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Most real-world systems are affected by external disturbances, which may beimpossible or costly to measure. For instance, when autonomous robots move industy environments, the perception of their sensors is disturbed. Moreover,uneven terrains can cause ground robots to deviate from their plannedtrajectories. Thus, learning the external disturbances and incorporating thisknowledge into the future predictions in decision-making can significantlycontribute to improved performance. Our core idea is to learn the externaldisturbances that vary with the states of the system, and to incorporate thisknowledge into a novel formulation for robust tube model predictive control(TMPC). Robust TMPC provides robustness to bounded disturbances considering theknown (fixed) upper bound of the disturbances, but it does not consider thedynamics of the disturbances. This can lead to highly conservative solutions.We propose a new dynamic version of robust TMPC (with proven robust stability),called state-dependent dynamic TMPC (SDD-TMPC), which incorporates the dynamicsof the disturbances into the decision-making of TMPC. In order to learn thedynamics of the disturbances as a function of the system states, a fuzzy modelis proposed. We compare the performance of SDD-TMPC, MPC, and TMPC viasimulations, in designed search-and-rescue scenarios. The results show that,while remaining robust to bounded external disturbances, SDD-TMPC generatesless conservative solutions and remains feasible in more cases, compared toTMPC.

State-Dependent Dynamic Tube MPC: A Novel Tube MPC Method with a Fuzzy Model of Disturbances