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 a closed-loop. This technical note considers input-constrained MPC problems and exploits the structure of the resulting box-constrained QPs. Then, we propose a cost-free and data-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 only dimension-dependent (data-independent), simple-calculated, and exact (not worst-case) with the value (2n{) }/-2 ({2n2n+2-1) } \!+ 1, where n denotes the problem dimension and 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.