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In this paper, we present two control laws that are tailored for controlapplications in which computational and/or communication resources are scarce.Namely, we consider minimum attention control, where the `attention' that acontrol task requires is minimised given certain performance requirements, andanytime attention control, where the performance under the `attention' given bya scheduler is maximised. Here, we interpret `attention' as the inverse of thetime elapsed between two consecutive executions of a control task. By focussingon linear plants, by allowing for only a finite number of possible intervalsbetween two subsequent executions of the control task, by making a novelextension to the notion of control Lyapunov functions and taking these novelextended control Lyapunov function to be infinity-norm-based, we can formulatethe aforementioned control problems as online linear programs, which can besolved efficiently. Furthermore, we provide techniques to construct suitableinfinity-norm-based extended control Lyapunov functions for our purposes.Finally, we illustrate the resulting control laws using numerical examples. Inparticular, we show that minimum attention control outperforms an alternativeimplementation-aware control law available in the literature.

On the Minimum Attention and the Anytime Attention Control Problems for Linear Systems: A Linear Programming Approach