Observer Synthesis for a Class of Nonlinear Control Systems

Besançon, Gildas; Bornard, G.; Hammouri, Hassan

doi:10.1016/s0947-3580(96)70043-2

Cited by 124 publications

(80 citation statements)

References 15 publications

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“…Assuming the existence of a TOF, a Kalman-like observer design can be performed as in [18,Thm. 3.1].…”

Section: Observer Design Implementation and Robustness Issuesmentioning

confidence: 99%

“…Relative to the result in [18] an additional condition (24) is required to ensure the error dynamics stability. However, the proposed observer benefits from a simpler observer gain and implementation.…”

Section: Observer Design Implementation and Robustness Issuesmentioning

confidence: 99%

“…With the starting vector fieldsḡ k = sg k , k = 1, 2, Lie bracket conditions (16) hold for 0 ≤ k, l ≤ 1; 1 ≤ r, q ≤ 2. The state transformation is computed as Φ(x) = (x 11 , x 12 /s, x 21 , x 22 /s) T by solving (18).…”

Section: A Single Time Scaling Transformation Examplementioning

confidence: 99%

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Multiple Time Scalings of a Multi-Output Observer Form

Wang

Lynch

2010

IEEE Trans. Automat. Contr.

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Time scalings in the multi-output observer form for uncontrolled nonlinear continuous-time systems are considered in this paper. It is the multi-output version of an existing single-input result. Time scaling broadens the class of systems which admits an exact error linearization observer design by including time scaling transformations. The existence conditions of the time scaling transformation and the change of state coordinates to time-scaled observer form are provided. IEEE Transactions on Automatic ControlThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved.

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“…Assuming the existence of a TOF, a Kalman-like observer design can be performed as in [18,Thm. 3.1].…”

Section: Observer Design Implementation and Robustness Issuesmentioning

confidence: 99%

Section: Observer Design Implementation and Robustness Issuesmentioning

confidence: 99%

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Multiple Time Scalings of a Multi-Output Observer Form

Wang

Lynch

2010

IEEE Trans. Automat. Contr.

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“…Further on, a Kalman-like observer can be designed as in Equations (20) and (21), which offers arbitrarily fast exponential convergence provided the existence of sufficient excitation (Besançon et al, 1996).…”

Section: Bus Voltage and Rotor Angle Estimationmentioning

confidence: 99%

Infinite-Bus-Equivalent Estimation From Local Measurements on a Synchronous Machine

Ţiclea¹,

Besançon²

2005

IFAC Proceedings Volumes

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The present paper treats the rotor angle estimation problem in a singlemachine infinite bus setup. The components of the infinite bus voltage phasor are estimated in a coordinate frame that turns with the rotor by means of a Kalman-like filter from exclusively local measurements. Therefore, in addition to the rotor angle, the observer also provides an estimate of the infinite bus voltage. The proposed methodology is tested in simulation.

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“…In a dual to the work of [3] approach, the problem of state reconstruction in state-affine systems of the typė x = A(u)x y = Cx has been solved in [4] (and followed up in [5]) by the observerẋ…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Convergence Rate for Linear-Quadratic Optimal Time-varying Observers

Stocks

Medvedev

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-A well-known method by Anderson and Moore for optimal quadratic feedback design with guaranteed convergence rate for linear time-invariant systems is generalized to linear complex-valued time-varying systems and convergence rates. The resulting method is applied to observer design and illustrated by solving the problem of flux estimation in induction machines. A pre-assigned time-varying convergence rate is shown to improve the observer's transients in comparison with a constant one. The suggested design technique can be readily utilized for nonlinear state-affine systems. I. BACKGROUNDConsider a linear time-invariant systeṁwhereis a controllable pair and A, B, C are real matrices of suitable dimensions. The problem of optimal quadratic control of (1) with a prescribed degree of stability was first solved in [1] and later presented in book format in [2].LetP be the stationary solution (i. e.P = lim t→−∞ P(t, t 0 )) of the Riccati equationwith the boundary condition P(t 0 , t 0 ). Then the constant feedback gain control lawwhere R > 0, (G, A) is an observable pair and α is a nonnegative constant. Besides, the closed-loop state vector governed byẋapproaches zero at least as fast as e − 1 2 αt . Since α can be chosen freely and beforehand, the latter property is referred to as prescribed degree of stability.Generalizing the method of Anderson-Moore to a timevarying case, Linear-Quadratic (LQ) optimality of the design † Systems and Interaction, Luleå University of Technology, SE-971 87 Luleå, SWEDEN, e-mail: Stocks@ltu.se ‡ Information Technology, Uppsala University, SE-75105 Uppsala, SWE-DEN, e-mail: Alexander.Medvedev@it.uu.se is usually sacrificed for the sake of simplicity. In [3], the stabilization ofẋwith the transition matrix Φ A (t, t 0 ) being the unique solution toΦis considered assuming that the controllability gramianis non-singular and bounded from above. Then, for any α > 0, the control law A (t + τ, t)x(t) whereand β ∈ [ 1 2 , ∞) stabilizes (2) with a prescribed degree of stability of at least where P is the solution to the Lyapunov equationAny vector norm · of the estimation error e =x − x satisfies e(t) ≤ ke − 1 2 αt , t ≥ 0 and some constant k, whose value depends only on the initial conditions and u. It worth to notice here that the actual upper bound provided in [4] relates to the convergence of a Lyapunov function and does not take into account the fact that the estimation error norm converges as a square root of it, thus necessitating the factor 1 2 in the exponential. The observer exists when, for some t 0 , u satisfies the "persistency" property

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Observer Synthesis for a Class of Nonlinear Control Systems

Cited by 124 publications

References 15 publications

Multiple Time Scalings of a Multi-Output Observer Form

Multiple Time Scalings of a Multi-Output Observer Form

Infinite-Bus-Equivalent Estimation From Local Measurements on a Synchronous Machine

Guaranteed Convergence Rate for Linear-Quadratic Optimal Time-varying Observers

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