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This paper investigates adaptive model predictive control (MPC) for a classof constrained linear systems with unknown model parameters. This is also posedas the dual control problem consisting of system identification and regulation.We first propose an online strategy for simultaneous unknown parameteridentification and uncertainty set estimation based on the recursive leastsquare technique. The designed strategy provides a contractive sequence ofuncertain parameter sets, and the convergence of parameter estimates isachieved under certain conditions. Second, by integrating tube MPC withproposed estimation routine, the developed adaptive MPC provides a lessconservative solution to handle multiplicative uncertainties. This is madepossible by constructing the polytopic tube based on the consistently updatednominal system and uncertain parameter set. In addition, the proposed method isextended with reduced computational complexity by sacrificing some degrees ofoptimality. We theoretically show that both designed adaptive MPC algorithmsare recursively feasible, and the perturbed closed-loop system isasymptotically stable under standard assumptions. Finally, numericalsimulations and comparison are given to illustrate the proposed method.

Adaptive Model Predictive Control for A Class of Constrained Linear Systems with Parametric Uncertainties