A condition for dynamic feedback linearization of control-affine nonlinear systems

被引：17

作者：

Guay, M ^{[1
]}

McLellan, PJ ^{[1
]}

Bacon, DW ^{[1
]}

机构：

[1] QUEENS UNIV, DEPT CHEM ENGN, KINGSTON, ON K7L 3N6, CANADA

来源：

INTERNATIONAL JOURNAL OF CONTROL | 1997年 / 68卷 / 01期

关键词：

D O I：

10.1080/002071797223749

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, a necessary and sufficient condition for dynamic feedback linearizability by endogenous feedback of control-affine nonlinear systems is presented. The condition is based on a modified derived flag of a Pfaffian system associated with a control system which takes into account the presence of a precompensator. It is shown that the generators associated with this modified derived flag must satisfy a number of congruences. The congruences ensure that the conditions of the GS algorithm are satisfied for the prolongated system and thus provide an algorithm to calculate the required feedback and state space transformations. A tower structure is identified with respect to a set of indices corresponding to a set of generalized Kronecker indices. Using these conditions, a bound related to the extent of precompensation required for each input channel is obtained. It is shown how linearizing outputs can be identified by studying the derived flag of the Pfaffian system associated with a nonlinear system.

引用

页码：87 / 106

页数：20

共 12 条

[1] A LINEAR ALGEBRAIC FRAMEWORK FOR DYNAMIC FEEDBACK LINEARIZATION [J].

ARANDABRICAIRE, E ;

MOOG, CH ;

POMET, JB .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1995, 40 (01) :127-132

[2]

ARANDABRICAIRE E, 1993, PROCEEDINGS OF THE 32ND IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, P3441, DOI 10.1109/CDC.1993.325852

[3] ON DYNAMIC FEEDBACK LINEARIZATION [J].

CHARLET, B ;

LEVINE, J ;

MARINO, R .

SYSTEMS & CONTROL LETTERS, 1989, 13 (02) :143-151

[4] SUFFICIENT CONDITIONS FOR DYNAMIC STATE FEEDBACK LINEARIZATION [J].

CHARLET, B ;

LEVINE, J ;

MARINO, R .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1991, 29 (01) :38-57

[5] FLATNESS AND DEFECT OF NONLINEAR-SYSTEMS - INTRODUCTORY THEORY AND EXAMPLES [J].

FLIESS, M ;

LEVINE, J ;

MARTIN, P ;

ROUCHON, P .

INTERNATIONAL JOURNAL OF CONTROL, 1995, 61 (06) :1327-1361

[6]

FLIESS M, 1994, IEEE DECIS CONTR P, P339, DOI 10.1109/CDC.1994.410906

[7] THE GS ALGORITHM FOR EXACT LINEARIZATION TO BRUNOVSKY NORMAL-FORM [J].

GARDNER, RB ;

SHADWICK, WF .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1992, 37 (02) :224-230

[8]

MARTIN P, 1993, PROCEEDINGS OF THE 32ND IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, P3431, DOI 10.1109/CDC.1993.325850

[9]

Rouchon P., 1994, J. Math. Syst. EstimationControl, V4, P257

[10] ABSOLUTE EQUIVALENCE AND DYNAMIC FEEDBACK LINEARIZATION [J].

SHADWICK, WF .

SYSTEMS & CONTROL LETTERS, 1990, 15 (01) :35-39

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