On the minimum attention and anytime attention problems for nonlinear systems

The current convergence of control, communication and computation opens the door to new avenues for the applicability of control systems, but it also leads to new constraints and requirements. The traditional quadratic cost function has become too plain to represent the diverse performance indices of today´s complex applications. For instance, the implementation cost of a control law has become a major factor, since resources are frequently shared among different tasks. Implementation costs of control laws depend on a wide range of factors: computation complexity, sensor accuracy, required bandwidth, actuation speed, or sampling rates, to name a few. In this paper we focus on the notion of attention, that is, how often the loop needs to be closed in order to achieve a desired performance. We propose two attention-aware control laws: first, a technique to construct minimum attention control laws that maximizes the open loop operation of a nonlinear control system; and second, a control algorithm that permits the system run in open loop for a pre-scheduled amount of time.