On the Dynamics of Control

TL;DR

This paper introduces a fiber bundle framework for controlling nonlinear dynamical systems, enabling the use of dynamical systems theory tools to analyze control properties and system behavior, with applications across multiple areas.

Contribution

It develops a novel dynamical system approach using fiber bundles to analyze and control nonlinear systems, including the generation of NHIM/NAIM structures.

Findings

Time scale separation analysis

Decoupling of system dynamics

Application to three main areas

Abstract

We present a dynamical system approach for the control of a nonlinear dynamical system by defining the control problem in a Fiber bundle framework. The constructive procedure derived results in the generation of a NHIM/NAIM which facilitates the use of tools and ideas from dynamical system theory to analyze and understand the properties associated with the controlled system. The time scale separation, decoupling of system dynamics, and their role in the system behavior are analyzed. An overview of the benefits of the above approach is demonstrated by briefly discussing three main application areas.