Minimum attention control for linear systems

In this paper, we present a novel solution to the minimum attention control problem for linear systems. 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 interexecution time, i.e., the inverse of the time between two consecutive executions. Instrumental for our approach is a particular extension of the notion of a control Lyapunov function and the fact that we allow for only a finite number of possible interexecution times. By choosing this extended control Lyapunov function to be an a-norm-based function, the minimum attention control problem can be formulated as a linear program, which can be solved efficiently online. Furthermore, we provide a technique to construct a suitable a-norm-based (extended) control Lyapunov function. Finally, we illustrate the theory using a numerical example, which shows that minimum attention control outperforms an alternative 'attention-aware' control law available in the literature.