A recursive identification algorithm for switched linear/affine models

Bako, Laurent; Boukharouba, K.; Duviella, E.; Lecœuche, S.

doi:10.1016/j.nahs.2010.05.003

Cited by 77 publications

(76 citation statements)

References 19 publications

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“…wheref is defined as in (4). For this sparsity measure to make sense in the present recursive context, the temporal distribution of nonzero vectors in the sequence {f (t)} needs to be uniform.…”

Section: Identification Results For a Model Of The Form (1)mentioning

confidence: 99%

“…In more details, we follow a similar idea as in [4,13] and select σ(t) to coincide with the index of the matrix H i (t − 1), i ∈ S that minimizes the relative fitting error i.e,…”

Section: Application To Jump Markov Linear Systemsmentioning

confidence: 99%

“…A particularly interesting application of the above problem concerns, as will be suggested later in the paper, the identification of switched linear models. In this case, if one focuses on the problem of recovering a specific linear multi-variable submodel, then the data generated by the other submodels can be regarded as a sparse sequence of errors [2][3][4]. We will elaborate more on this point in Section 3.…”

Section: Introductionmentioning

confidence: 99%

“…The second contribution of this work is an application of the method developed in the first part to the identification of Jump Markov Linear Systems (JMLS). If s denotes the number of subsystems composing the JMLS under consideration, we show that the submodels can, following a similar procedure as in [4], be recursively identified using s W-RLS identifiers operating in parallel.…”

Section: Introductionmentioning

confidence: 99%

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A Recursive Sparse Learning Method: Application to Jump Markov Linear Systems

Chen

Bako

Lecœuche

2011

IFAC Proceedings Volumes

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This paper addresses the problem of identifying linear multi-variable models from the inputoutput data which is corrupted by an unknown, non-centered, and sparse vector error sequence. This problem is sometimes referred to as error correcting problem in coding theory and robust estimation problem in statistics. By taking advantage of some recent developments in sparse optimization theory, we present here a recursive approach. We then show that the proposed identification method can be adapted to estimate parameter matrices of Jump Markov Linear Systems (JMLS), that is, switched linear systems in which the discrete state sequence is a stationary Markov chain. Some numerical simulation results illustrate the potential of the new method.

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Section: Identification Results For a Model Of The Form (1)mentioning

confidence: 99%

“…In more details, we follow a similar idea as in [4,13] and select σ(t) to coincide with the index of the matrix H i (t − 1), i ∈ S that minimizes the relative fitting error i.e,…”

Section: Application To Jump Markov Linear Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Recursive Sparse Learning Method: Application to Jump Markov Linear Systems

Chen

Bako

Lecœuche

2011

IFAC Proceedings Volumes

Self Cite

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“…Despite of the difficulty, there are recently proposed techniques dealing with the issue: Bayesian procedure [12], the bounded-error procedure [5], the clustering-based procedure [8] and the Mixed-Integer Programming procedure [18]. Further results on identification of subclasses of PWA systems can be found in [1], [22]. Most of the work in the area of identifying PWA systems focuses on the development of identification algorithms for discrete-time piecewise affine functions in regression form and the algorithms are offline.…”

Section: Introductionmentioning

confidence: 99%

Online identification of continuous bimodal and trimodal piecewise affine systems

Thuan

Boom

Baldi

2016

2016 European Control Conference (ECC)

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Abstract-This paper investigates the identification of continuous piecewise affine systems in state space form with jointly unknown partition and subsystem matrices. The partition of the system is generated by the so-called centers. By representing continuous piecewise affine systems in the max-form and using a recursive Gauss-Newton algorithm for a suitable cost function, we derive adaptive laws to online estimate parameters including both subsystem matrices and centers. The effectiveness of the proposed approach is demonstrated with a numerical example.

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Fault detection and identification for a class of continuous piecewise affine systems with unknown subsystems and partitions

Moustakis

Zhou

Quang

et al. 2018

Adaptive Control & Signal

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This paper establishes a novel online fault detection and identification strategy for a class of continuous piecewise affine (PWA) systems, namely, bimodal and trimodal PWA systems. The main contributions with respect to the state-of-the-art are the recursive nature of the proposed scheme and the consideration of parametric uncertainties in both partitions and in subsystems parameters. In order to handle this situation, we recast the continuous PWA into its max-form representation and we exploit the recursive Newton-Gauss algorithm on a suitable cost function to derive the adaptive laws to estimate online the unknown subsystem parameters, the partitions, and the loss in control authority for the PWA model. The effectiveness of the proposed methodology is verified via simulations applied to the benchmark example of a wheeled mobile robot.

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A recursive identification algorithm for switched linear/affine models

Cited by 77 publications

References 19 publications

A Recursive Sparse Learning Method: Application to Jump Markov Linear Systems

A Recursive Sparse Learning Method: Application to Jump Markov Linear Systems

Online identification of continuous bimodal and trimodal piecewise affine systems

Fault detection and identification for a class of continuous piecewise affine systems with unknown subsystems and partitions

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