Normal forms for x-flat two-input control-affine systems in dimension five

被引：2

作者：

Nicolau, F. ^{[1
,2
]}

Gstoettner, C. ^{[3
]}

Respondek, W. ^{[4
]}

机构：

[1] ENSEA, Quartz EA 7393, F-95014 Cergy Pontoise, France

[2] Univ Paris Saclay, L2S, Cent Supelec, CNRS, F-91190 Gif Sur Yvette, France

[3] Johannes Kepler Univ Linz, Inst Automat Control & Control Syst Technol, Linz, Austria

[4] Normandie Univ, LMI, INSA Rouen, F-76801 St Etienne Du Rouvray, France

来源：

IFAC PAPERSONLINE | 2022年 / 55卷 / 30期

基金：

奥地利科学基金会;

关键词：

Flatness; normal forms; nonlinear control systems; dynamic linearization; FEEDBACK LINEARIZATION;

D O I：

10.1016/j.ifacol.2022.11.085

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we give normal forms for flat two-input control-affine systems in dimension five that admit a flat output depending on the state only (we call systems with that property x-flat systems). We discuss relations of x-flatness in dimension five with static and dynamic feedback linearization and show that if a system is x-flat it becomes linearizable via at most three prolongations of a suitably chosen control. Therefore x-flat systems in dimension five can be, in general, brought into normal forms generalizing the Brunovsky canonical form. If a system becomes linear via at most two-fold prolongation, the normal forms are structurally similar to the Brunovsky form: they have a special triangular structure consisting of a linear chain and a nonlinear one with at most two nonlinearities. If a system becomes linear via a three-fold prolongation, we obtain not only triangular structures but also a nontriangular one, and face new interesting phenomena. Copyright (C) 2022 The Authors.

引用

页码：394 / 399

页数：6

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