Robust adaptive tube tracking model predictive control for piece‐wise constant reference signals

Robust tracking of piece‐wise constant reference signals for constrained systems with parametric plant uncertainty and additive disturbances is addressed in this paper. The parametric uncertainty is decreased online by set‐membership estimation and a nominal model is updated for improving set‐point tracking. The online estimated parametric uncertainty is used for an online‐determined terminal set which enlarges the set of reachable references close to the system constraints when compared to an offline worst‐case consideration. An artificial target state is introduced which can deviate from the nominal target state. This new target state is used to ensure recursive feasibility for unreachable references and changes in the reference signal. Moreover, a novel “recovery mode” is specified which is deployed in case the new nominal model yields an infeasible control problem. Control algorithms are developed for time‐invariant systems and systems with arbitrarily fast changing plants but known relative bounds. Constraint satisfaction and l2$$ {l}_2 $$‐stability are guaranteed for the proposed algorithms. Controlling the engine load of a self‐propelled work machine is used as a practical example.