Adaptation in Stochastic Dynamic Systems—Survey and New Results IV: Seeking Minimum of API  in Parameters of Data

Semushin, I. V.; Tsyganova, Julia V.

doi:10.4236/ijcns.2013.612055

Cited by 6 publications

(3 citation statements)

References 3 publications

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“…Thus, we develop the existing APA approach for the systems with the high level of uncertainty. In all previous related works [Semushin, 2011a;Semushin, 2011b;Tsyganova, 2011;Semushin and Tsyganova, 2013;Semushin, 2014;Semushin et al, 2018] it was assumed that exogenous inputs are known or they are Gaussian white noises.…”

Section: Resultsmentioning

confidence: 99%

“…In this paper, for solving the parameter identification problem, we use an alternative approach that is the Active Principle of Adaptation (APA) [Semushin, 2011a;Semushin, 2011b;Semushin and Tsyganova, 2013;Semushin, 2014]. The main idea for it is to construct an auxiliary identification criterion J ε (θ) [Tsyganova, 2011;Semushin and Tsyganova, 2013;Semushin et al, 2018] which is instrumental because it depends on only directly observed values and can be minimized with the use of a known numerical optimization methods.…”

Section: Parameter Identification Problemmentioning

confidence: 99%

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Parameter identification of the linear discrete-time stochastic systems with unknown exogenous inputs

Tsyganova,

Tsyganov

2023

CAP

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The paper addresses a parameter identification problem for linear discrete-time stochastic systems with unknown exogenous inputs. Such systems are considered when solving practical problems related to the measurements processing in the case when it is impossible to do any assumptions about the evolution of unknown input signal or its statistical characteristics that can change over time. We consider a class of discrete time linear stochastic systems with unknown exogenous inputs, where an additional source of a priori uncertainty of the system model is introduced, namely, the unknown parameter, on the elements of which the system model matrices can depend. This formulation of the parameter identification problem under the conditions of unknown inputs and the presence of random noises describes a high degree of uncertainty of a discrete time linear stochastic system. We propose a novel solution to this problem based on the construction of a new instrumental identification criterion. Minimization of this criterion allows for evaluating the unknown system model parameters simultaneously with the estimating of the state vector and unknown exogenous inputs of the system. Numerical experiments confirm the validity and efficiency of the proposed parameter identification method.

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Section: Resultsmentioning

confidence: 99%

Section: Parameter Identification Problemmentioning

confidence: 99%

Parameter identification of the linear discrete-time stochastic systems with unknown exogenous inputs

Tsyganova,

Tsyganov

2023

CAP

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“…Such criteria include the well-known least squares and maximum likelihood criteria. An alternative approach is the auxiliary performance index method [18]. Thus, the algorithm of numerical minimization of the original functional (12) by the parameter θ is replaced by the algorithm of numerical minimization of the selected instrumental criterion, which is practically feasible.…”

Section: The Problem Of Parameter Identificationmentioning

confidence: 99%

SVD-Based Identification of Parameters of the Discrete-Time Stochastic Systems Models with Multiplicative and Additive Noises Using Metaheuristic Optimization

Tsyganov,

Tsyganova

2023

Mathematics

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The paper addresses a parameter identification problem for discrete-time stochastic systems models with multiplicative and additive noises. Stochastic systems with additive and multiplicative noises are considered when solving many practical problems related to the processing of measurements information. The purpose of this work is to develop a numerically stable gradient-free instrumental method for solving the parameter identification problems for a class of mathematical models described by discrete-time linear stochastic systems with multiplicative and additive noises on the basis of metaheuristic optimization and singular value decomposition. We construct an identification criterion in the form of the negative log-likelihood function based on the values calculated by the newly proposed SVD-based Kalman-type filtering algorithm, taking into account the multiplicative noises in the equations of the state and measurements. Metaheuristic optimization algorithms such as the GA (genetic algorithm) and SA (simulated annealing) are used to minimize the identification criterion. Numerical experiments confirm the validity of the proposed method and its numerical stability compared with the usage of the conventional Kalman-type filtering algorithm.

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Dynamical physically structured data modeling vs. classical time series analysis: A case study related to clinical trial data analysis

Semushin

Tsyganova

2019

J. Phys.: Conf. Ser.

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At the time series analysis’s core is the fitting of a preselected model—in the most straightforward case a linear combination of basis functions—to experimental data with one of the performance indices, for example, least squares criterion. However, no matter what the type of such a model is and whatever be the fitting performance index, such an approach does not stipulate for reliance on the understanding those dynamical laws of physics dictating the observable data behavior, given their complexity or uncertainty. Our research looks into a question: “What benefits or advantages could mathematical modeling of such laws be capable of giving when included in nature or experimental data analysis?—nowhere more so than in deciding on life-changing events based on time series analysis in medical practice”.

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Adaptation in Stochastic Dynamic Systems—Survey and New Results IV: Seeking Minimum of API in Parameters of Data

Cited by 6 publications

References 3 publications

Parameter identification of the linear discrete-time stochastic systems with unknown exogenous inputs

Parameter identification of the linear discrete-time stochastic systems with unknown exogenous inputs

SVD-Based Identification of Parameters of the Discrete-Time Stochastic Systems Models with Multiplicative and Additive Noises Using Metaheuristic Optimization

Dynamical physically structured data modeling vs. classical time series analysis: A case study related to clinical trial data analysis

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