Robust almost sure stability for uncertain stochastically scheduled anytime controllers

In this paper we consider closed loop stability of a number of different software tasks implementing a hierarchy of real-time controllers for a given plant, i.e. "anytime controllers". The execution of the control tasks are driven by the available computational time of an embedded platform under stringent real-time constraints. Hence, preemptive scheduling schemes are considered, under which the maximum execution time allowed for control software tasks is not a-priori known. A stochastic description of the scheduler accounting for the presence of some uncertainties in the model, is provided. An anytime control hierarchy of controllers for the same plant, in which higher controllers in the hierarchy provide better closed-loop performance but require larger worst-case execution times, is assumed to be given. Since the ensuing switching system is prone to instability, the presented method allows to robustly condition the partially known stochastic scheduler so as to obtain a better exploitation of computing capabilities, while guaranteeing almost sure stability of the resulting switching system.