Generalized state-dependent scaling: Backstepping for local optimality, global inverse optimality, and global robust stability

This paper addresses the inverse optimal robust control problem for uncertain nonlinear systems. A new version of robust backstepping is proposed in which inverse optimality is achieved through the selection of generalized state-dependent scaling factors. The design procedure is always successful for uncertain nonlinear systems in strict-feedback form. The class of cost functionals allowed in the inverse optimal design is such that the uncertainty structure and desired level of global robustness can be prescribed a priori. Furthermore, the inverse optimal control law can always be designed such that its linearization is identical to a linear optimal control law for the linearized system with respect to a prescribed cost functional.