Disturbance‐Observer‐Based Tube Model Predictive Control for Constrained Systems

ABSTRACT This paper proposes a disturbance‐observer‐based tube model predictive control (DTMPC) strategy to address the regulation problem of continuous‐time linear systems with additive bounded disturbances. The strategy integrates two elements: disturbance compensation and optimal control inputs. The former is designed using the estimation information from the disturbance observer to actively compensate for disturbances. The latter employs the estimation error bound to calculate the disturbance invariant set, which is then incorporated into the DTMPC design to determine the optimal control input. By compensating for the disturbances, the system's uncertainty and steady‐state error are minimized. As the estimation error bound decreases and stabilizes, the disturbance invariant set reduces, thereby expanding the feasible set of the nominal state. Finally, recursive feasibility and robust stability of the system are analyzed. The performance of the proposed DTMPC is verified by applying it to a self‐balancing vehicle system and comparing it with the TMPC.