On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh–Nagumo (FN) mathematical model

Chavarette, Fábio Roberto; Balthazar, José Manoel; Peruzzi, Nelson José; Rafikov, Marat

doi:10.1016/j.cnsns.2007.10.016

Cited by 11 publications

(5 citation statements)

References 15 publications

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“…O desenvolvimento do projeto de Controle Ótimo é baseado nos trabalhos (CHAVARETTE et al, 2009a;CHAVARETTE et al, 2009b;FERREIRA et al, 2015;FERREIRA et al, 2014a;FERREIRA et al, 2014b). Um sistema controlado é governado pela Equação ( 22), no qual 𝒚 ∈ ℝ 𝑛 é um vetor de estado, 𝐀 ∈ ℝ 𝑛×𝑛 é uma matriz de parâmetros (matriz Jacobiana), 𝐁 ∈ ℝ 𝑛×𝑚 é uma matriz constante responsável por definir quais variáveis de estado serão controladas e 𝒖 ∈ ℝ 𝑚 é o vetor de controle, cuja solução tem a forma apresentada pela Equação ( 23…”

Section: Controle Linear óTimo -Regulador Quadrático Linear (Lqr)unclassified

Potência Gerada Em Um Sistema Dinâmico Decaptação De Energia Controlado via Método Lqr: Comparação Entre Excitação Periódica E Não-Ideal

2020

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Most of active control in vibrational dynamic systems is used to reduce vibrations. However,the aim of this research is specifically the use of vibrations to generate electrical energy, in such a way that the vibration becomes a desired phenomenon. In this way, the intention is to use the Optimal Control via Linear Quadratic Regulator (LQR), resulting in greater transduction of vibrational energy to electric power, varying the excitation type and performing an analysis of the stabilityand the effects of control to the dynamic system.The analyzed system is a bimodal mass-spring-damper with piezoelectric coupling-mechanic who suffers excitations periodic and non-ideal. This work intends to determine which system generates more electric power.

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Section: Controle Linear óTimo -Regulador Quadrático Linear (Lqr)unclassified

Potência Gerada Em Um Sistema Dinâmico Decaptação De Energia Controlado via Método Lqr: Comparação Entre Excitação Periódica E Não-Ideal

2020

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“…The first characteristic of system non-ideal is that it presents an equation that describes the interaction of the energy source with the ideal dynamic system and the second characteristic, is observed that the dynamics of a non-ideal system approaches of the ideal case as the supplied potency becomes sufficiently big and vice-versa. Several contributions to the study of non-ideal problems were presented in the current literature, [1]- [5] and recently [6]- [9]. Among the various ways to minimize vibrations and reduce the oscillatory motion caused by non-ideal power source in the structure is discussed [13] in this paper the application of the structural control.…”

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confidence: 99%

Control Design Applied to a Non-Ideal Structural System With Behavior Chaotic

Chavarette¹

2013

Int. J. of Pure and Appl. Math.

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In this paper we study the behavior of a structure vulnerable to excessive vibrations caused by an non-ideal power source. To perform this study, the mathematical model is proposed, derive the equations of motion for a simple plane frame excited by an unbalanced rotating machine with limited power (non-ideal motor). The non-linear and non-ideal dynamics in system is demonstrated with a chaotic behavior. We use a State-Dependent Riccati Equation Control technique for regulate the chaotic behavior, in order to obtain a periodic orbit small and to decrease its amplitude. The simulation results show the identification by State-Dependent Riccati Equation Control is very effective.

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“…Kalman filter-based techniques have been applied to control single (Ullah and Schiff 2009) and networked (Schiff and Sauer 2008) neuron dynamics and estimate model parameters. Optimal control techniques have been used to stabilize Hodgkin-Huxley (Chavarette et al 2009a) and Fitzhugh-Nagumo (Chavarette et al 2009b) based neuron models. Stochastic optimal control has been used to force a fixed mean neuron firing rate with assumed minimal variance (Feng and Tuckwell 2003).…”

Section: Introductionmentioning

confidence: 99%

Exploring optimal current stimuli that provide membrane voltage tracking in a neuron model

et al. 2011

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Studying neurons from an energy efficiency perspective has produced results in the research literature. This paper presents a method that enables computation of low energy input current stimuli that are able to drive a reduced Hodgkin-Huxley neuron model to approximate a prescribed time-varying reference membrane voltage. An optimal control technique is used to discover an input current that optimally minimizes a user selected balance between the square of the input stimulus current (input current 'energy') and the difference between the reference voltage and the membrane voltage (tracking error) over a stimulation period. Selecting reference signals to be membrane voltages produced by the neuron model in response to common types of input currents i(t) enables a comparison between i(t) and the determined optimal current stimulus i*(t). The intent is not to modify neuron dynamics, but through comparison of i(t) and i*(t) provide insight into neuron dynamics. Simulation results for four different bifurcation types demonstrate that this method consistently finds lower energy stimulus currents i*(t) that are able to approximate membrane voltages as produced by higher energy input currents i(t) in this neuron model.

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On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh–Nagumo (FN) mathematical model

Cited by 11 publications

References 15 publications

Potência Gerada Em Um Sistema Dinâmico Decaptação De Energia Controlado via Método Lqr: Comparação Entre Excitação Periódica E Não-Ideal

Potência Gerada Em Um Sistema Dinâmico Decaptação De Energia Controlado via Método Lqr: Comparação Entre Excitação Periódica E Não-Ideal

Control Design Applied to a Non-Ideal Structural System With Behavior Chaotic

Exploring optimal current stimuli that provide membrane voltage tracking in a neuron model

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