Model-free observer backstepping control design for nonlinear systems in strict feedback form

A model-free control system design for nonlinear system in strict feedback form is presented. A type of neurofuzzy system is used as a system identifier. A Luenberger-type observer is designed from the identifier structure. The controller is based on backstepping and Lyapunov design schemes. Variable structure control is added to deal with uncertainties arising from estimation errors. Together, this control system is capable of controlling a system where the system model is not known and only output is measurable. However, some assumptions of the actual system are required. A tracking problem example is provided together with stability proofs of the closed loop signals.