Nonlinear region of attraction analysis for flight control verification and validation

Chakraborty, Abhijit; Seiler, Peter; Balas, Gary J.

doi:10.1016/j.conengprac.2010.12.001

Cited by 93 publications

(99 citation statements)

References 33 publications

(42 reference statements)

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“…This choice may seem restrictive, but in fact many mechanical systems (e.g. aircraft [1]- [3], walking robots [4]), can be approximated by polynomials quite well. Stability conditions for systems with impact and friction can be formulated in terms of polynomial inequalities [5].…”

Section: Introductionmentioning

confidence: 99%

A Matlab tool for regions of attraction estimation via numerical algebraic geometry

Demenkov¹

2015

2015 International Conference on Mechanics - Seventh Polyakhov's Reading

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For a locally stable polynomial dynamical system its region of attraction can be estimated by a polynomial Lyapunov function level set. We formulate this problem in terms of global minimization of a polynomial function over single polynomial constraint. We describe a simple Matlab tool, which employs numerical algebraic geometry methods for computing all local solutions of the optimization problem and therefore its global solution.

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Section: Introductionmentioning

confidence: 99%

A Matlab tool for regions of attraction estimation via numerical algebraic geometry

Demenkov¹

2015

2015 International Conference on Mechanics - Seventh Polyakhov's Reading

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“…Por exemplo, no estudo da 1 yribeiro@usp.br 2 lfcalberto@usp.br 2 imunização de uma população com respeito a uma dada doença (ver [8]), em controle automático de vôo (ver [3]) ou no estudo de estabilidade transitória de sistemas elétricos de potência (ver [7]). …”

Section: Introductionunclassified

Estimativa de Parte Relevante da Fronteira da Região de Estabilidade usando Função Energia Generalizada

Ribeiro¹,

Alberto²

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. Neste trabalho, apresentamos um método para estimar parte relevante da fronteira da região de estabilidade associada a um conjunto atrativo de um sistema não linear através do uso de uma função energia generalizada. A teoria desenvolvida permite concluir que a estimativa obtidaé sempre conservadora, em um certo sentido. Apresentamos um algoritmo conceitual e sua aplicaçãoé ilustrada por meio de um exemplo.Palavras-chave. Método CUEP, Funções Energia Generalizadas, Região de Estabilidade, Sistemas Elétricos de Potência, Estabilidade Transitória. IntroduçãoConsidere o sistema de equações diferenciaiṡondeẋ(t) denota a derivada de x(t) com respeito a variável t e f : R n → R né uma aplicação de classe C 1 . Denotaremos por t → Φ(t, x 0 ), aúnica solução de (1) satisfazendo Φ(0, x 0 ) = x 0 . Um conjunto atrativo σé um conjunto fechado e invariante que possui uma vizinhança aberta U tal que, para todo x 0 ∈ U , temos Φ(t, x 0 ) → σ quando t → ∞, ou seja, a distância entre Φ(t, x 0 ) e σ tende para zeroà medida que t → ∞.O conjunto ω-limite de x, denotado por ω(x),é o conjunto de todos os pontos p para os quais existe uma sequência de tempos {t n } com t n → ∞ e |Φ(t n , x) − p| → 0 quando n → ∞.Se σé um conjunto atrativo, definimos a região de estabilidade de σ por A(σ) = {x ∈ R n : ω(x) ⊂ σ}.

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“…Vehicle upset conditions can involve highly nonlinear flight dynamics, so these methods and tools are needed to gain insight into nonlinear dynamics and control mechanisms that can lead to LOC, and for assessing the effectiveness of technologies developed for LOC prevention and recovery. Analytical methods and software tools have been developed for nonlinear region of attraction analysis, 8 uncertainty quantification and stochastic robustness analysis of nonlinear systems, 9 and nonlinear dynamics and control analysis. 10 The region of attraction for a nonlinear system provides an indication of the region of stability around an equilibrium point.…”

Section: A Advanced Analysis Methodsmentioning

confidence: 99%

Validation of Safety-Critical Systems for Aircraft Loss-of-Control Prevention and Recovery

Belcastro

2012

AIAA Guidance, Navigation, and Control Conference

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Validation of technologies developed for loss of control (LOC) prevention and recovery poses significant challenges. Aircraft LOC can result from a wide spectrum of hazards, often occurring in combination, which cannot be fully replicated during evaluation. Technologies developed for LOC prevention and recovery must therefore be effective under a wide variety of hazardous and uncertain conditions, and the validation framework must provide some measure of assurance that the new vehicle safety technologies do no harm (i.e., that they themselves do not introduce new safety risks). This paper summarizes a proposed validation framework for safety-critical systems, provides an overview of validation methods and tools developed by NASA to date within the Vehicle Systems Safety Project, and develops a preliminary set of test scenarios for the validation of technologies for LOC prevention and recovery.

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Nonlinear region of attraction analysis for flight control verification and validation

Cited by 93 publications

References 33 publications

A Matlab tool for regions of attraction estimation via numerical algebraic geometry

A Matlab tool for regions of attraction estimation via numerical algebraic geometry

Estimativa de Parte Relevante da Fronteira da Região de Estabilidade usando Função Energia Generalizada

Validation of Safety-Critical Systems for Aircraft Loss-of-Control Prevention and Recovery

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