We introduce a new algorithm for solving unconstrained discrete-time optimal control problems. Our method follows a direct multiple shooting approach, and consists of applying the SQP method together with an $\ell_2$ augmented Lagrangian primal-dual merit function. We use the LQR algorithm to efficiently solve the primal-dual SQP problem. As our algorithm is a specialization of NPSQP (Gill et al. 1992), it inherits its generic properties, including global convergence, fast local convergence, and the lack of need for second order corrections, improving on existing direct multiple shooting approaches such as GNMS (Giftthaler et al. 2018) and FDDP (Mastalli et al. 2020).

翻译：我们提出了一种求解无约束离散时间最优控制问题的新算法。该方法采用直接多重打靶策略，通过结合SQP方法与ℓ2增广拉格朗日原对偶评价函数实现。我们利用LQR算法高效求解原对偶SQP问题。由于本算法是NPSQP（Gill等，1992）的特化版本，因此继承了其通用特性，包括全局收敛性、快速局部收敛性以及无需二阶校正等优势，改进了现有直接多重打靶方法如GNMS（Giftthaler等，2018）和FDDP（Mastalli等，2020）的性能。