Robust tube-based NMPC for dynamic systems with discrete degrees of freedom

Abstract

We present a robust nonlinear model predictive control (NMPC) algorithm for dynamic systems with mixed degrees of freedom, i.e., continuous and discrete manipulated variables. The discrete variables are often excluded from the NMPC layer and determined at a supervisory layer, which typically leads to suboptimal solutions. In contrast, the proposed controller optimizes both classes of degrees of freedom within the NMPC layer, thereby enhancing the closed-loop performance. Our approach relies on a computationally efficient relaxation and integrality restoration strategy. Initially, a nominal controller computes relaxed central reference trajectories for the states and the input variables. These trajectories are then tracked by an ancillary NMPC controller before the integrality of the discrete variables is restored. The role of the ancillary controller is to ensure robustness against the integer restoration error as well as other disturbances based on a nonlinear Tube MPC approach. Furthermore, we provide sufficient conditions to establish recursive feasibility and guarantee robust closed-loop stability. Finally, the effectiveness of the approach is demonstrated through two nonlinear simulation examples, affirming its viability and robustness.