An Optimization-Based Approach for Dynamic Actuator Scheduling in Distributed Processes Controlled Over Networks

Abstract

This work presents an optimization-based approach for the placement and dynamic scheduling of control actuators in networked spatially-distributed processes described by uncertain Partial Differential Equations (PDEs) with low-order dominant dynamics and network resource constraints. A finite-dimensional model that captures the slow dynamics of the infinite-dimensional system is initially used to synthesize a model-based feedback controller and characterize its closed-loop stability properties in terms of the model update period and the control actuator locations. On the basis of this characterization, a finite-horizon optimization problem is formulated to determine the control actuator locations and update rates that simultaneously optimize the closed-loop performance as well as the extent of network resource utilization. The objective function includes appropriate penalties on the response speed, the control action and the frequency of model updates, and is minimized subject to appropriate networked closed-loop stability constraints. A receding horizon strategy is used to solve the optimization problem online, resulting in a dynamic scheduling policy that varies the actuator locations and sensor-controller communication rate, and allows the system to respond adaptively to its uncertain operating environment. The implementation and efficacy of the developed approach are demonstrated using a diffusion-reaction process example.