Constrained Adaptive Model-Predictive Control for a Class of Discrete-Time Linear Systems with Parametric Uncertainties

In this technical note, an adaptive model-predictive control (MPC) is proposed for a class of discrete-time linear systems with constant parametric uncertainties and control constraint. The proposed adaptive MPC originates from the principle of min-max optimization, which cannot be solved in a direct numerical way. An adaptive strategy is proposed to estimate the uncertain parameters, such that the estimated error converges, and the optimization in the MPC can be transferred into a solvable simple structure. Feasibility of the optimization and stability of the closed-loop system are proved theoretically, and a simulation example is presented to illustrate the theoretical result.