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Gotowe bibliografie tematyczne / Lyapunov Functions

Gotowa bibliografia na temat „Lyapunov Functions”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 31 lipca 2024

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Artykuły w czasopismach na temat "Lyapunov Functions"

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Stawiska, Małgorzata. "Plurisubharmonic Lyapunov functions". Michigan Mathematical Journal 52, nr 1 (kwiecień 2004): 131–40. http://dx.doi.org/10.1307/mmj/1080837739.

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Olas, Andrzej. "Recursive Lyapunov Functions". Journal of Dynamic Systems, Measurement, and Control 111, nr 4 (1.12.1989): 641–45. http://dx.doi.org/10.1115/1.3153107.

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The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a concept of a recursive Lyapunov function. For the very important applications case of exponential stability the procedure is effective under very weak conditions imposed on the function V = U(0). The procedure may be particularly applicable for the systems dependent on parameters, when the Lyapunov function determined from one set of parameters may be employed at the first step of the procedure.

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Avallone, Anna. "Lyapunov modular functions". Rendiconti del Circolo Matematico di Palermo 53, nr 2 (czerwiec 2004): 195–204. http://dx.doi.org/10.1007/bf02872871.

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Sassano, Mario, i Alessandro Astolfi. "Dynamic Lyapunov functions". Automatica 49, nr 4 (kwiecień 2013): 1058–67. http://dx.doi.org/10.1016/j.automatica.2013.01.027.

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Fathi, Albert, i Pierre Pageault. "Smoothing Lyapunov functions". Transactions of the American Mathematical Society 371, nr 3 (10.09.2018): 1677–700. http://dx.doi.org/10.1090/tran/7329.

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Sassano, M., i A. Astolfi. "Dynamic Lyapunov Functions". IFAC Proceedings Volumes 44, nr 1 (styczeń 2011): 3409–14. http://dx.doi.org/10.3182/20110828-6-it-1002.03522.

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Levit, M. "Optimum Lyapunov functions". Dynamics and Control 5, nr 2 (kwiecień 1995): 163–90. http://dx.doi.org/10.1007/bf01973947.

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Pappalardo, Massimo, i Mauro Passacantando. "Gap Functions and Lyapunov Functions". Journal of Global Optimization 28, nr 3/4 (kwiecień 2004): 379–85. http://dx.doi.org/10.1023/b:jogo.0000026455.72523.ed.

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Köksal, S., i V. Lakshmikantham. "Higher derivatives of Lyapunov functions and cone-valued Lyapunov functions". Nonlinear Analysis: Theory, Methods & Applications 26, nr 9 (maj 1996): 1555–64. http://dx.doi.org/10.1016/0362-546x(94)00002-y.

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Ates, Muzaffer, i Nezir Kadah. "Novel stability and passivity analysis for three types of nonlinear LRC circuits". An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 11, nr 2 (31.07.2021): 227–37. http://dx.doi.org/10.11121/ijocta.01.2021.001073.

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In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The results are provided within and are of central importance for the analysis of nonlinear electrical, mechanical, and neural systems which based on the system energy perspective. The simulation results given from Matlab successfully verifies the theoretical predictions.

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Rozprawy doktorskie na temat "Lyapunov Functions"

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Otsuki, Nobukazu. "Lyapunov-like functions and geodesic flows". 京都大学 (Kyoto University), 1985. http://hdl.handle.net/2433/86363.

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Elragig, Aiman Saleh. "On transients, Lyapunov functions and Turing instabilities". Thesis, University of Exeter, 2013. http://hdl.handle.net/10871/13789.

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Motivated by the papers [84, 85], this thesis considers the concepts of reactivity, Lyapunov stability and Turing patterns. We introduce the notion of P-reactivity, a new measure for transient dynamics. We extend a result by Shorten and Narendra [108] regarding joint dissipativity for second order systems. We derive an easy verifiable formula that determines systems P-reactivity with respect to a norm induced by the positive definite matrix P. An optimization problem aiming to determine the positive definite P with respect to which a stable system is most reactive is posed and solved numerically for second order systems. The stability radius is adopted as a measure of robustness of joint disspaptivity. We characterise the stability radius of joint dissipativity when the underlying systems are subject to certain specific perturbation structures. A detailed robustness analysis of the Shorten and Narendra conditions is also presented. Using the notion of common Lyapunov function we show that the necessary condition in [85] is a special case of a more powerful (i.e tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We also further extend this to include more complicated movement mechanisms such as chemotaxis. Unlike the traditional techniques, this new necessary condition can be used to check Turing instability for systems with any dimension and any number of parameters. We apply our new conditions to various models in literature.

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Marikar, Mohamed Tariq. "Polyhedral Lyapunov functions and stabilization under polyhedral constraints". Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266114.

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Della, rossa Matteo. "Non smooth Lyapunov functions for stability analysis of hybrid systems". Thesis, Toulouse, INSA, 2020. http://www.theses.fr/2020ISAT0004.

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La Nature, dans ses multiples manifestations, nous fournit un grand nombre d’exemples pour lesquels il est nécessaire d’aller au-delà de la distinction classique entre modèles où le temps est décrit comme une entité continue et modèles où le temps est discret/discrétisé. En particulier, pour une multitude de systèmes en physique/ingénierie, ces deux aspects temporels sont fondamentalement liés, et nécessitent donc que ces deux paradigmes soient connectés et mis en relation, pour une meilleure précision et fidélité dans la représentation du phénomène. Cette famille de systèmes est souvent appelée ``systèmes hybrides’’, et différentes formalisations mathématiques ont été proposées.L’objectif de cette thèse est l’analyse et l’étude de la stabilité (asymptotique) pour certaines classes de systèmes hybrides, en proposant des conditions suffisantes à la Lyapunov. Plus spécifiquement, nous nous concentrerons sur des fonctions de Lyauponv non-lisses ; pour cette raison, les premiers chapitres de cette thèse peuvent être considérés comme une introduction générale de ce sujet, proposant les instruments nécessaires issus de l’analyse non-lisse.Tout d'abord, grâce à ces outils, nous pourrons étudier une classe de fonctions de Lyapunov construites par morceaux, avec une attention particulière aux propriétés de continuité des inclusions différentielles qui composent le système hybride considéré. Nous proposons des conditions qui doivent être vérifiées seulement sur un sous-ensemble dense, et donc allant au-delà de résultats existants.En négligeant les hypothèses de continuité, nous étudions ensuite comment les notions de dérivées généralisées se spécialisent en considérant des fonctions construites comme combinaisons de maximum/ minimum de fonctions lisses. Cette structure devient particulièrement fructueuse quand on regarde la classe des systèmes à commutation dépendant de l’état du système. Dans le cas où les sous-dynamiques sont linéaires, nous étudions comment les conditions proposées peuvent être vérifiées algorithmiquement.L’utilité des notions de dérivées généralisées est finalement explorée dans le contexte de la stabilité entrée-état (ISS) pour inclusions différentielles avec perturbations extérieures. Ces résultats nous permettent de proposer des critères de stabilité pour systèmes interconnectés, et notamment une application du synthèse de contrôleurs pour systèmes à commutation dépendant de l’état
Modeling of many phenomena in nature escape the rather common frameworks of continuous-time and discrete-time models. In fact, for many systems encountered in practice, these two paradigms need to be intrinsically related and connected, in order to reach a satisfactory level of description in modeling the considered physical/engineering process.These systems are often referred to as hybrid systems, and various possible formalisms have appeared in the literature over the past years.The aim of this thesis is to analyze the stability of particular classes of hybrid systems, by providing Lyapunov-based sufficient conditions for (asymptotic) stability. In particular, we will focus on non-differentiable locally Lipschitz candidate Lyapunov functions. The first chapters of this manuscript can be considered as a general introduction of this topic and the related concepts from non-smooth analysis.This will allow us to study a class of piecewise smooth maps as candidate Lyapunov functions, with particular attention to the continuity properties of the constrained differential inclusion comprising the studied hybrid systems. We propose ``relaxed'' Lyapunov conditions which require to be checked only on a dense set and discuss connections to other classes of locally Lipschitz or piecewise regular functions.Relaxing the continuity assumptions, we then investigate the notion of generalized derivatives when considering functions obtained as emph{max-min} combinations of smooth functions. This structure turns out to be particularly fruitful when considering the stability problem for differential inclusions arising from regularization of emph{state-dependent switched systems}.When the studied switched systems are composed of emph{linear} sub-dynamics, we refine our results, in order to propose algorithmically verifiable conditions.We further explore the utility of set-valued derivatives in establishing input-to-state stability results, in the context of perturbed differential inclusions/switched systems, using locally Lipschitz candidate Lyapunov functions. These developments are then used in analyzing the stability problem for interconnections of differential inclusion, with an application in designing an observer-based controller for state-dependent switched systems

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Dos, Santos Paulino Ana Carolina. "Robust analysis of uncertain descriptor systems using non quadratic Lyapunov functions". Thesis, Strasbourg, 2018. http://www.theses.fr/2018STRAD049.

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Les systèmes descripteurs incertains sont convenables pour la représentation des incertitudes d’un modèle, du comportement impulsif et des contraintes algébriques entre les variables d’état. Ils peuvent décrire bien plus de phénomènes qu’un système dynamique standard, mais, en conséquence, l’analyse des systèmes descripteurs incertains est aussi plus complexe. Des recherches sont menées de façon à réduire le degré de conservatisme dans l’analyse des systèmes descripteurs incertains. L’utilisation des fonctions de Lyapunov qui sont en mesure de générer des conditions nécessaires et suffisantes pour une telle évaluation y figurent. Les fonctions de Lyapunov polynomiales homogènes font partie de ces classes, mais elles n’ont jamais été employées pour les systèmes descripteurs incertains. Dans cette thèse, nous comblons ce vide dans la littérature en étendant l’usage des fonctions de Lyapunov polynomiales homogènes du cas incertain standard vers les systèmes descripteurs incertains
Uncertain descriptor systems are a convenient framework for simultaneously representing uncertainties in a model, as well as impulsive behavior and algebraic constraints. This is far beyond what can be depicted by standard dynamic systems, but it also means that the analysis of uncertain descriptor systems is more complex than the standard case. Research has been conducted to reduce the degree of conservatism in the analysis of uncertain descriptor systems. This can be achieved by using classes of Lyapunov functions that are known to be able to provide necessary and sufficient conditions for this evaluation. Homogeneous polynomial Lyapunov functions constitute one of such classes, but they have never been employed in the context of uncertain descriptor systems. In this thesis, we fill in this scientific gap, extending the use of homogeneous polynomial Lyapunov functions from the standard uncertain case for the uncertain descriptor one

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Chao, Chien-Hsiang. "Robust stabilization of linear time-invariant uncertain systems via Lyapunov theory". Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/53928.

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This dissertation is concerned with the problem of synthesizing a robust stabilizing feedback controller for linear time-invariant systems with constant uncertainties that are not required to satisfy matching conditions. Only the bounds on the uncertainties are required and no statistical property of the uncertainties is assumed. The systems under consideration are described by linear state equations with uncertainties. I.e. x(t) = A̅(γ)x(t) +B̅(γ)u(t), where A̅(γ) is an n x n matrix and B̅(γ) is an n x m matrix. Lyapunov theory is exploited to establish the conditions for stabilizability of the closed loop system. We consider a Lyapunov function with an uncertain symmetric positive definite matrix P. The uncertain matrix P satisfies the Lyapunov equation A^TP + PA + Q = 0, where the matrix A is in companion form and the matrix Q is symmetric and positive definite. In the solution of the Lyapunov equation, m rows of the matrix P are fixed in our approach of designing a robust controller. We derive necessary and sufficient conditions on these fixed m rows of the matrix P such that for given positive definite and symmetric Q the solution of the Lyapunov equation yields a positive definite matrix P and a companion matrix A that is Hurwitz. A discontinuous robust stabilizing controller is given. Linear controller design is also investigated in this research. Under the same assumptions for the existence of a stabilizing discontinuous controller, we show that a linear robust stabilizing controller always exists. The dissertation includes three examples to illustrate the design procedures for robust controllers. Example 2 shows that the design procedure may be applied to time-varying nonlinear systems.
Ph. D.

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Tan, Bin. "Invariant manifolds, invariant foliations and linearization theorems in Banach spaces". Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/29421.

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Kuhn, Zuzana. "Ranges of vector measures and valuations". Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/30875.

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Silva, Flávio Henrique Justiniano Ribeiro da. "Funções de Lyapunov para a análise de estabilidade transitória em sistemas de potência". Universidade de São Paulo, 2001. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-07032016-111317/.

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Os métodos diretos são adequados à análise de estabilidade transitória em sistemas de potência, já que não requerem a resolução, integração numérica, do conjunto de equações diferenciais que representam o sistema. Os métodos diretos utilizam as idéias de Lyapunov associadas ao princípio de invariância de LaSalle para estimar a área de atração dos sistemas de potência. A grande dificuldade dos métodos diretos está em encontrar uma função auxiliar V, denominada função de Lyapunov que satisfaça as condições estabelecidas pelo Teorema de Lyapunov. Neste trabalho é realizada uma revisão bibliográfica das funções de Lyapunov utilizadas para análise de estabilidade transitória em sistemas de potência. Analisa-se o problema da existência de funções de Lyapunov quando as condutâncias de transferência são consideradas. Utilizando-se de uma extensão do princípio de Invariância de LaSalle, apresenta-se uma nova função a qual é uma função de Lyapunov no sentido mais geral da extensão do princípio de invariância de LaSalle quando as condutâncias de transferência da matriz admitância da rede reduzida são consideradas. Estudou-se também a existência de funções de Lyapunov no sentido mais geral de extensão do princípio de invariância de LaSalle para modelos que preserva a estrutura da rede. Neste caso, infelizmente não encontramos uma função satisfazendo todas as hipóteses requeridas.
The direct methods are well-suited for transient stability analysis to power systems, since they do not require the solution of the set of differential equations of the system model. The direct methods use the Lyapunov\'s ideas related to the LaSalle\'s invariance principle to estimate the power system attraction area. The great difficulty of the direct methods is to find an auxiliar function V, called Lyapunov function, which satisfies the conditions of Lyapunov\'s theorem. In this work, a bibliographic review of the Lyapunov functions used in transient stability analysis of power systems is done. The problem of existence of Lyapunov functions, when the transfer conductances are considered, is analysed. Using LaSalle\'s invariance principle extension, a Lyapunov function considering the transfer conductances is presented. The existence of Lyapunov functions for models that preserv the network structure was studied using the LaSalle\'s invariance principle. Unfortunately, in these cases, we did not find a function satisfing all the required hypothesis.

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Marinósson, Sigurour Freyr. "Stability analysis of nonlinear systems with linear programming a Lyapunov functions based approach /". [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=982323697.

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Książki na temat "Lyapunov Functions"

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Malisoff, Michael, i Frédéric Mazenc. Constructions of Strict Lyapunov Functions. London: Springer London, 2009. http://dx.doi.org/10.1007/978-1-84882-535-2.

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Frédéric, Mazenc, i SpringerLink (Online service), red. Constructions of Strict Lyapunov Functions. London: Springer London, 2009.

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1943-, Abdulin R. Z., red. Vector Lyapunov functions in stability theory. [Atlanta]: World Federation Publishers, 1996.

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Martyni︠u︡k, A. A. Stability of motions: The role of multicomponent Liapunov's functions. Cambridge, UK: Cambridge Scientific Pub, 2007.

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Giesl, Peter. Construction of Global Lyapunov Functions Using Radial Basis Functions. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-69909-5.

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I, Zinober A. S., red. Variable structure and Lyapunov control. London: Springer-Verlag, 1994.

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Bogatyrev, A. V. Metody analiza ustoĭchivosti nelineĭnykh sistem upravlenii͡a na ĖVM. Moskva: Institut problem upravlenii͡a, 1989.

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Reĭzinʹ, L. Ė. Funkt︠s︡ii Li︠a︡punova i problemy razlichenii︠a︡. Riga: "Zinatne,", 1986.

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Li︠a︡punov, A. M. Izbrannye trudy: Raboty po teorii ustoĭchivosti. Moskva: Nauka, 2007.

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Behal, Aman. Lyapunov-based control of robotic systems. Boca Raton: CRC Press, 2009.

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Części książek na temat "Lyapunov Functions"

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Han, Xiaoying, i Peter Kloeden. "Lyapunov Functions". W SpringerBriefs in Mathematics, 41–48. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61934-7_4.

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Aubin, Jean-Pierre. "Lyapunov Functions". W Viability Theory, 315–50. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4910-4_11.

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Henry, C. "Lyapunov Functions". W The New Palgrave Dictionary of Economics, 8062–69. London: Palgrave Macmillan UK, 2018. http://dx.doi.org/10.1057/978-1-349-95189-5_932.

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Kloeden, Peter, i Martin Rasmussen. "Lyapunov functions". W Mathematical Surveys and Monographs, 129–45. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/surv/176/07.

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Henry, C. "Lyapunov Functions". W The New Palgrave Dictionary of Economics, 1–8. London: Palgrave Macmillan UK, 1987. http://dx.doi.org/10.1057/978-1-349-95121-5_932-1.

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Henry, C. "Lyapunov Functions". W The New Palgrave Dictionary of Economics, 1–8. London: Palgrave Macmillan UK, 2008. http://dx.doi.org/10.1057/978-1-349-95121-5_932-2.

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Barreira, Luís. "Lyapunov Functions and Cones". W Lyapunov Exponents, 223–36. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71261-1_11.

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Blanchini, Franco, i Stefano Miani. "Lyapunov and Lyapunov-like functions". W Set-Theoretic Methods in Control, 27–91. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17933-9_2.

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Orlov, Yury. "Control Lyapunov Functions". W Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions, 113–46. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37625-3_5.

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Sontag, Eduardo D. "Control-Lyapunov functions". W Open Problems in Mathematical Systems and Control Theory, 211–16. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0807-8_40.

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Streszczenia konferencji na temat "Lyapunov Functions"

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Liberzon, Daniel, Charles Ying i Vadim Zharnitsky. "On almost Lyapunov functions". W 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7039864.

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Lazar, M. "Flexible control Lyapunov functions". W 2009 American Control Conference. IEEE, 2009. http://dx.doi.org/10.1109/acc.2009.5160426.

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Goebel, Rafal, Christophe Prieur i Andrew R. Teel. "Smooth patchy control Lyapunov functions". W Proceedings of the 45th IEEE Conference on Decision and Control. IEEE, 2006. http://dx.doi.org/10.1109/cdc.2006.377706.

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Miani, Stefano, i Carlo Savorgnan. "Complex polytopic control Lyapunov functions". W Proceedings of the 45th IEEE Conference on Decision and Control. IEEE, 2006. http://dx.doi.org/10.1109/cdc.2006.377752.

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"2. Methods of Lyapunov functions". W 2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP). IEEE, 2015. http://dx.doi.org/10.1109/scp.2015.7342043.

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Athanasopoulos, N., i R. M. Jungers. "Polyhedral Path-Complete Lyapunov Functions". W 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9029905.

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Balestrino, Aldo, Andrea Caiti, Emanuele Crisostomi i Sergio Grammatico. "R-composition of Lyapunov functions". W 2009 17th Mediterranean Conference on Control and Automation (MED). IEEE, 2009. http://dx.doi.org/10.1109/med.2009.5164527.

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Kim, Kyung Soo, Ho Sub Lee i PooGyeon Park. "Membership-Function-Dependent Stability Conditions Using Fuzzy Lyapunov Functions". W 2022 22nd International Conference on Control, Automation and Systems (ICCAS). IEEE, 2022. http://dx.doi.org/10.23919/iccas55662.2022.10003823.

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Ebenbauer, Christian. "Detecting oscillatory behavior using Lyapunov functions". W 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4434537.

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Argáez, Carlos, Peter Giesl i Sigurdur Hafstein. "Iterative Construction of Complete Lyapunov Functions". W 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. SCITEPRESS - Science and Technology Publications, 2018. http://dx.doi.org/10.5220/0006835402110222.

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Raporty organizacyjne na temat "Lyapunov Functions"

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Scheinker, Alexander. Introduction to Control Theory. Part 3. State Space, Stability, and Lyapunov Functions. Office of Scientific and Technical Information (OSTI), wrzesień 2015. http://dx.doi.org/10.2172/1214625.

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Schaub, H., J. L. Junkins i R. D. Robinett. Adaptive external torque estimation by means of tracking a Lyapunov function. Office of Scientific and Technical Information (OSTI), marzec 1996. http://dx.doi.org/10.2172/212517.

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Kozmina, Jelena, i Alytis Gruodis. Tool QUATTRO-20 for Examining of the Recurrent Sequencies Generated by Discrete Analogue of the Verhulst Equation. Publishing House - Vilnius Business College, czerwiec 2023. http://dx.doi.org/10.57005/ab.2023.1.3.

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QUATTRO-20 as advanced tool for estimation of the recurrent sequences was created and tested. Discrete analogue of Verhulst equation x(t+1)=F(x(t)), F(x)=rx(1-x), t=0, 1, 2, ..., was selected as the model of recurrent sequence. Related mathematical material is presented in user-friendly form: convergence conditions, Lyapunov index, behaviour of the sequencies generated by second, third, fourth compositions of function F(x). QUATTRO-20 contains several visualization methods such as xy plot, Bifurcation diagram, distribution of Lyapunov index, CobWeb plot, graphical solution. Novel graphical technique of realization of the sequence convergence was presented.

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Mitra, Joydeep, Mohammed Ben-Idris, Omar Faruque, Scott Backhaus i Sidart Deb. A Lyapunov Function Based Remedial Action Screening Tool Using Real-Time Data. Office of Scientific and Technical Information (OSTI), marzec 2016. http://dx.doi.org/10.2172/1421846.

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Event-Triggered Adaptive Robust Control for Lateral Stability of Steer-by-Wire Vehicles with Abrupt Nonlinear Faults. SAE International, lipiec 2022. http://dx.doi.org/10.4271/2022-01-5056.

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Because autonomous vehicles (AVs) equipped with active front steering have the features of time varying, uncertainties, high rate of fault, and high burden on the in-vehicle networks, this article studies the adaptive robust control problem for improving lateral stability in steer-by-wire (SBW) vehicles in the presence of abrupt nonlinear faults. First, an upper-level robust H∞ controller is designed to obtain the desired front-wheel steering angle for driving both the yaw rate and the sideslip angle to reach their correct values. Takagi-Sugeno (T-S) fuzzy modeling method, which has shown the extraordinary ability in coping with the issue of nonlinear, is applied to deal with the challenge of the changing longitudinal velocity. The output of the upper controller can be calculated by a parallel distributed compensation (PDC) scheme. Then an event-triggered adaptive fault-tolerant lower controller (ET-AFTC) is proposed to drive the whole SBW system driving the desired steering angle offered by the upper controller with fewer communication resources and strong robustness. By employing a backstepping technique, the tracking performance is improved. The dynamic surface control (DSC) approach is used to avoid the problem of repeated differentiations, and Nussbaum function is adopted to overcome the difficulty of unknown nonlinear control gain. Both the stability of the upper and lower controllers can be guaranteed by Lyapunov functions. Finally, the simulations of Matlab/Simulink are given to show that the proposed control strategy is effectively able to deal with the abrupt nonlinear fault via less communication resources and perform better in ensuring the yaw stability of the vehicle.

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