Applications of a gradient flow algorithm for parameter identification of non-linear systems in continuous-time

Abstract

An efficient methodology for parameter identification is developed for general multi-degree of freedom linear or nonlinear systems in continuous time. The new methodology is based on a gradient flow algorithm and demonstrated to be useful in identifying unknown parameters for the systems defined by both linear and nonlinear differential equations. The new methodology identifies the unknown parameters by solving a system of differential equations rather than the conventional post-data fitting analysis. It is named the trajectory gradient integral flow (TGIF) algorithm. For the cases of stable, one-dimensional linear systems, the asymptotic stability of the TGIF algorithm is guaranteed in the neighborhood of the operating point. For higher order linear or nonlinear systems, certain criteria for stability are developed using the eigenvalue analysis and the Routh-Hurwitz stability criteria. A well-known system identification result is that any method works the best with non-steady, non-periodic data set that is driven by randomized inputs, however this is not an essential requirement with the TGIF algorithm. In fact, it is possible to perform efficient parameter identification with the TGIF algorithm using an unit step input or a simple sine input. Improvements over previous approaches include: (1) the new methodology is easy to apply for nonlinear systems, (2) it works well with a simple unit step or sinusoidal inputs as well as bounded (control) inputs, (3) it demonstrates a reasonable large "domain of attraction", (4) it can be applied for either "on-line" or "off-line" parameter identification processes.