Robust Optimal Control for Nonlinear Systems with Parametric Uncertainties via System Level Synthesis

This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal trajectory of the nonlinear system and an error feedback, requiring minimal offline design effort and offering low conservatism. This is achieved by reformulating the uncertain nonlinear system as an uncertain linear time-varying system accounting for linearization errors, additive disturbances, and parametric uncertainties. This decomposition enables the application of established tools from system level synthesis to convexly over-bound all the uncertainties online, leading to a tractable nonlinear optimization problem. With this novel controller parameterization, we can formulate a convex constraint to ensure robust performance guarantees for the nonlinear system. The presented method is relevant for numerous applications related to trajectory optimization, e.g., in robotics and aerospace engineering. We demonstrate the performance of the approach and its low conservatism through the simulation example of a post-capture satellite stabilization.