Review, Evaluation and Application of Condensing Algorithms for Model Predictive Control based on a First-Order Method

In this paper, techniques for reducing the number of optimization variables for quadratic programs arising in model predictive control are reviewed. Focusing on optimization with a first-order method, numerical properties such as the condition number of the Hessian are evaluated and suboptimality due to early termination of the optimization algorithm is investigated. The state elimination condensing approach and a recently proposed numerically robust approach based on the QR factorization are compared to the existing methods of prestabilizing the prediction and preconditioning for reducing the Hessian condition number for linear MPC. For the application example of controlling a fuel cell system, the worst-case turnaround time of the control algorithm can be reduced by more than 30% compared to standard state elimination algorithms. Thus the controller is shown to be real-time feasible using the QR factorization or additional preconditioning.