A direct optimization algorithm for input-constrained MPC

Providing an execution time certificate is a pressing requirement when deploying Model Predictive Control (MPC) in real-time embedded systems such as microcontrollers. Real-time MPC requires that its worst-case (maximum) execution time must be theoretically guaranteed to be smaller than the sampling time in closed-loop. This technical note considers input-constrained MPC problems and exploits the structure of the resulting box-constrained QPs. Then, we propose a textitcost-free and textitdata-independent initialization strategy, which enables us, for the first time, to remove the initialization assumption of feasible full-Newton interior-point algorithms. We prove that the number of iterations of our proposed algorithm is textitonly dimension-dependent (textitdata-independent), textitsimple-calculated, and textitexact (not textitworst-case) with the value leftlceilfraclog(frac2nε)-2log(frac√2n√2n+√2-1)rightrceil !+ 1, where n denotes the problem dimension and ε denotes the constant stopping tolerance. These features enable our algorithm to trivially certify the execution time of nonlinear MPC (via online linearized schemes) or adaptive MPC problems. The execution-time-certified capability of our algorithm is theoretically and numerically validated through an open-loop unstable AFTI-16 example.