Convergence analysis of a real-time identification algorithm for switched linear systems with bounded noise

Goudjil, Abdelhak; Pouliquen, Mathieu; Pigeon, Eric; Gehan, Olivier

doi:10.1109/cdc.2016.7798710

Cited by 9 publications

(6 citation statements)

References 31 publications

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“…In [33] the author studies online identification of switched systems as an extension of the offline algebraic method (see (a) above). The works [5,18,14] employ two-step procedures for online identification of switched systems. First, candidate estimates for each subsystem are built, and second, at every time, the active subsystem is determined by assigning the data to one of the candidates according to some criteria and the estimates of the candidates are updated.…”

Section: Related Workmentioning

confidence: 99%

“…First, candidate estimates for each subsystem are built, and second, at every time, the active subsystem is determined by assigning the data to one of the candidates according to some criteria and the estimates of the candidates are updated. In particular, [5] employs prior or posterior residual error for the identification of active subsystems and recursive least squares for updating the candidate estimates, while [18] employs minimization of prior residual error for the identification of active subsystems and a modified outer bounding ellipsoid algorithm for the updation of candidate estimates. The residual error approach for the identification of active subsystem at every time step is modified to a robust version by incorporating an upper bound on estimation error in [14].…”

Section: Related Workmentioning

confidence: 99%

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Learning event-driven switched linear systems

Kundu¹,

Prabhakar²

2020

Preprint

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We propose an automata theoretic learning algorithm for the identification of black-box switched linear systems whose switching logics are event-driven. A switched system is expressed by a deterministic finite automaton (FA) whose node labels are the subsystem matrices. With information about the dimensions of the matrices and the set of events, and with access to two oracles, that can simulate the system on a given input, and provide counter-examples when given an incorrect hypothesis automaton, we provide an algorithm that outputs the unknown FA. Our algorithm first uses the oracle to obtain the node labels of the system run on a given input sequence of events, and then extends Angluin's L * -algorithm to determine the FA that accepts the language of the given FA. We demonstrate the performance of our learning algorithm on a set of benchmark examples.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Learning event-driven switched linear systems

Kundu¹,

Prabhakar²

2020

Preprint

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“…The work in [13] is one of the first to study online identification of switched systems using an extension of the offline algebraic method [14]. In the algorithms proposed in [2], [5], candidate estimates are built for each of the subsystems first. Then, every time a new data point arrives, the discrete state is determined by assigning the data to one of the candidates according to some criterion, and then the estimate of chosen candidate is updated with the new data.…”

Section: Prior Workmentioning

confidence: 99%

“…The algorithm in [2] first identifies the discrete states based on prior or posterior residual error, and then updates the estimate using recursive least squares. The algorithm in [5] identifies the discrete states by minimizing prior residual error similarly and then update the estimates with a modified Outer Bounding Ellipsoid (OBE) algorithm.…”

Section: Prior Workmentioning

confidence: 99%

“…Existing algorithms e.g. [2], [5], commonly have a two-step structure after candidate estimate for each of the subsystem is initialized: (1) every time new data is available, it is assigned to the candidate with minimum prior/posterior residual error; (2) the parameter estimate of the chosen candidate is updated with this data. We will show that using only residual error as the criterion to assign data can be unreliable.…”

Section: Drawbacks Of Existing Algorithmsmentioning

confidence: 99%

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A Robust Algorithm for Online Switched System Identification

Balzano

Özay

2018

IFAC-PapersOnLine

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In this paper, we consider the problem of online identification of Switched AutoRegressive eXogenous (SARX) systems, where the goal is to estimate the parameters of each subsystem and identify the switching sequence as data are obtained in a streaming fashion. Previous works in this area are sensitive to initialization and lack theoretical guarantees. We overcome these drawbacks with our two-step algorithm: (i) every time we receive new data, we first assign this data to one candidate subsystem based on a novel robust criterion that incorporates both the residual error and an upper bound of subsystem estimation error, and (ii) we use a randomized algorithm to update the parameter estimate of chosen candidate. We provide a theoretical guarantee on the local convergence of our algorithm. Though our theory only guarantees convergence with a good initialization, simulation results show that even with random initialization, our algorithm still has excellent performance. Finally, we show, through simulations, that our algorithm outperforms existing methods and exhibits robust performance.

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