Canonical form observer design for non-linear time-variable systems

Bestle, Dieter; Zeitz, Μ.

doi:10.1080/00207178308933084

Cited by 533 publications

(216 citation statements)

References 5 publications

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“…The literature about this technique is vast. Since the pioneer works of (Bestle and Zeitz (1983); Krener and Isidori (1983)) for single output systems and (Krener and Respondek (1985); Xia and Gao (1989)) for the case of MIMO systems, many other results (see Keller (1987); Marino and Tomei (1996); Lynch and Bortoff (2001); Phelps (1991); Boutat et al (2009)) were published by following the same idea. However, the solvability of the problem requires the restrictive commutative Lie bracket condition for the deduced vector fields.…”

Section: Introductionmentioning

confidence: 99%

Partial observer normal form for nonlinear system

et al. 2016

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In this paper, we investigate the estimation problem for a class of partially observable nonlinear systems. For the proposed Partial Observer Normal Form (PONF), necessary and sufficient conditions are deduced to guarantee the existence of a change of coordinates which can transform the studied system into the proposed PONF. Examples are provided to illustrate the effectiveness of the proposed results.

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Section: Introductionmentioning

confidence: 99%

Partial observer normal form for nonlinear system

et al. 2016

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“…Our approach is in some sense dual to the extended Luenberger observer [5,6]. The controller gain (5) is equivalent to the time-varying gain derived in [7].…”

Section: Exactly Linear Tracking Controlmentioning

confidence: 99%

Approximately linear tracking control of nonlinear systems

Röbenack

Paschke

2012

Proc Appl Math and Mech

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An elegant approach to control nonlinear state-space systems is the exact input-to-state linearization, where a nonlinear change of coordinates combined with a nonlinear feedback law yields a linear controllable system. In this contribution, we treat the single-input case, where input-to-state linearizability is equivalent to flatness. Sufficient and necessary existence conditions are well-known, but quite restrictive. We propose the design of a tracking controller for flat single-input systems, where the explicit knowledge of the flat output is not required. Our approach is based on a series expansion of the tracking error along a given reference trajectory. The controller gain can even be computed for non-flat systems with regular controllability matrix.

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“…The key idea in such approaches is to produce approximate measures of nonlinearity of the order 1, as in Extended Luenberger Observers (ELOs) (Ciccarella et al, 1993). The approximation of nonlinearities in the canonical form (which results in an ELO) has already been suggested (Bestle and Zeitz, 1983), and this approach can be extended to higher order approximations (Röbenack and Lynch, 2004). An observer using a Partial nonlinear Observer Canonical Form (POCF) (Röbenack and Lynch, 2006) has weaker observability and integrability existence conditions than the well-established nonlinear Observer Canonical Form (OCF).…”

Section: Introductionmentioning

confidence: 99%

State estimation for a class of nonlinear systems

Schwaller¹,

Ensminger²,

Dresp-Langley³

et al. 2013

International Journal of Applied Mathematics and Computer Science

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We propose a new type of Proportional Integral (PI) state observer for a class of nonlinear systems in continuous time which ensures an asymptotic stable convergence of the state estimates. Approximations of nonlinearity are not necessary to obtain such results, but the functions must be, at least locally, of the Lipschitz type. The obtained state variables are exact and robust against noise. Naslin's damping criterion permits synthesizing gains in an algebraically simple and efficient way. Both the speed and damping of the observer response are controlled in this way. Model simulations based on a Sprott strange attractor are discussed as an example.

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Canonical form observer design for non-linear time-variable systems

Cited by 533 publications

References 5 publications

Partial observer normal form for nonlinear system

Partial observer normal form for nonlinear system

Approximately linear tracking control of nonlinear systems

State estimation for a class of nonlinear systems

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