On the minimum attention control problem for linear systems: A linear programming approach

In this paper, we present a novel solution to the minimum attention control problem. In minimum attention control, the objective is to minimise the `attention´ that a control task requires, given certain performance requirements. Here, we interpret `attention´ as the inverse of the time elapsed between two consecutive executions of a control task. Instrumental for the solution will be a novel extension of the notion of a control Lyapunov function. By focussing on linear plants, by allowing for only a finite number of possible intervals between two subsequent executions of the control task and by taking the extended control Lyapunov function to be ∞-norm based, we can formulate the minimum attention control problem as a linear program, which can be solved efficiently online. Furthermore, we provide a technique to construct suitable ∞-norm-based (extended) control Lyapunov functions for our purposes. Finally, we illustrate the theory using a numerical example, showing that minimum attention control can outperform an alternative implementation-aware control law available in the literature.