Corrigendum to "Simplified Nonlinear Programs for NMPC Based on Active Set Construction" [2022 IEEE 61st Conference on Decision and Control (CDC), 2022, pp. 3699–3704]

Corrigendum to “Simplified Nonlinear Programs for NMPC Based on Active Set Construction” [2022 IEEE 61st Conference on Decision and Control (CDC), 2022, pp. 3699–3704] Raphael Dyrska∗aand Martin Mönnigmanna aAutomatic Control and Systems Theory, Ruhr-Universität Bochum, Germany October 2025 In [1], we present an approach for predicting future active sets, and we propose solving a simplified NLP (10) that we construct with the predicted active sets. We do not check if the predicted active sets do indeed belong to an optimal solution for the regular NLP (3). Sections I and III should be slightly adjusted to clarify that solutions found with the simplified NLP (10) can only be guaranteed to be feasible for the regular NLP (3) but not, in general, optimal. We note that the main contribution of [1], i.e., the prediction of active sets based on the feasible extension of previous solutions, is not affected by these corrections. We apologize for any inconvenience. In Section I, the sentences “If, for the successor state, a solution to this simplified NLP exists that respects all of the original constraints in spite of additive disturbances, we apply the resulting optimal input signal without solving the original optimization problem. While also a suboptimal NMPC solution itself already attains an inherent robustness [16], we follow the idea described in [14] and exploit the robustness coming with the regional characteristic of an active set for our optimal solution.” ∗Corresponding author. Email address: [email protected] 1 should be rewritten by dropping the term optimal: “If, for the successor state, a solution to the simplified NLP exists that respects all of the original constraints in spite of additive disturbances, we apply the resulting input signal without solving the original optimization problem. While also a suboptimal NMPC solution itself already attains an inherent robustness [16], we follow the idea described in [14] and exploit the robustness coming with the regional characteristic of an active set for our solution.” In Section III B, the following text should be added right after the paragraph following (10): “The simplified NLP (10) is inspired by active-set methods (see, e.g., [2], Chpt. 15.2). However, we do not check if the candidate active set belongs to an optimal solution for the regular NLP (3) before solving (10). Thus, all solutions to the simplified NLP (10) that fulfill the removed constraints can in general only be guaranteed to be feasible but not optimal for the regular NLP (3). We will see in the results section, however, that the applied input signals resulting from solving the simplified and the regular NLP are in general quite similar, if not identical. For readability, we keep the notation z⋆even if the solution is optimal for (10), but suboptimal (i.e., not optimal, but feasible) for (3).” In Section III C, the sentence “If this active set leads to a solution for problem (10) and all of the original constraints are satisfied, Ax+ nagain defines a region in the state space for which this active set is at least locally optimal (red region).” should require the solution to be optimal: “If this active set leads to a solution for problem (10) that satisfies all of the original constraints and that is optimal also for the regular problem (3), Ax+ nagain defines a region in the state space for which this active set is at least locally optimal (red region).” 2 References [1] R. Dyrska, M. Mönnigmann, Simplified Nonlinear Programs for NMPC Based on Active Set Construction, in: 2022 IEEE 61st Conference on Decision and Control (CDC), 2022, pp. 3699–3704, doi: https://doi.org/10.1109/CDC51059.2022.9992520. [2] J. Nocedal, S. J. Wright, Numerical Optimization, 2nd Edition, Springer New York, 2006, doi: https://doi.org/10.1007/978-0-387-40065-5. 3