| 3011. |
- González, Rodrigo A., 1992-
(författare)
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Consistency and efficiency in continuous-time system identification
- 2020
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Continuous-time system identification deals with the problem of building continuous-time models of dynamical systems from sampled input and output data. In this field, there are two main approaches: indirect and direct. In the indirect approach, a suitable discrete-time model is first determined, and then it is transformed into continuous-time. On the other hand, the direct approach obtains a continuous-time model directly from the sampled data. In both approaches there exists a dichotomy between discrete-time data and continuous-time models, which can induce robustness issues and complications in the theoretical analysis of identification algorithms. These difficulties are addressed in this thesis.First, we consider the indirect approach to continuous-time system identification. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree one, independent of the relative degree of the strictly proper true system. Inspired by the indirect prediction error method, we propose an indirect-approach estimator that enforces the desired number of poles and zeros in the continuous-time transfer function estimate, and show that the estimator is consistent and asymptotically efficient. A robustification of this method is also developed, by which the estimates are also guaranteed to deliver stable models.In the second part of the thesis, we analyze asymptotic properties of the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC), which is one of the most popular direct identification methods. This algorithm applies an adaptive prefiltering to the sampled input and output that requires assumptions on the intersample behavior of the signals. We present a comprehensive analysis on the consistency and asymptotic efficiency of the SRIVC estimator while taking into account the intersample behavior of the input signal. Our results show that the SRIVC estimator is generically consistent when the intersample behavior of the input is known exactly and subsequently used in the implementation of the algorithm, and we give conditions under which consistency is not achieved. In terms of statistical efficiency, we compute the asymptotic Cramér-Rao lower bound for an output error model structure with Gaussian noise, and derive the asymptotic covariance of the SRIVC estimates. We conclude that the SRIVC estimator is asymptotically efficient under mild conditions, and that this property can be lost if the intersample behavior of the input is not carefully accounted for in the SRIVC procedure.Moreover, we propose and analyze the statistical properties of an extension of SRIVC that is able to deal with input signals that cannot be interpolated exactly via hold reconstructions. The proposed estimator is generically consistent for any input reconstructed using zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. Comparisons with the Maximum Likelihood technique and an analysis of the iterations of the method are provided, in order to reveal the influence of the intersample behavior of the output and to propose new robustifications to the SRIVC algorithm.
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| 3012. |
- González, Rodrigo A., et al.
(författare)
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Consistent identification of continuous-time systems under multisine input signal excitation
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- For many years, the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) has been widely used for identification. The intersample behaviour of the input plays an important role in this method, and it has been shown recently that the SRIVC estimator is not consistent if an incorrect assumption on the intersample behaviour is considered. In this paper, we present an extension of the SRIVC algorithm that is able to deal with input signals that cannot be interpolated exactly through hold reconstructions. The proposed estimator is generically consistent for any input reconstructed through zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. The statistical performance of the proposed estimator is compared to the standard SRIVC estimator through extensive simulations.
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| 3013. |
- González, Rodrigo A., et al.
(författare)
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Consistent identification of continuous-time systems under multisine input signal excitation
- 2021
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 133
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Tidskriftsartikel (refereegranskat)abstract
- For many years, the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) has been widely used for identification. The intersample behaviour of the input plays an important role in this method, and it has been shown recently that the SRIVC estimator is not consistent if an incorrect assumption on the intersample behaviour is considered. In this paper, we present an extension of the SRIVC algorithm that is able to deal with continuous-time multisine signals, which cannot be interpolated exactly through hold reconstructions. The proposed estimator is generically consistent for any input reconstructed through zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. The statistical performance of the proposed estimator is compared to the standard SRIVC estimator through extensive simulations.
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| 3014. |
- González, Rodrigo A.
(författare)
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Continuous-time System Identification : Refined Instrumental Variables and Sampling Assumptions
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Continuous-time system identification deals with the problem of building continuous-time models of dynamical systems from sampled input and output data. There are two main approaches in this field: indirect and direct. In the indirect approach, a suitable discrete-time model is first determined, and then it is transformed into continuous-time. On the other hand, the direct approach obtains a continuous-time model from the sampled data without an intermediate discrete-time model. In both approaches there exists a dichotomy between discrete-time data and continuous-time models, which can induce robustness issues and complications in the theoretical analysis of identification methods. These difficulties are addressed in this thesis.First, we consider the indirect approach to continuous-time system identification. For a zero-order hold sampling mechanism, this approach usually leads to an excess of model zeros when the true system has a relative degree greater than one. Inspired by the indirect prediction error method, we propose an indirect-approach estimator that guarantees stability in the model and enforces the desired number of poles and zeros in the continuous-time transfer function estimate.The second part of this thesis concerns the asymptotic properties and extensions of direct continuous-time identification methods. We provide a comprehensive statistical analysis of the simplified refined instrumental variable method for continuous-time systems (SRIVC), which is a widely-used direct identification algorithm that applies an adaptive prefiltering to the sampled input and output data. We prove that the SRIVC estimator is generically consistent and asymptotically efficient under some mild conditions when taking into account the intersample behavior of the signals in the analysis, and we give conditions under which these statistical properties are not achieved. An extended analysis is provided for when the model is over-parameterized. Later, we propose and analyze the statistical properties of an extension of the SRIVC estimator that can deal with input signals that cannot be interpolated exactly via hold reconstructions. The standard SRIVC estimator and its extension for arbitrary inputs, together with other refined instrumental variable methods, are also investigated in closed-loop settings and are further enhanced to deal with the identification of unstable systems.The last part of this thesis focuses on the analysis and identification of continuous-time systems subject to band-limited input excitations. The non-causal behavior of the band-limited discrete-time equivalent system is studied in detail, and the findings are later used for designing novel non-parametric and parametric identification methods for when the input is band-limited. Special treatment is given to identification with continuous-time multisine inputs. For that case, we investigate fundamental relations between prediction error methods, optimal refined instrumental variables, and interpolation and approximation of frequency response function estimates.All of the methods and theoretical results are accompanied by extensive simulation tests that verify our findings.
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| 3015. |
- González, Rodrigo A., et al.
(författare)
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Enforcing stability through ellipsoidal inner approximations in the indirect approach for continuous-time system identification
- 2020
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963.
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Konferensbidrag (refereegranskat)abstract
- Recently, a new indirect approach method for continuous-time system identification has been proposed that provides complete freedom on the number of poles and zeros of the linear and time-invariant continuous-time model structure. However, this procedure has reliability issues, as it may deliver unstable estimates even if the initialisation model and true system are stable. In this paper, we propose a method to overcome this problem. By generating ellipsoids that contain parameter vectors whose coefficients yield stable polynomials, we introduce a convex constraint in the indirect prediction error method formulation, and show that the proposed method enjoys optimal asymptotic properties while being robust in small and noisy data set scenarios. The effectiveness of the novel method is tested through extensive simulations.
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| 3016. |
- González, Rodrigo A., et al.
(författare)
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Finite sample deviation and variance bounds for first order autoregressive processes
- 2020
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Ingår i: 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing. - : IEEE. ; , s. 5380-5384
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Konferensbidrag (refereegranskat)abstract
- In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by at least a positive epsilon from its true value. Our results consider both stable and unstable processes. Afterwards, we obtain problem-dependent non-asymptotic bounds on the variance of this estimator, valid for sample sizes greater than or equal to seven. Via simulations we analyze the conservatism of our bounds, and show that they reliably capture the true behavior of the quantities of interest.
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| 3017. |
- González, Rodrigo A., et al.
(författare)
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Necessary and sufficient conditions for mean square stabilization over SNR-constrained channels With colored and spatially correlated additive noises
- 2019
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 64:11, s. 4825-4832
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Tidskriftsartikel (refereegranskat)abstract
- This note addresses the problem of stabilizing a multi-input multi-output (MIMO) discrete-time linear time invariant (LTI) system over a MIMO additive noise channel. To treat this problem, we assume that the communication link between the plant output and the controller input consists of multiple additive colored mutually correlated noise channels subject to independent signal-to-noise ratio (SNR) constraints. We derive analytical conditions for which mean square stabilization (MSS) can be achieved under such constraints. We also formulate numerical methods to test these conditions when the noise is white and correlated. Moreover, for simpler plant models, a characterization of the set of power constraints compatible with MSS is obtained. Our results show that the frequency response of the spectral factor related to the channel noise affects the minimum SNR for stability depending mostly on the unstable poles and their directions. This is aggravated by the existence of nonminimum phase zeros and higher relative degree of the plant. On the other hand, we detect that systems under highly correlated noise show lower SNR requirements for stability compared to ones with independent noise channels. Numerical simulations are provided to illustrate the theoretical results.
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| 3018. |
- González, Rodrigo A., et al.
(författare)
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Non-causal regularized least-squares for continuous-time system identification with band-limited input excitations
- 2021
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Ingår i: Proceedings 2021 60th IEEE conference on decision and control (CDC). - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 114-119
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Konferensbidrag (refereegranskat)abstract
- In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is band-limited. The sinc interpolation property of these input signals yields equivalent discrete-time representations that are non-causal. This observation, often overlooked in the literature, is exploited in this work to study non-parametric frequency response estimators of linear continuous-time systems. We study the properties of non-causal least-square estimators for continuous-time system identification, and propose a kernel-based non-causal regularized least-squares approach for estimating the band-limited equivalent impulse response. The proposed methods are tested via extensive numerical simulations.
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| 3019. |
- González, Rodrigo A., et al.
(författare)
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On the Relation Between Discrete and Continuous-Time Refined Instrumental Variable Methods
- 2023
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Ingår i: IEEE Control Systems Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 2475-1456. ; 7, s. 2233-2238
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Tidskriftsartikel (refereegranskat)abstract
- The Refined Instrumental Variable method for discrete-time systems (RIV) and its variant for continuous-time systems (RIVC) are popular methods for the identification of linear systems in open-loop. The continuous-time equivalent of the transfer function estimate given by the RIV method is commonly used as an initialization point for the RIVC estimator. In this letter, we prove that these estimators share the same converging points for finite sample size when the continuous-time model has relative degree zero or one. This relation does not hold for higher relative degrees. Then, we propose a modification of the RIV method whose continuous-time equivalent is equal to the RIVC estimator for any non-negative relative degree. The implications of the theoretical results are illustrated via a simulation example.
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| 3020. |
- González, Rodrigo A., et al.
(författare)
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Parsimonious Identification of Continuous-Time Systems: A Block-Coordinate Descent Approach
- 2023
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Ingår i: 22nd IFAC World CongressYokohama, Japan, July 9-14, 2023. - : Elsevier BV. ; , s. 4216-4221
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Konferensbidrag (refereegranskat)abstract
- The identification of electrical, mechanical, and biological systems using data can benefit greatly from prior knowledge extracted from physical modeling. Parametric continuous-time identification methods can naturally incorporate this knowledge, which leads to interpretable and parsimonious models. However, some applications lead to model structures that lack parsimonious descriptions using unfactored transfer functions, which are commonly used in standard direct approaches for continuous-time system identification. In this paper we characterize this parsimony problem, and develop a block-coordinate descent algorithm that delivers parsimonious models by sequentially estimating an additive decomposition of the transfer function of interest. Numerical simulations show the efficacy of the proposed approach.
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