A parameter estimation approach to state observation of nonlinear systems

Ortega, Roméo; Bobtsov, Alexey A.; Pyrkin, Anton A.; Aranovskiy, Stanislav

doi:10.1016/j.sysconle.2015.09.008

Cited by 92 publications

(67 citation statements)

References 22 publications

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“…A sliding-window filtering technique to identify the virtual output is then proposed in [9], which is used to design an (augmented) output-feedback control law. See also [37] where a slight extension of this technique is used to enlarge the domain of applicability of the parameter estimation-based observer proposed in [23].…”

Section: Introductionmentioning

confidence: 99%

On generation of virtual outputs via signal injection: Application to observer design for electromechanical systems

Siguerdidjane

Machado

Zhang

2020

European Journal of Control

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Probing signal injection is a well-established technique to extract additional information from a weakly (or non) observable dynamical system. Using averaging theory, a framework to analyse such schemes for general nonlinear systems has been recently proposed in [9], where it is shown that the signal injection may be used to generate a new high frequency output that can be used for state observation or controller design. A key step for the success of this technique is the implementation of a filter to reconstruct this virtual output from the measurement of the overall systems output. The main contribution of this paper is to propose a new filter with guaranteed convergence properties that outperforms the classical designs. The method is applied to a general class of electromechanical systems, and its performance is assessed via simulations and experiments of the 1-DOF magnetic levitation system.

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Section: Introductionmentioning

confidence: 99%

On generation of virtual outputs via signal injection: Application to observer design for electromechanical systems

Siguerdidjane

Machado

Zhang

2020

European Journal of Control

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“…Remark 5. In the adaptive control method of Krstic, 22 an extra term − e T Pb with ∈ R + is applied in its control law (11) to establish closed-loop stability, and exponential convergence of either the tracking error e or the estimation error cannot be guaranteed unless the PE condition is satisfied. In the proposed control law (16), closed-loop stability is established without − e T Pb, and exponential convergence of both e and̃is guaranteed by the IE condition, which significantly relaxes the PE condition.…”

Section: Incorporate With Indirect Adaptive Controlmentioning

confidence: 99%

“…As the base of adaptive control, parameter estimation is an exciting field in the control community and has still attracted great concern in recent years; for the latest results on parameter estimation and adaptive control, readers can refer to other works. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] There exist two parameter estimation schemes in adaptive control, namely, indirect and direct schemes. 19 In the indirect scheme, plant parameters are estimated online for the calculation of controller parameters, whereas in the direct scheme, the plant model is parameterized regarding controller parameters that are estimated directly without plant parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

On parameter convergence in least squares identification and adaptive control

Sun

2019

Intl J Robust & Nonlinear

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Summary Least squares estimation is appealing in performance and robustness improvements of adaptive control. A strict condition termed persistent excitation (PE) needs to be satisfied to achieve parameter convergence in least squares estimation. This paper proposes a least squares identification and adaptive control strategy to achieve parameter convergence without the PE condition. A modified modeling error that utilizes online historical data together with instant data is constructed as additional feedback to update parameter estimates, and an integral transformation is introduced to avoid the time derivation of plant states in the modified modeling error. On the basis of these results, a regressor filtering–free least squares estimation law is proposed to guarantee exponential parameter convergence by an interval excitation condition, which is much weaker than the PE condition. And then, an identification‐based indirect adaptive control law is proposed to establish exponential stability of the closed‐loop system under the interval excitation condition. Illustrative results considering both identification and control problems have verified the effectiveness and superiority of the proposed approach.

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“…However, as shown below, the solution for the levitated ball turns out to be much more complicated. The first step in our design is the reconstruction of the flux, which is done by combining the parameter estimation-based observers (PEBO) recently reported in Ortega et al (2015) with the dynamic regressor extension and mixing (DREM) parameter estimation technique of Aranovskiy et al (2017)-see also Ortega et al (2018) for the reformulation of DREM as a functional Luenberger observer. With the knowledge of the flux we propose suitably tailored nonlinear observers for the mechanical coordinates, obtaining in this way a globally convergent The remainder of the paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Sensorless Control of the Levitated Ball

et al. 2019

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One of the most widely studied dynamical systems in nonlinear control theory is the levitated ball. Several full-state feedback controllers that ensure asymptotic regulation of the ball position have been reported in the literature. However, to the best of our knowledge, the design of a stabilizing law measuring only the current and the voltage-so-called sensorless control-is conspicuous by its absence. Besides its unquestionable theoretical interest, the high cost and poor reliability of position sensors for magnetic levitated systems, makes the problem of great practical application. Our main contribution is to provide the fist solution to this problem. Instrumental for the development of the theory is the use of parameter estimationbased observers, which combined with the dynamic regressor extension and mixing parameter estimation technique, allow the reconstruction of the magnetic flux. With the knowledge of the latter it is shown that the mechanical coordinates can be estimated with suitably tailored nonlinear observers. Replacing the observed states, in a certainty equivalent manner, with a full information asymptotically stabilising law completes the sensorless controller design. Simulation results are used to illustrate the performance of the proposed scheme.

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A parameter estimation approach to state observation of nonlinear systems

Cited by 92 publications

References 22 publications

On generation of virtual outputs via signal injection: Application to observer design for electromechanical systems

On generation of virtual outputs via signal injection: Application to observer design for electromechanical systems

On parameter convergence in least squares identification and adaptive control

Sensorless Control of the Levitated Ball

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