Identification of nonlinearly parameterized nonlinear models: application to mass balance systems

A new framework to design parameter estimators for nonlinearly parameterized systems is proposed in this paper. The key step is the construction of a monotone function, which explicitly depends on some of the estimator tuning parameters. Monotonicity-or the related property of convexity-have already been explored by several authors with monotonicity (or convexity) being a priori assumptions that are, usually, valid only on some region of state space. In our approach monotonicity is enforced by the designer, effectively becoming a synthesis tool. In order to dispose of degrees of freedom to render the function monotone we depart from standard (gradient or least-squares) estimators and adopt instead the recently introduced immersion and invariance approach for adaptation.