A Sparsity Approach to Scheduling and Control of Networked Systems

Abstract: We study the design of scheduling logic and control logic for networked control systems (NCSs) where plants communicate with their remotely located controllers over a shared band-limited communication network. Due to a limited capacity of the network, only a subset of the plants can exchange information with their controllers at any instant of time and the remaining plants operate in open-loop. Our key contribution is a new algorithm that co-designs (a) an allocation scheme of the communication network among the plants (scheduling logic) and (b) the control inputs for the plants accessing the network (control logic) under which given non-zero initial states are steered to zero in a given time horizon for all the plants in the NCS. Sparse optimization is the primary apparatus for our analysis. We also provide sufficient conditions on the plant dynamics, capacity of the communication network and the given time horizon that lead to a numerically tractable implementation of our algorithm. A numerical experiment is presented to demonstrate the proposed results.