Regulation is a costly aspect of power system operation, which has long been inadequately and inconsistently incentivized via ill-formulated pricing schemes, as recently acknowledged by regulators. We propose a pricing formulation in which regulation prices are the optimal dual multipliers or costate of an optimal control problem. More precisely, we use the linear quadratic regulator to formulate a regulation pricing policy. We then construct a Vickrey-Clarke-Groves mechanism to induce honest participation among selfish agents. We apply the formulation to a scenario combining traditional frequency regulation and the California Independent System Operator's Flexible Ramping Product.