Dynamic reference programming-based model predictive control for optimal robust tracking

In this paper, a new idea of dynamic reference programming (DRP) is proposed and applied to the design of robust tube-based model predictive control (RTMPC) to realize tracking of the system under additive bounded uncertainty and robust constraints. The cost function of the resulting DRP-based RTMPC simultaneously penalizes: i) the weighted Euclidean distance (WED) between the nominal state trajectory and the reference-determined steady states; and ii) the WED between the last-step-ahead-reference-determined steady state and the setpoint, which causes the nominal state to converge to the optimal tracking point. As the decision variables for online RTMPC optimization, the multi-step-ahead references also take on the responsibilities of constraint satisfaction and recursive feasibility. Consequently, the proposed strategy can drive the system state to converge to the disturbance invariant set centered on the optimal tracking point, and thus, realize the optimal robust tracking. A numerical example verifies that the proposed DRP-based RTMPC can, not only realize the optimal robust tracking of the system, but also effectively reduce the controller burden and avoid drastic state changes because the multistep references can make the degree of freedom for online optimization flexible.