Method of stochastic sensitivity synthesis in a stabilisation problem for nonlinear discrete systems with incomplete information

Bashkirtseva, Irina

doi:10.1080/00207179.2016.1216608

Cited by 7 publications

(2 citation statements)

References 27 publications

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“…Moreover, for discrete-time systems, the theory of stochastic sensitivity was elaborated also for closed invariant curves [35] and chaotic attractors [36]. This theory is effectively used in the stochastic analysis of nonlinear dynamic models in various fields of science (see, e.g., [33,[37][38][39]), and also in control problems [40,41]. Geometrically, the stochastic sensitivity function technique can be applied in the form of confidence domains [29,32].…”

Section: Stochastic Modelmentioning

confidence: 99%

Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger

Bashkirtseva,

Pavletsov,

Perevalova

et al. 2023

Mathematics

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Motivated by the increasingly important role of mathematical modeling and computer-aided analysis in engineering applications, we consider the problem of the mathematical modeling and computer-aided analysis of complex stochastic processes in thermo-kinetics. We study a mathematical model of the dynamic interaction of reagent concentration and temperature in autocatalysis. For the deterministic variant of this model, mono- and bistability parameter zones as well as local and global bifurcations are revealed, and we show how random multiplicative disturbances can deform coexisting equilibrium regimes. In a study of noise-induced transitions, we apply direct numerical simulation and an analytical approach based on the stochastic sensitivity technique. Two variants of bistability with different scenarios of stochastic transformations are studied and compared.

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Section: Stochastic Modelmentioning

confidence: 99%

Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger

Bashkirtseva,

Pavletsov,

Perevalova

et al. 2023

Mathematics

Self Cite

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“…The problem of the synthesis of the stochastic sensitivity for systems with incomplete information by static feedback regulators was considered in [22,23]. A novelty of the present paper is that for the first time the problem of the synthesis of the stochastic sensitivity for systems with the incomplete information is solved by the help of dynamic regulators.…”

Section: Introductionmentioning

confidence: 99%

Controlling stochastic sensitivity by the dynamic regulators

Bashkirtseva¹

2017

AIP Conference Proceedings

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Abstract.A problem of the control of stochastically forced equilibria in nonlinear dynamic systems with incomplete information is considered. Our approach is based on the idea of the synthesis of the required stochastic sensitivity for the equilibrium. We consider an important, from engineering point of view, case when the system states are observed partially, and these observations contain random noises. To solve this problem, a dynamic regulator consisting of the feedback and filter is constructed. Mathematically, the problem of the synthesis of the assigned stochastic sensitivity is reduced to the solution of the matrix equations for coefficients of the regulator. Problems of the controllability and attainability are discussed. The effectiveness of the proposed approach is demonstrated on the examples.

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On Business Cycles and Growth

Orlando

Sportelli

2021

Dynamic Modeling and Econometrics in Economics and Finance

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Method of stochastic sensitivity synthesis in a stabilisation problem for nonlinear discrete systems with incomplete information

Cited by 7 publications

References 27 publications

Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger

Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger

Controlling stochastic sensitivity by the dynamic regulators

On Business Cycles and Growth

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