Tube-based model predictive control for linear systems with bounded disturbances and input delay

This paper proposes a tube-based model predictive control strategy for linear systems with bounded disturbances and input delay to ensure input-to-state stability. Firstly, the actual disturbed system is decomposed into a nominal system without disturbances and an error system. For the nominal system, solving an optimization problem, where the delayed control input is set as an optimization variable, yields a nominal control law that enables the nominal state signal to approach to zero. Then, for the error system, the Razumikhin approach is used to identify a robust control invariant set. Using the set invariance theorem, an ancillary control law is developed to confine the error state signal in the invariant set. Combining the two results, we obtain a control law that enables the state signal to remain within a robustly invariant tube. Finally, the effectiveness of the developed control strategy is validated by simulations.