This work presents an event-based control structure using the generalized predictive control (GPC) algorithm with actuator deadband. The main objective of this work is to limit the number of controlled system updates. In this approach, the controlled process is sampled with a constant sampling time and is updated in an asynchronous way that depends on the obtained control signal value. To achieve the desired control properties, a hybrid system framework is used to model the virtual actuator deadband. The deadband is modeled as system input constraints in the GPC's optimization procedure, exploring mixed integer quadratic programming (MIQP) techniques. The presented control structure considers adjustable actuator deadband as an additional tuning parameter and allows a tradeoff between control performance and the number of events/updates. This fact is very important for the lifetime of the actuators and minimizes their wear, especially for mechanical and electromechanical systems. The minimization of actuator usage can be also understood as an economical saving. Other benefits can be found in distributed control systems, where various control system agents are connected through computer networks, and where a reduction in communication is always welcome.