Controllability Issues in Nonlinear State-Dependent Riccati Equation Control

In the last few years, algorithms using state-dependent Riccati equations (SDREs) have been proposed for solving nonlinear control problems. Under state feedback, pointwise solutions of an SDRE must be obtained along the system trajectory. To ensure the control is well-defined, global controllability and observability of state-dependent system factorizations are commonly assumed. This paper rigorously establishes connections between controllability of the state-dependent factorizations and true system controllability. It is shown that a local equivalence always holds for the class of systems considered, and special cases which imply global equivalence are also given. Additionally, a notion of nonlinear stabilizability is introduced, which is a necessary condition for global closed loop stability. The theory is illustrated by application to a five-state nonlinear model of a dual-spin spacecraft.