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

$\left\lceil {\log (\frac{2n}{\epsilon })}/{-2\log (\frac{\sqrt{2n}}{\sqrt{2n}+\sqrt{2}-1})}\right\rceil \!+ 1$

, where

$n$

denotes the problem dimension and

$\epsilon$

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.">

A Direct Optimization Algorithm for Input-Constrained MPC (original) (raw)

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