Quasi-unknown input based 2-DOF control for a class of flat nonlinear SISO systems

The property of quasi unknown-input observability is put in perspective for the design of adaptive feedforward-feedback control for flat SISO systems. It is well-known that feedforward-feedback control for flat systems is quite straightforward given that the (flat) output dynamics is completely determined by the input and succesive output derivatives, thus allowing a direct algebraic solution to the feedforward control problem in absence of unknown inputs. In the presence of unknown inputs, their effects on the dynamics has to be compensated by some adaptation scheme. In this paper such an adaptation scheme is proposed for the SISO case (with respect to output, control input, and unknown input) for piecewise constant unknown inputs with relative degree n. The underlying observability property is discussed and a rigorous assessment of sufficient conditions for closed-loop exponential stability is provided. A representative case example with bistability and double saddle-node bifurcation is used to illustrate the main features of the approach.