A Theory for Sparse Event-Based Closed Loop Control

Most dynamic systems are controlled by discrete time controllers. One of the main challenges faced during the design of a digital control law is the selection of the appropriate sampling time. A small sampling time will increase the accuracy of the controlled output at the expense of heavy computations. In contrast, a large sampling time will decrease the computational power needed to update the control law at the expense of a smaller stability region. In addition, once the setpoint is reached, the controlled input is still updated, making the overall controlled system not energetically efficient. To be more efficient, one can update the control law based on a significant fixed change of the controlled signal (send-on-delta or event-based controller). Like for time-based discretization, the amplitude of the significant change must be chosen carefully to avoid oscillations around the setpoint (e.g., if the setpoint is in between two samples) or an unnecessary increase of the samples number needed to reach the setpoint with a given accuracy. This paper proposes a novel non-linear event-based discretization method based on inter-events duration. We demonstrate that our new method reaches an arbitrary accuracy independently of the setpoint amplitude without increasing the network data transmission bandwidth. The method decreases the overall number of samples needed to estimate the states of a dynamical system and the update rate of an actuator, making it more energetically efficient.