A Distributionally Robust Optimization-Based Stochastic Self-Triggered Model Predictive Control

In this article, we propose a self-triggered distributionally robust model predictive control algorithm for linear discrete systems with state chance constraints and unbounded stochastic disturbances. Assuming that only the first and second moments of the disturbance are accessible, we transform the objective function into a compact quadratic form and reformulate the state chance constraints into linear inequalities, which is more tractable when solving. In order to reduce communication and sampling times of the system, we propose a self-triggered update scheme, in which the state sampling and the control input sequence are updated when the control performance predicted based on the current sampling exceeds that of the periodic sampling scheme. We demonstrate that the optimization problem in the proposed self-triggered model predictive control (MPC) method is recursively feasible and stable. Numerical simulation results verify the effectiveness of the proposed algorithm.