Robust Nonlinear Optimal Control via System Level Synthesis

TL;DR

This paper introduces a robust nonlinear optimal control method using system level synthesis that decomposes the system into a nominal part and an error, enabling less conservative and constraint-satisfying control for nonlinear systems under disturbances.

Contribution

It proposes a novel approach combining system level synthesis with a first-order Taylor expansion to handle nonlinearities and uncertainties in robust optimal control.

Findings

Achieves less conservative control compared to existing methods.

Successfully controls rigid body rotation with constraints.

Demonstrates robustness against norm-bounded disturbances.

Abstract

This paper 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 over-bound 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.