A Computationally Efficient Robust Tube-Based MPC for Tracking of Linear Systems

This paper addresses a computationally efficient robust tube-based model predictive control (RTBMPC) strategy of linear systems in the presence of bounded disturbance. In the RTBMPC strategy, a nominal system is introduced by ignoring the disturbances of uncertain system, and then the uncertain system will be controlled in a robust manner through its nominal system as well as an additional feedback term which rejects a bounded additive disturbance. In this paper, the tracking problem is converted into the regulation problem by introducing an extra system called regulation nominal system that its constraints are translated from tracking into regulation. It leads to a reduction in complexity of the objective function and simplification of driving the stability theory. On the other hand, RTBMPC strategy solves optimization problem for nominal system which ignores the disturbances. Since in the absence of disturbances, the state measured at the following sample will be the same as the one predicted by model, a variable prediction horizon is suggested to reduce the computational burden. In addition, new constraints are introduced to prove the recursive feasibility, local and asymptotic stability. The constrained sampled double integrator is presented to illustrate the effectiveness of the proposed RTBMPC.