Robust self-triggered model predictive control for constrained discrete-time LTI systems based on homothetic tubes

In this paper we present a robust self-triggered model predictive control (MPC) scheme for discrete-time linear time-invariant systems subject to input and state constraints and additive disturbances. In self-triggered model predictive control, at every sampling instant an optimization problem based on the current state of the system is solved in order to determine the input applied to the system until the next sampling instant, as well as the next sampling instant itself. This leads to inter-sampling times that depend on the trajectory of the system. By maximizing the inter-sampling time, the amount of communication in the control system is reduced. In order to guarantee robust constraint satisfaction, Tube MPC methods are employed. Specifically, in order to account for the uncertainty in the system, homothetic sets are used in the prediction of the future evolution of the system. The proposed controller is shown to stabilize a closed and bounded set including the origin in its interior.