Removing erroneous history stack elements in concurrent learning

Kersting, Stefan; Buss, Martin

doi:10.1109/cdc.2015.7403421

Cited by 6 publications

(10 citation statements)

References 10 publications

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“…The parameters of the control law (34), filters ( 9), (35), estimation algorithm (16), and adaptive law (19) were chosen as follows:…”

Section: Switched System Identificationmentioning

confidence: 99%

“…Many authors 13,14,18,20,[33][34][35][36] have pointed out the vital necessity to derive adaptive laws that could also provide the identification of piecewise constant parameters with exponential or finite-time convergence. In 18 , it is mentioned that a reinitialization procedure is required for a scheme with the excited regressor generation.…”

Section: Introductionmentioning

confidence: 99%

“…It should be applied each time when the unknown parameters of RE change their values. In [34][35][36] various methods are proposed to overcome superpositional mixing of data in the data stack, which is caused by the unknown parameters switch. In 37 , the dynamic regressor extension and mixing scheme 17 sensitivity to the unknown parameters switching is discussed.…”

Section: Introductionmentioning

confidence: 99%

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Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Glushchenko¹,

Lastochkin²

2022

Preprint

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The scope of this research is the identification of piecewise constant parameters of linear regression equations under the finite excitation condition. Such an equation is considered as a switched system, which identification usually consists of three main steps: a switching time instant detection, choice of the most appropriate model from the known set or generation of a new one, online adjustment of the chosen model parameters. Compared to the known methods, to make the computational burden lower and simplify the stability analysis, we use only one model to identify all switching states of the regression. So, the proposed identification procedure includes only two main approaches. The first one is a new estimation algorithm to detect switching time and preserve time alertness, which is based on a well-known DREM procedure and ensures adjustable detection delay. Unlike existing solutions, it does not involve an offline operation of data monitoring and stacking. The second one is the adaptive law, which provides element-wise monotonous exponential convergence of the regression parameters to their true values over the time range between two consecutive switches. Its convergence condition is that the regressor is finitely exciting somewhere inside such time interval. The robustness of the proposed identification procedure to the influence of external disturbances is analytically proved.Its effectiveness is demonstrated via numerical experiments, in which both abstract regressions and a second-order plant model are used.

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“…The parameters of the control law (34), filters ( 9), (35), estimation algorithm (16), and adaptive law (19) were chosen as follows:…”

Section: Switched System Identificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Glushchenko¹,

Lastochkin²

2022

Preprint

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“…Here we describe the first algorithm to detect and remove erroneous stack elements online (Kersting & Buss, 2015), which is based on the result of Section 3: i.e. estimated parameters converge to an ellipsoidal set in the parameter space (depicted in Figure 2) in the presence of erroneous history stack elements.…”

Section: Detecting Erroneous History Stack Elementsmentioning

confidence: 99%

“…Second, we analyse the convergence of concurrent-learning-based parameter identifiers in more detail and propose algorithms to detect and remove erroneous history stack elements online. The extension of Kersting and Buss (2015) to PWA systems is particularly useful due to erroneous stack elements introduced by switching. This not only enables better estimation of the system parameters but also restores the tracking ability of concurrent-learning-based algorithms.…”

Section: Introductionmentioning

confidence: 99%

Recursive estimation in piecewise affine systems using parameter identifiers and concurrent learning

Kersting

Buss

2017

International Journal of Control

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Piecewise affine systems constitute a popular framework for the approximation of non-linear systems and the modelling of hybrid systems. This paper addresses the recursive subsystem estimation in continuoustime piecewise affine systems. Parameter identifiers are extended from continuous-time state-space models to piecewise linear and piecewise affine systems. The convergence rate of the presented identifiers is improved further using concurrent learning, which makes concurrent use of current and recorded measurements. In concurrent learning, assumptions on persistence of excitation are replaced by the less restrictive linear independence of the recorded data. The introduction of memory, however, reduces the tracking ability of concurrent learning because errors in the recorded measurements prevent convergence to the true parameters. In order to overcome this limitation, an algorithm is proposed to detect and remove erroneous measurements at run-time and thereby restore the tracking ability. Detailed examples are included to validate the proposed methods numerically.

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Command governor‐based adaptive control for dynamical systems with matched and unmatched uncertainties

Yayla

Arabi

Kutay

et al. 2018

Adaptive Control & Signal

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SummaryIn this paper, we propose a command governor‐based adaptive control architecture for stabilizing uncertain dynamical systems with not only matched but also unmatched uncertainties and achieving the desired command following performance of a user‐defined subset of the accessible states. In our proposed solution, online least‐squares solutions for the matched and unmatched parameters are obtained through integration method and they are employed in the adaptive control framework. Specifically, the matched uncertainty is identified and its effect upon the system behavior is entirely attenuated. Moreover, using the unmatched uncertainty approximation obtained through radial basis function neural networks, the command governor signal is designed to achieve the desired command following performance of the user‐defined subset of the accessible states. With this command governor‐based model reference adaptive control architecture, the tracking error of the selected states can be made arbitrarily small by judiciously tuning the design parameters. In addition to the analysis of the closed‐loop system stability using methods from the Lyapunov theory, our findings are also illustrated through numerical examples.

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Removing erroneous history stack elements in concurrent learning

Cited by 6 publications

References 10 publications

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Recursive estimation in piecewise affine systems using parameter identifiers and concurrent learning

Command governor‐based adaptive control for dynamical systems with matched and unmatched uncertainties

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