| Summary: | This paper proposes a robust self-triggered model
predictive control (MPC) algorithm for a class of constrained
linear systems subject to bounded additive disturbances, in which
the inter-sampling time is determined by a fast convergence
self-triggered mechanism. The main idea of the self-triggered
mechanism is to select a sampling interval so that a rapid
decrease in the predicted costs associated with optimal predicted
control inputs is guaranteed. This allows for a reduction in
the required computation without compromising performance.
By using a constraint tightening technique and exploring the
nature of the open-loop control between sampling instants, a
set of minimally conservative constraints is imposed on nominal
states to ensure robust constraint satisfaction. A multi-step openloop MPC optimization problem is formulated, which ensures
recursive feasibility for all possible realisations of the disturbance.
The closed-loop system is guaranteed to satisfy a mean-square
stability condition. To further reduce the computational load,
when states reach a predetermined neighbourhood of the origin,
the control law of the robust self-triggered MPC algorithm
switches to a self-triggered local controller. A compact set
in the state space is shown to be robustly asymptotically
stabilized. Numerical comparisons are provided to demonstrate
the effectiveness of the proposed strategies.
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