UNKNOWN INPUT AND STATE ESTIMATION FOR UNOBSERVABLE SYSTEMS

被引：66

作者：

Bejarano, Francisco J. ^{[1
]}

Fridman, Leonid ^{[1
]}

Poznyak, Alexander ^{[2
]}

机构：

[1] Univ Nacl Autonoma Mexico, Dept Control, Div Elect Engn, Mexico City 04510, DF, Mexico

[2] IPN, CINVESTAV, Dept Automat Control, Mexico City 07000, DF, Mexico

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2009年 / 48卷 / 02期

关键词：

unknown input estimation; strong detectability; sliding mode observer; SLIDING MODE OBSERVERS; DIFFERENTIATION; DESIGN; ORDER;

D O I：

10.1137/070700322

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The concept of strong detectability and its relation with the concept of invariant zeros is reviewed. For strongly detectable systems (which includes the strongly observable systems), it is proposed a hierarchical design of a robust observer whose trajectories converge to those of the original state vector. Furthermore, it is shown that neither left invertibility is a sufficient condition nor strong detectability is a necessary condition to estimate the unknown inputs. It is shown that the necessary and sufficient condition for estimating the unknown inputs is that the set of the invariant zeros that do not belong to the set of unobservable modes be within the interior of the left half plane of the complex space. This shows that the unknown inputs could be estimated even if it is impossible to estimate the entire state vector of the system. Two numerical examples illustrate the effectiveness of the proposed estimation schemes.

引用

页码：1155 / 1178

页数：24

共 27 条

[1] Sliding observer-controller design for uncertain triangular nonlinear systems [J].

Ahmed-Ali, T ;

Lamnabhi-Lagarrigue, F .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1999, 44 (06) :1244-1249

[2] An invariance principle for discontinuous dynamic systems with application to a Coulomb friction oscillator [J].

Alvarez, J ;

Orlov, I ;

Acho, L .

JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME, 2000, 122 (04) :687-690

[3]

Barbot JP, 2002, CONTROL ENGN SER, V11, P103

[4] A survey of applications of second-order sliding mode control to mechanical systems [J].

Bartolini, G ;

Pisano, A ;

Punta, E ;

Usai, E .

INTERNATIONAL JOURNAL OF CONTROL, 2003, 76 (9-10) :875-892

[5]

Bartolini G, 2002, LECT NOTES CONTR INF, V274, P83

[6]

Basile G, 1992, Controlled and conditioned invariants in linear system theory

[7] Exact state estimation for linear systems with unknown inputs based on hierarchical super-twisting algorithm [J].

Bejarano, F. J. ;

Fridman, L. ;

Poznyak, A. .

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2007, 17 (18) :1734-1753

[8] Hierarchical second-order sliding-mode observer for linear time invariant systems with unknown inputs [J].

Bejarano, F. J. ;

Poznyak, A. ;

Fridmanz, L. .

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2007, 38 (10) :793-802

[9] Observation and identification of mechanical systems via second order sliding modes [J].

Davila, J. ;

Fridman, L. ;

Poznyak, A. .

INTERNATIONAL JOURNAL OF CONTROL, 2006, 79 (10) :1251-1262

[10]

Edwards C, 2002, LECT NOTES CONTR INF, V274, P253

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