An improved self-triggered implementation for linear controllers

Abstract

Research in networked control systems raised the importance of understanding what are the timing requirements for control. In recent years this problem has been attacked from multiple angles including the computation of Maximal Allowable Transmission Intervals, event-triggered, and self-triggered controller implementations. In a self-triggered implementation the controller is responsible for computing the next time instant at which the actuator values should be updated by evaluating the control law on fresh sensor measurements. One of the main challenges in self-triggered control is how to perform the exact calculation of the time at which these updates should take place. In this paper we present a new technique to compute lower bounds on the self-triggered update times in a computationally light manner. We evaluate the algorithm on numerical examples and we observe that the algorithm performs well when compared to other existing methods and provides tight lower bounds on the exact update times. Additionally, we propose a Semidefinite Programming-based technique that produces triggering conditions that are less conservative than the existing ones and for which the update times are larger.