Optimal mean square control using the continuous stream model of computation

Daniele Fontanelli (1) , Luca Greco (2) , Luigi Palopoli (1)

1 DISI - Dipartimento di Ingegneria e Scienza dell'Informazione
2 L2S - Laboratoire des signaux et systèmes

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.

Domaines: Automatique / Robotique

Daniele Fontanelli, Luca Greco, Luigi Palopoli. Optimal mean square control using the continuous stream model of computation. 54th IEEE Conference on Decision and Control (CDC), Dec 2015, Osaka, Japan. pp.1958 - 1965, ⟨10.1109/CDC.2015.7402494⟩. ⟨hal-01322834⟩