A cost-effective sparse communication strategy for networked linear control systems: an SVD-based approach

In networked control, there is often an incentive to communicate only what is absolutely necessary to achieve the desired performance goals. This is true to both the downlink (between a control base station and actuators) and the uplink (between the sensors and base station). Here, we present a strategy aimed at this problem based on a singular value decomposition of the Hessian of the quadratic performance index generally considered in Model Predictive Control. The singular vectors are employed to generate an orthonormal basis function expansion of the unconstrained solution to the finite horizon optimal control problem. These are preloaded into each actuator and each sensor. On the downlink, the actuators are informed, in real-time, about which basis functions they should use. On the uplink, after a 'burn in period', the sensors need only communicate when their response departs from that pre-calculated for the given basis functions. We show that this strategy facilitates communication in both the downlink and uplink in a cost-effective fashion. We also show that the strategy can be modified so that input constraints are satisfied. We illustrate the proposed results by applying them to a simulation of the cross direction control of a paper machine. Potential extensions and other applications of the proposed strategy are also discussed