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

Abstract: 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 nonlinear trajectory and an error feedback, requiring minimal offline design effort and offering low conservatism. This is achieved by decomposing the affine-in-the-parameter uncertain nonlinear system into a nominal $\textit{nonlinear}$ system and an uncertain linear time-varying system. Using this decomposition, we can apply established tools from system level synthesis to $\textit{convexly}$ over-bound all uncertainties in the nonlinear optimization problem. Moreover, it enables tight joint optimization of the linearization error bounds, parametric uncertainties bounds, nonlinear trajectory, and error feedback. 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.