Arthur J. Krener and Witold Respondek. Nonlinear observers with linearizable error dynamics. SIAM Journal on Control and Optimization, 23(2):197--216, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the differential equation d dt e = A LC)e (11) that is linear and spectrally assignable under the assumption that (C; A) is observable. In such case we can resort to the linear case and achieve arbitrarily fast error decays. This technique was proposed and studied in the last ten years [4, 9, 10, 11, 13, 15]. 3 The observer linearization problem As a result of the above discussion, we may give a precise definition of what we mean by the solution of the observer linearization problem . We say that the observer linearization problem (OLP) is solvable for the model (2) if and only if we can find ....

A. J. Krener and W. Respondek. Nonlinear observers with linearizable error dynamics. SIAM J. Control and Optimization, 1985.

.... with a moderate computational burden have been introduced to perform state estimation for nonlinear systems, where the nonlinearity is accounted for by considering its Lipschitz constant [1] Another solution to the observer problem consists in applying a canonical state space transformation [2, 3]. This representation of the system dynamics enables one to easily find an observer with linear error dynamics in the transformed state space. The so called high gain observers have been considered, for example, in [4] where a fast convergence of the estimation error is obtained for general ....

A. J. Krener and W. Respondek, "Nonlinear observer with linearizable error dynamics", SIAM J. on Control and Optimization,vol. 23, no. 2, pp. 197--216, 1985.

.... the system and channel equations, the problem of state reconstruction can be faced using various techniques [4, 5] One solution consists in applying a canonical state space transformation so as to concentrate nonlinearities to a function dependent only on known input and output variables [6, 7]. This enables one to design an observer with linear error dynamics in the transformed statespace. Unfortunately, it is difficult to find this transformation for general nonlinear systems. Therefore, simpler observers are usually considered (and stability results are proved for them) like, for ....

A. J. Krener and W. Respondek, "Nonlinear observer with linearizable error dynamics", SIAM J. Control and Optimization,vol. 23, no. 2, pp. 197--216, 1985.

....observer is of interest. 1 Introduction During the last two decades, the construction of nonlinear observer has been very actively studied (see e.g. 1] and the references therein) In particular, the most wellknown design method for nonlinear observer is the approach of linear error dynamics [2 4] originated by [5] Furthermore, in order to extend the class with linear error dynamics, several authors has begun to utilize the input derivatives in the designed observer (e.g. 6,7] However, these designs have a serious drawback that one should solve some partial di#erential equations to ....

A. Krener and W. Respondek, "Nonlinear observers with linearizable error dynamics," SIAM J. Control Optim., vol. 23, no. 2, pp. 197--216, 1985.

....2 e x 3 3 5 Now, instead of two observations, we takejustone y = x 1 (23) It can easily be seen that for this observation System (20) is still in index one DAE observer normal form (9) but Theorem 1 does not hold any longer. More importantly, the conditions of nonlinear observer design of [2]or[7](or[6] for the single output case) applied on System (20) show that System (20) cannot be transformed into nonlinear observer form and, consequently, that it has no linear error equation for the output (23) 6]gives sufficient conditions for the single output case. Let System (20) define x = ....

A. J. Krener and W. Respondek, "Nonlinear observers with linearizable error dynamics", SIAM J. Contr. Opt.,Vol. 23, No. 2, pp. 197-216, 1985.

....the same token, also observer design for systems that may be transformed into a system in observer form by means of a coordinate transformation and an output transformation is relatively easy. Observer design for systems in observer form was first studied, in the continuous time setting, in [10] [11] (see also [15] In these papers, conditions were given under which a nonlinear continuous time system may be transformed into a system in observer form by means of a coordinate transformation and an output transformation. Basically, these conditions were given in terms of the integrability of ....

....systems generalize the conditions given in [13] for single output systems to the case where, besides a coordinate transformation, also an output transformation is allowed. The conditions for the existence of an observer form for continuous time systems and discrete time systems given in [10] [11], 1] 12] 13] are quite restrictive. Therefore, generalizations have been considered, both in the continuous time case and the discrete time case. In the continuous time case, so called generalized observer forms were considered. These generalized observer forms consist of an observable linear ....

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Krener, A.J., and W. Respondek, Nonlinear observers with linearizable error dynamics, SIAM J. Control Optimiz., 23, pp. 197--216, 1985.

....e x 3 3 5 Now, instead of two observations, we take just one y = x 1 (23) It can easily be seen that for this observation System (20) is still in index one DAE observer normal form (9) but Theorem 1 does not hold any longer. More importantly, the conditions of nonlinear observer design of [2] or [7] (or [6] for the single output case) applied on System (20) show that System (20) cannot be transformed into nonlinear observer form and, consequently, that it has no linear error equation for the output (23) 6] gives sufficient conditions for the single output case. Let System (20) define x = ....

A. J. Krener and W. Respondek, "Nonlinear observers with linearizable error dynamics", SIAM J. Contr. Opt., Vol. 23, No. 2, pp. 197-216, 1985.

....nonlinearity is known exactly. More recent results allow the system to be non Affine (see, for example, Fliess 1990) Others have also looked at output feedback control systems (see, for example, Marino and Tomei 1991, 1992) or reconstructing the state by a nonlinear observer (see, for example, Krener and Respondek 1985, Bastin and Gevers 1988) When the nonlinear plant has a known structure (of either the state equation or input output relation) and is linearly parametrized by unknown parameters, standard adaptive control techniques can sometimes be used (see, for example, Narendra and Annaswamy 1989, Liu and ....

KRENER A. and RESPONDEK W., 1985, Nonlinear Observers with linearizable error dynamcis, SIAM J. Control and Optimization, 23(2), 197-216.

....are viewed as disturbances. A fundamental issue in deriving a state estimator (observer) is of course observability, which for linear systems is a necessary and sufficient condition for having an estimation error with spectrally assignable dynamics. For nonlinear systems the issue is more subtle [9, 12]; however, at least local weak observability is required in order to be able to state sufficient conditions for the existence of an observer with linear and spectrally assignable error dynamics. Other traditional state estimation techniques, such as the Extended Kalman Filter (EKF) 11, 10] are ....

Krener, A. J., and Respondek, W. Nonlinear observers with linearizable error dynamics. SIAM J. Control Optim. vol. 23 (2) (1985).

....1 forms 1 ; 2 , and 3 in x coordinates: 1 = 3; 3 Gamma x 2 ; 1] 2 = 3 Gamma x 2 ; 1; 0] 3 = 1; 0; 0] Since d 2 = Gammadx 2 dx 1 is nonzero, the observer form (6) 7) does not exist. An observer form would exist however if we allowed transformation of the output coordinates [13]. Since 1 and 3 are exact, we need only compute the decomposition for 2 . First, we use the homotopy operator (20) to obtain OE 2 = H 2 = 3x 1 x 2 Gamma x 1 x 2 =2. Integrating 1 gives OE 1 = 3x 1 3x 2 x 3 Gamma x 2 2 =2 (where we have chosen the integration constant for OE 1 ....

A.J. Krener and W. Respondek, "Nonlinear observers with linearizable error dynamics," SIAM J. Control Optim., 23, pp. 197-216, 1985.

.... introduction to nonlinear control theory,we refer the reader to Isidori [9] and Nijmeijer and van der Schaft [18] Necessary and sufficient conditions for linearization by output injection for autonomous nonlinear systems (i.e. without input) were given in [11] by Krener and Isidori, and in [12] by Krener and Respondek along with a constructive algorithm. Gauthier, Hammouri, and Othman [6] described an observer for affine control nonlinear systems whose gain is determined via the solution of an appropriate Lyapunovlike equation. Ciccarella et al. 4] proposed a similar observer whose ....

A. J. Krener and W. Respondek. Nonlinear observers with linearizable error dynamics. SIAM J. Control and Optimization, 23(2):197--216, 1985.

....to zero for small x(0) and (0) One technique of constructing an observer for continuous time systems is to find a nonlinear change of state and output coordinates vhich transforms the system 1. 2) into a system vith linear dynamics driven by nonlinear output injection and vith linear output map [10], 2] The design of an observer for such a system is relatively easy since the error dynamics can be made linear in the transformed coordinates. This approach vas extended to discrete time systems in [16] 17] 3] For more on discrete time observer design ve refer the reader to [5] and ....

A. J. Krener and W. Respondek. Nonlinear observers with linearizable error dynamics. SIAM J. Control and Optimization, Vol. 23, No. 2, 1985, pp. 197-216.

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Arthur J. Krener and Witold Respondek. Nonlinear observers with linearizable error dynamics. SIAM Journal on Control and Optimization, 23(2):197--216, 1985.

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A. J. Krener and W. Respondek, "Nonlinear observers with linearizable error dynamics," SIAM J. Control Optim., vol. 23, no. 2, pp. 197--216, 1985.

No context found.

A.J. Krener and W. Respondek. Nonlinear observers with linearizable error dynamics. SIAM J. Control and Optimization, vol. 23, no. 2, pp. 197-216, 1985.

No context found.

A. J. Krener and W. Respondek, "Nonlinear Observers with Linearizable Error Dynamics," SIAM Journal of Control and Optimization, vol. 23, pp. 197-216, 1985.

No context found.

A. J. Krener and W. Respondek. Nonlinear observers with linearizable error dynamics. SIAM J. Control and Optimization , 1985.

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A. J. Krener and W. Respondek, "Nonlinear observers with linearizable error dynamics," SIAM Journal of Control and Optimization, vol. 23, pp. 197--216, Mar. 1985.

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A. J. Krener and W. Respondek. Nonlinear observers with linearizable error dynamics. SIAM J. Control and Optimization , 1985.

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