Sampling period assignment: A cooperative design approach

In this paper, we assume that a set of non preemptive controller tasks should be implemented on a limited computational resource platform, and look for a sampling period assignment that allows to obtain the desirable performance. The problem is formulated as a multi-objective optimization problem under a resource constraint, where the cost functions depend on the sampling period. Linear-quadratic controllers are used, resulting on feedback gains that also depend on the sampling period. The global cost function is chosen as a weighted sum of all plants performances, translating the multi-objective optimization problem into a single-objective one which provides an additional degree of freedom and leads to a set of solutions denoted as Pareto efficient. To handle this additional variable, we assume a Nash bargaining cooperative game. An upper level task performs the update of the sampling period and of the plant input, to be used on a finite-horizon control strategy, for each control loop. A numerical example is provided to illustrate our approach.