Tube based Adaptive Model Predictive Control

The problem of controlling discrete-time linear time-invariant (LTI) systems with parametric uncertainties in the presence of hard state and input constraints is addressed in this paper. An estimated system, which is structurally correlated with the uncertain plant, is considered for predictive control design. The parameters of the estimated system are updated using gradient descent based adaptive law. The errors in the state predictions, arising due to mismatch between the uncertain plant and the estimated model are characterized and proved to be bounded provided certain state and input constraints are satisfied along with the imposed constraints. To account for constraint satisfaction in the presence of the state estimation errors, a tube based robust model predictive control is designed. The MPC optimization routine returns a tube pair and a corresponding control policy, which guarantees convergence of the uncertain plant states to a suitably characterized terminal set in finite time, while satisfying the imposed constraints robustly. The proposed tube based adaptive MPC strategy is proved to be recursively feasible if it is initially feasible and the states of the uncertain plant are proved to be bounded and asymptotically converging to the origin.