Optimal mean square control using the continuous stream model of computation

We consider the problem of optimal allocation of computation resources to a set of control tasks sharing a CPU. Each task is used to control a linear and time invariant plant affected by noise and is supposed to have a computation time with known distribution. The metric we use to express the Quality of Control (QoC) is a function of the steady state covariance of the state. We show how the combination of a Resource Reservation scheduler with an unconventional model of computation known as Continuous Stream produces a system that is easy to analyse. In particular, it is possible to compute the QoC of each control loop as a function of the fraction of CPU (bandwidth) that the task receives, and formalise an optimisation problem where a global QoC metric is defined that consolidates the QoC of each task. We show an efficient solution to this optimisation problem and validate its efficacy on a set of numeric examples.