We are designing, perhaps for the first time, closed-loop fault-tolerant control for uncertain nonlinear systems. Our solution is based on a new algebraic estimation technique of the derivatives of a time signal, which • yields good estimates of the unknown parameters and of the residuals, i.e., of the fault indicators, • is easily implementable in real time, • is robust with respect to a large variety of noises, without any necessity of knowing their statistical properties. Convincing numerical simulations are provided via a popular case-study in the diagnosis community, namely the three-tank system, which may be characterized as a flat hybrid system.