Real-Time Nonlinear Mixed-Integer Model Predictive Control With Horizon-Tail Relaxations

Abstract

Model predictive control (MPC) of nonlinear systems with discrete decisions leads to mixed-integer nonlinear programs (MINLPs) whose combinatorial complexity often prevents real-time deployment. In this paper, we propose a decomposition-based MPC method that reorders and reduces computations to shorten the delay between receiving a state measurement and applying the control input. Before the measurement arrives, we solve a continuous relaxation of the MINLP at a predicted state and construct a mixed-integer quadratic program (MIQP). Once the measured state is available, we solve the MIQP that reconstructs the discrete controls and simultaneously performs one sequential quadratic programming step toward the corresponding nonlinear solution. To reduce the combinatorial complexity in the horizon length, we either fix the integer controls or relax their integrality over the prediction horizon tail, while retaining an integer-feasible first control input. We derive error bounds relating the nonlinear objective values obtained with the horizon-tail approximations to the optimal value of the original mixed-integer problem. In a data center cooling example, the proposed method reduces mean feedback computation time by 94% relative to a state-of-the-art MINLP method with a total closed-loop cost difference of less than 1%.