The Dynamic Search for the Minimal Dynamic Extension

TL;DR

This paper presents a novel search-based approach to identify minimal dynamic extensions for feedback linearization in nonlinear control systems, offering a more systematic and potentially less restrictive method.

Contribution

It introduces a new perspective by framing the dynamic precompensator problem as a search over a category, utilizing dynamic programming and search algorithms.

Findings

Search algorithms can find minimal dynamic extensions efficiently.

Heuristic methods can guide the search towards feedback linearizable systems.

The approach offers a systematic framework for the dynamic precompensator problem.

Abstract

Identifying the dynamic precompensator that renders a nonlinear control system feedback linearizable is a challenging problem. Researchers have explored the problem -- dynamic feedback linearization -- and produced existence conditions and constructive procedures for the dynamic precompensator. These remain, in general, either computationally expensive or restrictive. Treating the challenge as intrinsic, this article views the problem as a search problem over a category. Dynamic programming applies and, upon restriction to a finite category, classic search algorithms find the minimal dynamic extension. Alternatively, a heuristic aiming towards feedback linearizable systems can be employed to select amongst the infinitely-many extensions. This framing provides a distinctive, birds-eye view of the search for the dynamic precompensator.