The focus then shifted to the general mathematical principles of non-linear least squares fitting. While acknowledging that this is fundamentally a numerical optimization problem with various algorithmic solutions, the session focused specifically on the Gauss-Newton algorithm. Exploring the mechanics of this algorithm facilitated a critical discussion on the potential vulnerabilities of non-linear parameter estimation, most notably the risk of algorithms converging to local minima rather than the true global optimum.

In the final segment of the class, these parameter estimation techniques were integrated into the broader context of a posteriori identification. The session concluded by introducing parameter sensitivity analysis, explaining how to use regression techniques to evaluate the reliability and precision of estimated parameters based on the experimental data.

Moving beyond linear systems with simple single-input/single-output structures, the session introduced a generalized framework for a priori identification compatible with both linear and non-linear models. Central to this approach was the introduction of the exhaustive summary concept. To illustrate its application, this framework was applied to Bolie's model for the glucose-insulin system. This example demonstrated how utilizing multiple input and output measurements can yield additional observational parameters within the exhaustive summary, successfully resolving identifiability challenges. 

In the final segment of the class, the focus shifted from theoretical identifiability to the practical Parameter Estimation problem. The session introduced linear least squares regression, explaining its application for estimating parameters in strictly linear functions, as well as in non-linear functions that can be mathematically linearized through transformations (e.g., the Michaelis-Menten enzyme kinetics model).