Robust Nonlinear Optimal Control via System Level Synthesis

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 optimize an affine error feedback while planning the nominal trajectory and ensuring robust constraint satisfaction for the nonlinear system. The proposed approach thereby results in a less conservative planning compared with state-of-the-art techniques. A tailored sequential quadratic programming strategy is proposed to solve the resulting nonlinear program efficiently. We demonstrate the benefits of the proposed approach to control the rotational motion of a rigid body subject to state and input constraints.