Optimal tracking with feedback-feedforward control separation over a network

This paper studies tracking of a reference path in a networked control system where the controller consists of a central decision maker and an on-site controller, which are connected through a discrete noiseless channel. The reference path is available noncausally to the central decision maker and the on-site controller has access to noisy observations from the plant and the reference information provided by the central decision maker. For a quadratic optimization objective, we provide the optimal control using dynamic programming and show that the optimal controller can be separated into a noncausal feedforward term (generated by the central decision maker) plus a feedback term (generated by the on-site controller) which has causal access to the controls applied without any loss of performance. We show that the feedforward control is the solution of a deterministic quadratic program, i.e., certainty equivalence holds. We later study the problem of transmission of the feedforward controls to the on-site controller over a discrete noiseless channel. We formulate and solve an optimization problem for the optimal time-varying and time invariant uniform quantization of the feedforward control signals sent by the central decision maker to the on-site controller over a communication network