Controllability Issues in Nonlinear State-Dependent Riccati Equation Control

Abstract

Inthelastfewyears,algorithmsusingstate-dependentRiccatiequations (SDREs)havebeenproposedforsolving nonlinear control problems. Under state feedback, pointwise solutions of an SDRE must be obtained along the system trajectory. To ensure the control is well deé ned, global controllability and observability of state-dependent system factorizations are commonly assumed. Here connections between controllability of the state-dependent factorizations and truesystem controllability are rigorously established. Itisshown thata localequivalencealways holdsfortheclassofsystemsconsidered,andspecialcasesthatimplyglobalequivalencearealsogiven.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 é ve-state nonlinear model of a dual-spin spacecraft.