A convex optimization approach to feedback scheduling

Adaptive tasks scheduling via feedback is an effective solution for the optimization of closed-loop control performance under computing power limitation, as in the computing nodes of embedded networked control systems. The problem of the feedback scheduling of a set of Linear-Quadratic controllers, based on both plant-state and resource utilization measurements is considered. The proposed feedback scheduler acts on tasks periods in order to minimize a quadratic cost functional over an infinite horizon, for the overall system, and to achieve a desired processor utilization. Based on Karush-Kuhn-Tucker conditions, it is shown that if Riccati matrix coefficients may be approximated using parabolic functions of the sampling frequency, the expressions of optimal sampling frequencies may be computed analytically. Examples where these approximations hold are presented and the approach is illustrated on a simulation example.