Computationally Efficient Adaptive Model Predictive Control for Constrained Linear Systems with Parametric Uncertainties

This paper investigates adaptive model predictive control (MPC) for constrained linear systems subject to multiplicative uncertainties. Different from robust MPC considering the worst-case disturbances, the proposed solution updates the unknown system model online based on input and state histories. We firstly propose a parameter estimator based on recursive least square technique, which guarantees the nonincreasing estimator error and a contractive sequence of uncertainty sets. Then a computationally tractable adaptive MPC method is developed to handle the multiplicative uncertainties directly by using the polytopic tube. Instead of designing the tube offline, we consider the homothetic tube in this work, where the tube parameters are the MPC optimization problem. This strategy allows that the tube can be optimized based on the updated system model to reduce the conservatism. We have proved that the proposed adaptive MPC method is recursively feasible and the closed-loop system is asymptotically stable. Finally, a numerical example is given to evaluate the proposed method.