Hysteretic Converters with Stochastic Parameters

Borzunov, Sergei; Семенов, Михаил Е.; Selvesyuk, N. I.; Meleshenko, Peter A.

doi:10.1134/s2070048220020040

Cited by 9 publications

(6 citation statements)

References 20 publications

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“…Therefore, we come to the following conclusion: in the production model (16) for any finite time moment T in the interval [0, T], there is a single solution c * (t) to the system (34), which is strictly monotonous on [0, T].…”

Section: U(t) P(t)mentioning

confidence: 91%

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A Model of Optimal Production Planning Based on the Hysteretic Demand Curve

et al. 2022

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The article considers a hysteretic model of consumer behaviour in mono-product markets. Demand generation with regard to an individual consumer is modeled using a non-ideal relay with inverted thresholds. Therefore, the sales rate is defined as an analogue of the Preisach converter. The article considers the problem of the optimal production, storage, and distribution of goods, taking into account the hysteretic nature of the demand curve. The problem is reduced to a non-classical optimal control problem with hysteretic non-linearities. The latter is solved using Pontryagin’s maximum principle. The adopted economic model is based on the binary relationship of consumers to the product: the product is bought or the product is not bought. Transitions between these states are determined within the framework of our model only by the price of the goods; therefore, only the operator of a non-ideal relay can accurately describe such a dependence. The article presents the results of computational experiments illustrating the theoretical assumptions.

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Section: U(t) P(t)mentioning

confidence: 91%

“…Thus, [32] investigated the response of a non-linear system to stochastic external factors, while [33] modified the said model to the threshold numbers characterised by random, rather than deterministic variables. In [34], hysteretic operators with stochastic parameters are discussed.…”

Section: Purpose/backgroundmentioning

confidence: 99%

A Model of Optimal Production Planning Based on the Hysteretic Demand Curve

et al. 2022

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“…However, the internal parameters of the hysteresis subsystem in these works were considered deterministic. A generalization of one of the simplest hysteresis model such as a generalized backlash has been considered in [95][96][97]: its defining curves were assumed to be subject to random disturbances, and the output of such a converter was treated as a random process. In the above papers, the correctness of the corresponding definition was proved and the basic properties of a stochastic converter were studied.…”

Section: Stochastic External Excitation and Non-deterministic Systemsmentioning

confidence: 99%

The Preisach model of hysteresis: fundamentals and applications

Semenov,

Borzunov,

Meleshenko

et al. 2024

Phys. Scr.

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The Preisach model is a well-known model of hysteresis in the modern nonlinear science. This paper provides an overview of works that are focusing on the study of dynamical systems from various areas (physics, economics, biology), where the Preisach model plays a key role in the formalization of hysteresis dependencies. Here we describe the input-output relations of the classical Preisach operator, its basic properties, methods of constructing the output using the demagnetization function formalism, a generalization of the classical Preisach operator for the case of vector input-output relations. Various generalizations of the model are described here in relation to systems containing ferromagnetic and ferroelectric materials. The main attention we pay to experimental works, where the Preisach model has been used for analytic description of the experimentally observed results. Also, we describe a wide range of the technical applications of the Preisach model in such fields as energy storage devices, systems under piezoelectric effect, models of systems with long-term memory. The properties of the Preisach operator in terms of reaction to stochastic external impacts are described and a generalization of the model for the case of the stochastic threshold numbers of its elementary components is given.

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“…This function significantly increases the flexibility of the UNC. It is obvious that this activation function helps to enhance the robustness of the neural network to various types of noise and improves the capacity of the intellectual output by adding degrees of freedom (i.e., parameters of the hysteresis model) [11][12][13][14][15][16] which determine the nonlinearity of the dynamics of the whole ANN. It is also important that the use of hysteresis functions with feedforward neural networks results in short-term memory effects.…”

Section: Neuron Activation Functionmentioning

confidence: 99%

A Model of a Universal Neural Computer with Hysteresis Dynamics for Avionics Problems

et al. 2022

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The paper proposes a method for implementing a universal neural network processor with hysteresis dynamics. This processor allows a wide range of heterogeneous tasks in real time to be performed without reprogramming and changing their internal structure. Adding hysteresis behavior to the system makes it possible to increase resistance to external influences, the complexity as well as non-linearity of intelligent output. The paper discusses the use of this processor as part of an on-board intelligent avionics system.

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Hysteretic Converters with Stochastic Parameters

Cited by 9 publications

References 20 publications

A Model of Optimal Production Planning Based on the Hysteretic Demand Curve

A Model of Optimal Production Planning Based on the Hysteretic Demand Curve

The Preisach model of hysteresis: fundamentals and applications

A Model of a Universal Neural Computer with Hysteresis Dynamics for Avionics Problems

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