Numerical homotopy continuation for control and online identification of nonlinear systems: the survey of selected results

TL;DR

This survey reviews the application of numerical homotopy continuation methods to control and online parameter identification of nonlinear systems, highlighting recent advances and practical examples.

Contribution

It provides a comprehensive overview of how numerical homotopy continuation techniques are used for control and parameter identification in nonlinear systems, including new approaches for nonconvex parameterization.

Findings

Effective control strategies demonstrated through simulations.

Successful online parameter identification with linear and nonlinear models.

Illustrative examples validate the methods' applicability.

Abstract

The article gives an overview of the parameter numerical continuation methodology applied to setpoint control and parameter identification of nonlinear systems. The control problems for affine systems as well as general (nonaffine) nonlinear systems are considered. Online parameter identification is also presented in two versions: with linear and nonlinear nonconvex parameterization. Simulation results for illustrative examples are shown.