Meta-State-Space Learning: An Identification Approach for Stochastic Dynamical Systems
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911860924612608 |
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| author | Beintema, Gerben I. Schoukens, Maarten Tóth, Roland |
| author_facet | Beintema, Gerben I. Schoukens, Maarten Tóth, Roland |
| contents | Available methods for identification of stochastic dynamical systems from input-output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability distributions. In this paper, we introduce a novel identification method of such systems, which results in a dynamical model that is able to produce the time-varying output distribution accurately without taking restrictive assumptions on the data-generating process. The method is formulated by first deriving a novel and exact representation of a wide class of nonlinear stochastic systems in a so-called meta-state-space form, where the meta-state can be interpreted as a parameter vector of a state probability function space parameterization. As the resulting representation of the meta-state dynamics is deterministic, we can capture the stochastic system based on a deterministic model, which is highly attractive for identification. The meta-state-space representation often involves unknown and heavily nonlinear functions, hence, we propose an Artificial Neural Network (ANN)-based identification method capable of efficiently learning nonlinear meta-state-space models. We demonstrate that the proposed identification method can obtain models with a log-likelihood close to the theoretical limit even for highly nonlinear, highly stochastic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06675 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Meta-State-Space Learning: An Identification Approach for Stochastic Dynamical Systems Beintema, Gerben I. Schoukens, Maarten Tóth, Roland Systems and Control Available methods for identification of stochastic dynamical systems from input-output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability distributions. In this paper, we introduce a novel identification method of such systems, which results in a dynamical model that is able to produce the time-varying output distribution accurately without taking restrictive assumptions on the data-generating process. The method is formulated by first deriving a novel and exact representation of a wide class of nonlinear stochastic systems in a so-called meta-state-space form, where the meta-state can be interpreted as a parameter vector of a state probability function space parameterization. As the resulting representation of the meta-state dynamics is deterministic, we can capture the stochastic system based on a deterministic model, which is highly attractive for identification. The meta-state-space representation often involves unknown and heavily nonlinear functions, hence, we propose an Artificial Neural Network (ANN)-based identification method capable of efficiently learning nonlinear meta-state-space models. We demonstrate that the proposed identification method can obtain models with a log-likelihood close to the theoretical limit even for highly nonlinear, highly stochastic systems. |
| title | Meta-State-Space Learning: An Identification Approach for Stochastic Dynamical Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2307.06675 |