Orbital Stabilization of Nonlinear Systems via the Immersion and Invariance Technique

TL;DR

This paper extends the Immersion and Invariance technique to achieve orbital stabilization in nonlinear systems, enabling the generation of attractive periodic solutions, demonstrated through classical mechanical and electronic examples.

Contribution

It introduces a novel application of the Immersion and Invariance method for orbital stabilization, expanding its use beyond equilibrium stabilization.

Findings

Successfully stabilizes periodic orbits in nonlinear systems.

Demonstrates effectiveness with mechanical and electronic examples.

Provides a new approach for orbital stabilization in control theory.

Abstract

Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated by some modern applications we show that the technique can also be used to solve the problem of orbital stabilization, where the final objective is to generate periodic solutions that are attractive. The feasibility of our result is illustrated with some classical mechanical engineering and electronics examples.