Optimal LQG Control under Delay-dependent Costly Information

In the design of closed-loop networked control systems (NCSs), induced transmission delay between sensors and control station is an often-present issue which compromises control performance and may even cause instability. Taking into account the current advances of communication technology, a very relevant scenario within which induced delay needs to be investigated is cost-prone usage of communication resources. More precisely, if information exchange over the network is costly, then induced delay is the matter of decision maker’s willingness to either pay the required cost to have immediate access to communication resource, or delay the access at a reduced price. In this article, we consider price-based decision making problem for a stochastic linear time-invariant system, and address the effect of induced delay on control performance based on LQG cost function. Assuming that network access with shorter delay is costlier, a decision maker installed at the control station determines real-time delay duration such that an optimal balance between the control performance and the communication cost is maintained. In this article, we show that, under mild assumptions on the available information for decision makers, the separation property holds between the optimal transmission and control policies. As the cost function is decomposable, the optimal policies are efficiently computed.