Robust Nonlinear Optimal Control via System Level Synthesis

• Published in: IEEE transactions on automatic control Vol. 70; no. 7; pp. 4780 - 4787
• Main Authors: Leeman, Antoine P., Kohler, Johannes, Zanelli, Andrea, Bennani, Samir, Zeilinger, Melanie N.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Constraints; Decomposition; Error feedback; Linear systems; NL predictive control; Nonlinear control; Nonlinear dynamical systems; Nonlinear systems; Optimal control; Optimization; Predictive control; Rigid structures; Robust control; Series expansion; Synthesis; system level synthesis (SLS); Taylor series; Time varying control systems; Time-varying systems; Training; Trajectory optimization; Vectors
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2025.3552482

This article addresses the problem of finite horizon constrained robust optimal control for nonlinear systems subject to norm-bounded disturbances. To this end, the underlying uncertain nonlinear system is decomposed based on a first-order Taylor series expansion into a nominal system and an error (deviation) described as an uncertain linear time-varying system. This decomposition allows us to leverage system level synthesis to jointly optimize an affine error feedback, a nominal nonlinear trajectory, and, most importantly, a dynamic linearization error overbound used to ensure robust constraint satisfaction for the nonlinear system. The proposed approach thereby results in less conservative planning compared with state-of-the-art techniques. We demonstrate the benefits of the proposed approach to control the rotational motion of a rigid body subject to state and input constraints.