CONTROLLABILITY ISSUES IN NONLINEAR STATE-DEPENDENT RICCATI EQUATION CONTROL

In the last few years, algorithms using state-dependent Riccati equati ons (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, g lobal controllability and observability of state-dependent system fact orizations are commonly assumed. Here connections between controllabil ity of the state-dependent. factorizations and true system controllabi lity are rigorously established. It is shown that a local equivalence always holds for the class of systems considered, and special cases th at imply global equivalence are also given. Additionally, a notion of nonlinear stabilizability is introduced, which is a necessary conditio n for global closed-loop stability. The theory is illustrated by appli cation to a five-state nonlinear model of a dual-spin spacecraft.