Robust energy-to-peak filter design for a class of unstable polytopic systems with a macroeconomic application

Gyurkovics, Éva; Takács, Tibor

doi:10.1016/j.amc.2021.126729

Cited by 5 publications

(5 citation statements)

References 36 publications

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“…Similarly to the paper Gyurkovics et al. ( 2022 ), it will be shown, how the requirement of asymptotic stability of the unperturbed system can be relaxed in order to apply the robust filtering to estimate the potential GDP.…”

Section: Robust Energy-to-peak Filteringmentioning

confidence: 94%

“…the uncertainty-free) system, which is a usual assumption in previously published papers (with the only exception of Gyurkovics et al. 2022 (cf. the references therein)).…”

Section: Problem Statementmentioning

confidence: 98%

“…The robust filter design methods proposed in the literature (with the only exception of Gyurkovics et al. ( 2022 )) can only be applied, if the magnitude of the eigenvalues of matrix is strictly less then 1, which is not satisfied for the models of Sect, 2 . Similarly to the paper Gyurkovics et al.…”

Section: Robust Energy-to-peak Filteringmentioning

confidence: 99%

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Estimation of the potential GDP by a new robust filter method

Gyurkovics

Takács

2023

Cent Eur J Oper Res

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The first purpose of this paper is to propose a theoretically new robust filter method to estimate non-observable macroeconomic indicators. The second purpose is to apply the proposed method to estimate the Hungarian potential GDP in 2000–2021. The novelty of the proposed filter method is that — unlike papers published so far — it does not require the stability of the dynamic model, only a partial stability condition must be satisfied. Moreover, such time-dependent uncertainties and nonlinearities can arise in the model that satisfy a general quadratic constraint. An important advantage of the proposed robust filter method over the traditional Kalman filter is that no stochastic assumptions is needed that may not be valid for the problem at hand. The proposed filter method has never been applied to estimate the potential GDP. To estimate the Hungarian potential GDP, the proposed method is applied using uni-, bi- and trivariate models. Estimations up to 2021 has not been published yet for the Hungarian economy. The examined period includes both the financial world crisis and the Covid-19 crisis. The results of the different models are consistent. It turned out that the economic policy was very procyclical after 2012, and the GDP gap was still positive during and also after the Covid-19 crisis.

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Section: Robust Energy-to-peak Filteringmentioning

confidence: 94%

“…the uncertainty-free) system, which is a usual assumption in previously published papers (with the only exception of Gyurkovics et al. 2022 (cf. the references therein)).…”

Section: Problem Statementmentioning

confidence: 98%

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Estimation of the potential GDP by a new robust filter method

Gyurkovics

Takács

2023

Cent Eur J Oper Res

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“…Using standard MI modelling techniques [42], we can then remodel the nonlinear complementarity conditions in (17) with equivalent MI linear inequalities by means of binary variables σ (h) , η (h) , θ (h) of suitable dimensions. These must satisfy (componentwise) the conditions:…”

Section: S (H)mentioning

confidence: 99%

“…By requiring one to solve a nonlinear multi-parametric optimization problem online, with the current state measurement serving as the parameter, this method directly enforces a certain degree of contraction possessed by the CLF at every control step. While solving a numerical optimization problem online provides flexibility and performance guarantees, the real-time computational efforts required complicate its application in polytopic linear systems characterized by the high sampling rates frequently encountered, e.g., in fault-tolerant control of aerial vehicles [15], [16], energy-to-peak filtering [17], or robot manipulators control [18].…”

mentioning

confidence: 99%

Neural network controllers for uncertain linear systems

Fabiani¹,

Goulart²

2022

Preprint

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We consider the design of reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems affected by polytopic uncertainty, including controllers with variable structure and those based on a minimal selection policy. We develop a systematic procedure to certify the closed-loop stability and performance of a polytopic system when a rectified linear unit (ReLU)-based approximation replaces such traditional controllers. We provide sufficient conditions to ensure stability involving the worst-case approximation error and the Lipschitz constant characterizing the error function between ReLU-based and traditional controller-based state-to-input mappings, and further provide offline, mixed-integer optimization-based methods that allow us to compute those quantities exactly.

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