{'fraction_non_alphanumeric': 0.01812688821752266, 'fraction_numerical': 0.0, 'mean_word_length': 5.716216216216216, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Lifted Newton-Type Optimization for Pseudospectral Methods in Nonlinear Model Predictive Control

Pseudospectral methods are often used as an efficient direct technique for solving a continuous-time optimal control problem (OCP). They namely offer exponential convergence with respect to the number of collocation nodes, in case of a smooth solution trajectory. The resulting optimization problem is generally dense, when using one high degree polynomial over the complete horizon. In this paper, we propose a lifted Newton-type optimization algorithm based on a tailored Jacobian approximation, in combination with a Gauss-Newton based Hessian, to improve the numerical efficiency of pseudospectral methods. The approach results in a structured sparsity exploiting optimization algorithm, even when using one high degree collocation polynomial. A preliminary implementation is shown to allow considerable numerical speedups for the optimal control case study of the nonlinear chain of masses.