Sparse networked control of input constrained linear systems

In networked control, there is often an incentive to communicate only what is absolutely necessary to achieve the desired performance goals. This is true of both the downlink (between a control base station and actuators) and the uplink (between the sensors and base station). Here we present a possible solution to this problem based on a singular value decomposition (SVD) of the Hessian of the quadratic performance index generally considered in Model Predictive Control (MPC). 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 pre-loaded 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 sparse communication in both the downlink and uplink. We also show that the strategy can be modified so that input constraints are satisfied. The proposed results are illustrated by an example.