guaranteed distributed online demand response approach
for heating, ventilation, and air-conditioning (HVAC) systems of commercial
buildings. We show the performance of our approach for fast timescale demand
response in numerical simulations and obtain demand response decisions that
closely reproduce the centralized optimal ones.
