Identificación de sistemas dinámicos lineales a través de la estructura de autoregresión con variables exógenas mediante gradiente decreciente y mínimos cuadrados para evaluar la mejor estimación.

Abstract

The main objective of this research was to identify lineal dynamic systems through auto-regression with external variables, done by decreasing gradient and least squares in order to evaluate the estimation. The dynamic systems chosen were those of first order such as low-pass and high-pass filters of active type which are commonly used in Electronics, Communications, and Digital Processing of Signals. Moreover, second order systems were also chosen such as the power drive unit of direct current and a band-pass filter that also has a wide application in different areas. In the process of identifying, the least squares method was applied with the aim of minimizing the cost function and to estimate the parameters of the system to be modelled. Likewise, the decreasing gradient method was put into place, through means of the approximation of the derivative and adjusting the parameters like learning and increment in order to achieve the modelling of the proposed system, in different equations or its corresponding transferring function. Once obtained the modelled systems through the said methods it was observed that the least square method could not identify the area where the system outcome its expressed in present values and only depends on past values, this for both outcome and income, meanwhile the gradient method did not present these issues. The hypothesis was accepted through the weighing with respect to the result and the process of developing the programming algorithms for each method of weighing parameters for the four set systems, which are common in the Electronics field. Concluding that the decreasing gradient method is better in the modelling of these type of systems in comparison to that of the least squares. Finally, strategies to initialize all the parameters that are part of the algorithm of decreasing gradient have been stablished in order to facilitate the modelling process.