The energy functions of coefficient identification algorithms

With reference to least squares identification of internode coefficients appearing in some linear and quasi-linear mass balance equations, we show that both output error and equation error are energy functions of the dynamical systems which model the iterative identification algorithm. In particular we examine a) the properties of a continuous time output error unconstrained minimisation algorithm and b) the connection between a substitution method and the one-step unconstrained minimisation of a weighted equation error function. In both cases we assume a reference solution (set of coefficients) to the inverse problem exists: by our approach we relate non uniqueness of the solution to the initial guess. All results have a straightforward geometrical interpretation.