In this paper, a cross-layer framework for joint control and distributed sensing in agile wireless networks is presented, where an agent schedules actions to control a partially observable Markov decision process, whose state is inferred by collecting measurements from nearby assistant wireless nodes with cognitive and sensing capabilities (ANs). The framework makes it possible to model practical constraints of wireless networks, such as the cost incurred by the ANs to sense and transmit to the agent and the shared wireless channel, as well as to jointly optimize the acquisition of state information at the agent via distributed sensing, and the scheduling policy, under sensing-transmission cost constraints for the ANs. The optimality of a two-stage decomposition is proved, which enables decoupling of the optimization of action scheduling and distributed sensing. This scheme is applied to spectrum sensing, where the activity of licensed (PU, primary) users is measured by distributed wireless assisting receivers, based on which an agile (SU, secondary) user adapts its transmissions over time. Simulation results demonstrate that the proposed adaptive joint sensing-scheduling policy improves the SU throughput up to 50% over a scheme employing non-adaptive sensing, for a given constraint on the throughput degradation to the PU pair and cost incurred by the ANs, and up to a three-fold increase over a scheme where sensing is performed only locally by the SU.