A randomized two-stage iterative method for switched nonlinear systems identification

Bianchi, Federico; Prandini, Maria; Piroddi, Luigi

doi:10.1016/j.nahs.2019.100818

Cited by 22 publications

(40 citation statements)

References 30 publications

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“…This choice can help in discriminating between models with similar performance by amplifying their differences [38]. The parameter K λ can be tuned in the first iteration of the algorithm as suggested in [6]:…”

Section: Distribution Updatementioning

confidence: 99%

“…According to the approach proposed in [6], MEPs η k t and RIPs µ j k are updated as discussed next. Given ξ t ∼ Cat η t (with t ∈ N), under the independence assumptions 2, for the total expectation theorem it holds that:…”

Section: Distribution Updatementioning

confidence: 99%

“…For these reasons the identification of SNARX models is a rather challenging problem. A first attempt to address this problem is presented in [6], where an iterative two-stage randomized approach for the identification of SNARX models with time-ordered data is proposed. This method relies on the definition of a probability distribution over the space of possible SNARX model structures, including in this concept not only the structure of the NARX sub-models but also the switching signal.…”

Section: Introductionmentioning

confidence: 99%

“…While relatively effective, this method heavily depends on the initial choice of the switching time instants and on the heuristic nature of the refinement stage. This article presents a new approach for the identification of parametric SNARX models, which incorporates some features of the described method of [6], and specifically the randomized approach to MSS, but addresses the sample-mode assignment in a completely different way, that does not require to limit a priori the number of switching time instants, and consequently avoids the necessity to resort to a refinement stage. More precisely, the proposed method builds on the general framework of [4], that alternates between parameter estimation and samplemode assignment, using a cost function that accounts for both tasks, and incorporates constraints on the switching mechanism directly within the objective.…”

Section: Introductionmentioning

confidence: 99%

“…To deal with the MSS task in the framework of [4], which is not naturally equipped with this ability 1 , we reformulate the learning problem in terms of the optimization of a probability distribution over the space of all possible model structures, along the lines of [6]. This distribution is progressively tuned via a sample-and-evaluate strategy, where each extracted structure is used to run an instance of the method of [4].…”

Section: Introductionmentioning

confidence: 99%

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Model structure selection for switched NARX system identification: A randomized approach

et al. 2021

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The identification of switched systems is a challenging problem, which entails both combinatorial (sample-mode assignment) and continuous (parameter estimation) features. A general framework for this problem has been recently developed, which alternates between parameter estimation and sample-mode assignment, solving both tasks to global optimality under mild conditions. This article extends this framework to the nonlinear case, which further aggravates the combinatorial complexity of the identification problem, since a model structure selection task has to be addressed for each mode of the system. To solve this issue, we reformulate the learning problem in terms of the optimization of a probability distribution over the space of all possible model structures. Then, a randomized approach is employed to tune this distribution. The performance of the proposed approach on some benchmark examples is analyzed in detail.

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Section: Distribution Updatementioning

confidence: 99%

Section: Distribution Updatementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Model structure selection for switched NARX system identification: A randomized approach

et al. 2021

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Unknown piecewise constant parameters identification with exponential rate of convergence

Glushchenko

Lastochkin

2022

Adaptive Control & Signal

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Summary The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one model to identify all switching states of the regression is used in the developed procedure with the following two‐fold contribution. First of all, we propose a new truly online estimation algorithm based on a well‐known DREM approach to detect switching time and preserve time alertness with adjustable detection delay. Second, despite the fact that a switching signal function is unknown, the adaptive law is derived that provides global exponential convergence of the regression parameters estimates to their true values in case the regressor is finitely exciting somewhere inside the time interval between two consecutive parameters switches. 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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A distributed randomized method for the identification of switched ARX systems

Yu,

Bianchi,

Piroddi

2024

Adaptive Control & Signal

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SummaryThe identification of switched systems amounts to a mixed integer nonlinear optimization problem, where the continuous variables are associated to the model parameterizations of the different modes, and the discrete ones are related to the switching signal (each data sample is assigned to a mode, and switching occurs when the mode assignment changes over time). In the batch form of the identification problem, the combinatorial complexity increases exponentially with the size of the training set, which makes the precise identification of the switching signal the most challenging task in the identification problem. To tackle this complexity we propose a distributed optimization approach, based on the solution of multiple instances of a much simpler problem, where switching can occur only at specific time instants (different for each subproblem), and an information sharing mechanism that preserves likely switching times to improve the local solutions. We employ an adapted version of a previously developed randomized algorithm to solve the individual subproblems. Another important feature of the proposed method is an a posteriori heuristic correction method, that is applied to further refine the switching locations based on the estimated local models before the information sharing phase. The performance of the proposed algorithm is analyzed and compared with other methods on synthetic datasets.

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A randomized two-stage iterative method for switched nonlinear systems identification

Cited by 22 publications

References 30 publications

Model structure selection for switched NARX system identification: A randomized approach

Model structure selection for switched NARX system identification: A randomized approach

Unknown piecewise constant parameters identification with exponential rate of convergence

A distributed randomized method for the identification of switched ARX systems

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