Relevant bibliographies by topics / Système polynomiaux invariants

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  2. Dissertations / Theses
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Academic literature on the topic 'Système polynomiaux invariants'

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Published: 25 May 2024

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Journal articles on the topic "Système polynomiaux invariants"

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Zakharov, Victor G. "Reproducing solutions to PDEs by scaling functions." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 03 (February 7, 2020): 2050017. http://dx.doi.org/10.1142/s0219691320500174.

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A generalization of the multivariate Strang–Fix conditions to no scale-invariant (only shift-invariant) polynomial spaces multiplied by exponents is introduced. A method to construct nonstationary compactly supported interpolating scaling functions that the scaling functions reproduce polynomials multiplied by exponents is presented. The polynomials (multiplied by exponents) are solutions to systems of linear constant coefficient PDEs, where the symbols of the differential operators that define PDEs can be no scale-invariant and can contain constant terms. Analytically calculated graphs of the scaling functions, including nonstationary, are presented. A concept of the so-called [Formula: see text]-separate MRAs is considered; and it is shown that, in the case of isotropic dilation matrices, the [Formula: see text]-separate scaling functions appear naturally.
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Wang, Maw-Ling, Shwu-Yien Yang, and Rong-Yeu Chang. "Application of Generalized Orthogonal Polynomials to Parameter Estimation of Time-Invariant and Bilinear Systems." Journal of Dynamic Systems, Measurement, and Control 109, no. 1 (March 1, 1987): 7–13. http://dx.doi.org/10.1115/1.3143824.

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Generalized orthogonal polynomials (GOP) which can represent all types of orthogonal polynomials and nonorthogonal Taylor series are first introduced to estimate the parameters of a dynamic state equation. The integration operation matrix (IOP) and the differentiation operation matrix (DOP) of the GOP are derived. The key idea of deriving IOP and DOP of these polynomials is that any orthogonal polynomial can be expressed by a power series and vice versa. By employing the IOP approach to the identification of time invariant systems, algorithms for computation which are effective, simple and straightforward compared to other orthogonal polynomial approximations can be obtained. The main advantage of using the differentiation operation matrix is that the parameter estimation can be carried out starting at an arbitrary time of interest. In addition, the computational algorithm is even simpler than that of the integral operation matrix. Illustrative examples for using IOP and DOP approaches are given. Very satisfactory results are obtained.
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Kiritsis, Konstadinos H. "Pole Assignment by Proportional-plus-derivative State Feedback for Multivariable Linear Time-invariant Systems." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 17 (June 16, 2022): 262–68. http://dx.doi.org/10.37394/23203.2022.17.30.

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In this paper the pole assignment problem by proportional-plus-derivative state feedback for multivariable linear-time invariant systems is studied. In particular, explicit necessary and sufficient conditions are established for a given polynomial with real coefficients to be characteristic polynomial of closed-loop system obtained by proportional-plus-derivative state feedback from the given multivariable linear time-invariant system. A procedure is given for the calculation of proportional-plus-derivative state feedback which places the poles of closed-loop system at desired locations. Our approach is based on properties of polynomial matrices.
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Vajda, S. "Deterministic identifiability and algebraic invariants for polynomial systems." IEEE Transactions on Automatic Control 32, no. 2 (February 1987): 182–84. http://dx.doi.org/10.1109/tac.1987.1104546.

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TAN, SHAOHUA, and JOOS VANDEWALLE. "Generalized invariant polynomials and the generalized companion form." International Journal of Control 45, no. 3 (March 1987): 811–16. http://dx.doi.org/10.1080/00207178708933771.

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Kiritsis, Konstadinos H. "Stabilization of Linear Time-Invariant Systems by State-Derivative Feedback." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 18 (March 24, 2023): 65–72. http://dx.doi.org/10.37394/23203.2023.18.7.

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In this paper is studied the stabilization problem by state-derivative feedback for linear time-invariant continuous-time systems. In particular, explicit necessary and sufficient conditions are established for the stability of a closed-loop system, obtained by state-derivative feedback from the given linear time-invariant continuous-time system. Furthermore a procedure is given for the computation of stabilizing state-derivative feedback. Our approach is based on properties of real and polynomial matrices.
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WEI, KEHUl, and B. ROSS BARMLSH. "Making a polynomial Hurwitz-invariant by choice of feedback gains†." International Journal of Control 50, no. 4 (October 1989): 1025–38. http://dx.doi.org/10.1080/00207178908953414.

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Mohan, B. M., and K. B. Datta. "Lumped and Distributed Parameter System Identification Via Shifted Legendre Polynomials." Journal of Dynamic Systems, Measurement, and Control 110, no. 4 (December 1, 1988): 436–40. http://dx.doi.org/10.1115/1.3152709.

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In this paper, one shot operational matrix for repeated integration of the shifted Legendre polynomial basis vector is developed and double-shifted Legendre series is introduced to approximate functions of two independent variables. Then using these, systematic algorithms for the identification of linear time-invariant single input-single output continuous lumped and distributed parameter systems are presented. Illustrative examples are provided with satisfactory results.
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Augusta, Petr, and Zdeněk Hurák. "Distributed stabilisation of spatially invariant systems: positive polynomial approach." Multidimensional Systems and Signal Processing 24, no. 1 (April 21, 2011): 3–21. http://dx.doi.org/10.1007/s11045-011-0152-5.

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Barabanov, A. E. "Invariance and polynomial design of strategies in the linear-quadratic game." Automation and Remote Control 67, no. 10 (October 2006): 1547–72. http://dx.doi.org/10.1134/s000511790610002x.

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Dissertations / Theses on the topic "Système polynomiaux invariants"

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Vu, Thi Xuan. "Homotopy algorithms for solving structured determinantal systems." Electronic Thesis or Diss., Sorbonne université, 2020. http://www.theses.fr/2020SORUS478.

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Les systèmes polynomiaux multivariés apparaissant dans de nombreuses applications ont des structures spéciales et les systèmes invariants apparaissent dans un large éventail d'applications telles que dans l’optimisation polynomiale et des questions connexes en géométrie algébrique réelle. Le but de cette thèse est de fournir des algorithmes efficaces pour résoudre de tels systèmes structurés. Afin de résoudre le premier type de systèmes, nous concevons des algorithmes efficaces en utilisant les techniques d’homotopie symbolique. Alors que les méthodes d'homotopie, à la fois numériques et symboliques, sont bien comprises et largement utilisées dans la résolution de systèmes polynomiaux pour les systèmes carrés, l'utilisation de ces méthodes pour résoudre des systèmes surdéterminés n'est pas si claire. Hors, les systèmes déterminants sont surdéterminés avec plus d'équations que d'inconnues. Nous fournissons des algorithmes d'homotopie probabilistes qui tirent parti de la structure déterminantielle pour calculer des points isolés dans les ensembles des zéros de tels systèmes. Les temps d'exécution de nos algorithmes sont polynomiaux dans la somme des multiplicités des points isolés et du degré de la courbe d'homotopie. Nous donnons également des bornes sur le nombre de points isolés que nous devons calculer dans trois contextes: toutes les termes de l'entrée sont dans des anneaux polynomiaux classiques, tous ces polynômes sont creux, et ce sont des polynômes à degrés pondérés. Dans la seconde moitié de la thèse, nous abordons le problème de la recherche de points critiques d'une application polynomiale symétrique sur un ensemble algébrique invariant. Nous exploitons les propriétés d'invariance de l'entrée pour diviser l'espace de solution en fonction des orbites du groupe symétrique. Cela nous permet de concevoir un algorithme qui donne une description triangulaire de l'espace des solutions et qui s'exécute en temps polynomial dans le nombre de points que nous devons calculer. Nos résultats sont illustrés par des applications à l'étude d'ensembles algébriques réels définis par des systèmes polynomiaux invariants au moyen de la méthode des points critiques
Multivariate polynomial systems arising in numerous applications have special structures. In particular, determinantal structures and invariant systems appear in a wide range of applications such as in polynomial optimization and related questions in real algebraic geometry. The goal of this thesis is to provide efficient algorithms to solve such structured systems. In order to solve the first kind of systems, we design efficient algorithms by using the symbolic homotopy continuation techniques. While the homotopy methods, in both numeric and symbolic, are well-understood and widely used in polynomial system solving for square systems, the use of these methods to solve over-detemined systems is not so clear. Meanwhile, determinantal systems are over-determined with more equations than unknowns. We provide probabilistic homotopy algorithms which take advantage of the determinantal structure to compute isolated points in the zero-sets of determinantal systems. The runtimes of our algorithms are polynomial in the sum of the multiplicities of isolated points and the degree of the homotopy curve. We also give the bounds on the number of isolated points that we have to compute in three contexts: all entries of the input are in classical polynomial rings, all these polynomials are sparse, and they are weighted polynomials. In the second half of the thesis, we deal with the problem of finding critical points of a symmetric polynomial map on an invariant algebraic set. We exploit the invariance properties of the input to split the solution space according to the orbits of the symmetric group. This allows us to design an algorithm which gives a triangular description of the solution space and which runs in time polynomial in the number of points that we have to compute. Our results are illustrated by applications in studying real algebraic sets defined by invariant polynomial systems by the means of the critical point method
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Fernandes, Wilker Thiago Resende. "Centers and isochronicity of some polynomial differential systems." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-12092017-080613/.

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The center-focus and isochronicity problems are two classic problem in the qualitative theory of ordinary differential equations (ODEs). Although such problems have been studied during more than hundred years a complete understanding of them is far from be reached. Recently the computational algebra tools have been contributing significantly with the development of such problems. The aim of this thesis is to contribute with the studies of the center-focus and isochronicity problem. Using computational algebra tools we find conditions for the existence of two simultaneous centers for a family of quintic systems possessing symmetry. The studies of the simultaneous existence of two centers in differential systems is known as the bi-center problem. We investigate conditions for the isochronicity of centers for families of cubic and quintic systems and we study its global behaviour in the Poincaré disk. Finally, we study the existence of invariant surfaces and first integrals in a family of 3-dimensional systems. Such family is known as the May-Leonard asymmetric system and it appears in modelling, for instance it is a model for the competition of three species.
Os problemas do foco-centro e da isocronicidade são dois problemas clássicos da teoria qualitativa das equações diferenciais ordinárias (EDOs). Apesar de tais problemas serem investigados a mais de cem anos ainda pouco se sabe sobre eles. Recentemente o uso e desenvolvimento de ferramentas algebro-computacionais tem contribuído significativamente em seu avanço. O objetivo desta tese é colaborar com o estudo do problema do foco-centro e da isocronicidade. Utilizando ferramentas algebro-computacionais encontramos condições para a existência simultânea de dois centros em famílias de sistemas diferenciais quínticos com simetria. O estudo sobre a existência simultânea de dois centros é também conhecido como problema do bi-centro. Investigamos condições para a isocronicidade de centros para famílias de sistemas cubicos e quínticos e estudamos o comportamento global de suas órbitas no disco de Poincaré. Finalmente, tratamos da existência de superfícies invariantes e integrais primeiras para uma familia de sistemas 3-dimensionais encontrado entre outras situações na modelagem da competição entre três espécies e conhecido como sistema de May-Leonard.
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Reinol, Alisson de Carvalho [UNESP]. "Integrabilidade e dinâmica global de sistema diferenciais polinomiais definidos em R³ com superfícies algébricas invariantes de graus 1 e 2." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/151140.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Neste trabalho, consideramos aspectos algébricos e dinâmicos de alguns problemas envolvendo superfícies algébricas invariantes em sistemas diferenciais polinomiais definidos em R³. Determinamos o número máximo de planos invariantes que um sistema diferencial quadrático pode ter e estudamos a realização e integrabilidade de tais sistemas. Fornecemos a forma normal para sistemas diferenciais com quádricas invariantes e estudamos de forma mais detalhada a dinâmica e integrabilidade de sistemas diferenciais quadráticos com um paraboloide elíptico como superfície algébrica invariante. Por fim, estudamos as consequências dinâmicas ao se perturbar um sistema diferencial, cujo espaço de fase é folheado por superfícies algébricas invariantes. Para tal, consideramos o sistema diferencial quadrático conhecido como sistema Sprott A, que depende de um parâmetro real a e apresenta comportamento caótico mesmo sem ter pontos de equilíbrio, tendo, assim, um hidden attractor para valores adequados do parâmetro a. Provamos que, para a=0, o espaço de fase desse sistema é folheado por esferas concêntricas invariantes. Utilizando a Teoria do Averaging e o Teorema KAM (Kolmogorov-Arnold-Moser), provamos que, para a>0 suficientemente pequeno, uma órbita periódica orbitalmente estável emerge de um equilíbrio do tipo zero-Hopf não isolado localizado na origem e que formam-se toros invariantes em torno desta órbita periódica. Concluímos que a ocorrência de tais fatos tem um papel importante na formação do hidden attractor.
In this work, we consider algebraic and dynamical aspects of some problems involving invariant algebraic surfaces in polynomial differential systems defined in R³. We determine the maximum number of invariant planes that a quadratic differential system can have and we study the realization and integrability of such systems. We provide the normal form for differential systems having an invariant quadric and we study in more detail the dynamics and integrability of quadratic differential systems having an elliptic paraboloid as invariant algebraic surface. Finally, we study the dynamic consequences of perturbing differential system whose phase space is foliated by invariant algebraic surfaces. For this we consider the quadratic differential system known as Sprott A system, which depends on one real parameter a and presents chaotic behavior even without having any equilibrium point, thus having a hidden attractor for suitable values of parameter a. We prove that, for a=0, the phase space of this system is foliated by invariant concentric spheres. By using the Averaging Theory and the KAM (Kolmogorov-Arnold-Moser) Theorem, we prove that, for a>0 sufficiently small, an orbitally stable periodic orbit emerges from a zero-Hopf nonisolated equilibrium point located at the origin and that invariant tori are formed around this periodic orbit. We conclude that the occurrence of these facts has an important role in the formation of the hidden attractor.
FAPESP: 2013/26602-7
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Pantazi, Chara. "Inverse problems of the Darboux theory of integrability for planar polynomial differential systems." Doctoral thesis, Universitat Autònoma de Barcelona, 2004. http://hdl.handle.net/10803/3083.

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Dehornoy, Pierre. "Invariants topologiques des orbites périodiques d'un champ de vecteurs." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00656900.

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Cette thèse se situe à l'interface entre théorie des nœuds et théorie des systèmes dynamiques. Le thème central consiste, étant donné un champ de vecteurs dans une variété de dimension 3, à considérer ses orbites périodiques, et à s'interroger sur les informations qu'elles donnent sur le champ de vecteurs et la variété initiaux.La première partie est consacrée au flot géodésique défini sur le fibré unitaire tangentd'une surface, ou d'une orbiface, à courbure constante. L'observation de certains exemples (sphère, tore, surface modulaire) suggère la conjecture suivante, due à Étienne Ghys : l'enlacement entre deux familles homologiquement nulles quelconques d'orbites périodiques est toujours négatif. En d'autres termes, le flot géodésique serait lévogyre. Quand la courbure est négative, par les travaux de David Fried sur les flots d'Anosov, cette conjecture implique une propriété étonnante et très particulière : n'importe quelle collection homologiquement nulle d'orbites périodiques borde une section de Birkhoff pour le flot géodésique, et est par conséquent la reliure d'un livre ouvert. En ce sens, cette conjecture propose une généralisation de la construction de Norbert A'Campo de livres ouverts sur les fibrés unitaires tangents. Nous proposons la démonstration de cette conjecture dans les cas du tore, des orbifolds de type (2, q, infini), et de l'orbifold de type (2, 3, 7). La seconde partie est consacrée au comportement asymptotique des invariants des nœuds formés par les orbites périodiques d'un champ de vecteur, quand la longueur de l'orbite tend vers l'infini. Le but est de définir des invariants de champs de vecteurs stables par difféomorphisme. Dans le cas particulier des nœuds de Lorenz, nous montrons que les racines du polynôme d'Alexander admettent un comportement particulier : elles s'accumulent au voisinage du cercle-unité.
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Schilli, Christian [Verfasser], Eva Barbara [Akademischer Betreuer] Zerz, and Sebastian [Akademischer Betreuer] Walcher. "Controlled and conditioned invariant varieties for polynomial control systems / Christian Schilli ; Eva Barbara Zerz, Sebastian Walcher." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/1130403009/34.

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Rezende, Alex Carlucci. "A geometria de algumas famílias tridimensionais de sistemas diferenciais quadráticos no plano." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-25112014-142038/.

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Sistemas diferenciais quadráticos planares estão presentes em muitas áreas da matemática aplicada. Embora mais de mil artigos tenham sido publicados sobre os sistemas quadráticos ainda resta muito a se conhecer sobre esses sistemas. Problemas clássicos, e em particular o XVI problema de Hilbert, estão ainda em aberto para essa família. Um dos objetivos dos pesquisadores contemporâneos é obter a classificação topológica completa dos sistemas quadráticos. Devido ao grande número de parâmetros (essa família possui doze parâmetros e, aplicando transformações afins e reescala do tempo, reduzimos esse número a cinco, sendo ainda um número grande para se trabalhar) usualmente subclasses são consideradas nas investigações realizadas. Quando características específicas são levadas em consideração, o número de parâmetros é reduzido e o estudo se torna possível. Nesta tese estudamos principalmente duas subfamílias de sistemas quadráticos: a primeira possuindo um nó triplo semielemental e a segunda possuindo uma selanó semi elemental finita e uma selanó semielemental infinita formada pela colisão de uma sela infinita com um nó infinito. Os diagramas de bifurcação para ambas as famílias são tridimensionais. A família tendo um nó triplo gera 28 retratos de fase topologicamente distintos, enquanto o fecho da família tendo as selasnós dentro do espaço de bifurcação de sua forma normal gera 417. Polinômios invariantes são usados para construir os conjuntos de bifurcação e os retratos de fase topologicamente distintos são representados no disco de Poincaré. Os conjuntos de bifurcação são a união de superfícies algébricas e superfícies cuja presença foi detectada numericamente. Ainda nesta tese, apresentamos todos os retratos de fase de um sistema diferencial conhecido como modelo do tipo SIS (sistema suscetívelinfectadosuscetível, muito comum na matemática aplicada) e a classificação dos sistemas quadráticos possuindo hipérboles invariantes. Ambos sistemas foram investigados usando de polinômios invariantes afins.
Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilberts 16th problem, are still open for this family. One of the goals of recent researchers is the topological classification of quadratic systems. As this attempt is not possible in the whole class due to the large number of parameters (twelve, but, after affine transformations and time rescaling, we arrive at families with five parameters, which is still a large number), many subclasses are considered and studied. Specific characteristics are taken into account and this implies a decrease in the number of parameters, which makes possible the study. In this thesis we mainly study two subfamilies of quadratic systems: the first one possessing a finite semielemental triple node and the second one possessing a finite semielemental saddlenode and an infinite semielemental saddlenode formed by the collision of an infinite saddle with an infinite node. The bifurcation diagram for both families are tridimensional. The family having the triple node yields 28 topologically distinct phase portraits, whereas the closure of the family having the saddlenodes within the bifurcation space of its normal form yields 417. Invariant polynomials are used to construct the bifurcation sets and the phase portraits are represented on the Poincaré disk. The bifurcation sets are the union of algebraic surfaces and surfaces whose presence was detected numerically. Moreover, we also present the analysis of a differential system known as SIS model (this kind of systems are easily found in applied mathematics) and the complete classification of quadratic systems possessing invariant hyperbolas.
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Corvez, Solen. "Etude de systèmes polynomiaux : contributions à la classification d'une famille de manipulateurs et au calcul des intersections de courbes A - splines : par Solen Corvez." Rennes 1, 2005. http://www.theses.fr/2005REN10020.

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Nous nous intéressons dans cette thèse à deux problèmes issus, l'un de la robotique et l'autre du dessin assisté par ordinateur, impliquant chacun l'étude de systèmes polynomiaux. La première partie de cette thèse est dédiée à la classification d'une famille de manipulateurs sériels, suivant qu'ils puissent ou non changer de posture sans passer par une singularité. Nous présentons une méthode générale d'étude d'une large classe de systèmes polynomiaux à paramètres faisant intervenir la notion nouvelle de variété disciminante. Elle nous a permis d'obtenir une classification complète dans le cas où l'effecteur présente un décalage axial. Dans la deuxième partie, nous proposons un algorithme de calcul des intersections de courbes A-splines cubiques. Ces courbes sont définies comme suite de segments de cubiques recollés continuement, inscrits chacun dans un triangle de contrôle. Cet algorithme est basé sur l'étude des perturbations des courbes rationnelles d'un faisceau de cubiques.
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Lindert, Sven-Olaf. "Beiträge zur Steuerung und Regelung von mehrvariablen linearen zeitinvarianten Systemen in polynomialer Darstellung." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-24944.

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In dieser Arbeit werden lineare zeitinvariante endlichdimensionale Systeme (LTI-Systeme) mit m > 1 Eingängen und p > 1 Ausgängen untersucht (MIMO-Systeme). Diese lassen sich darstellen durch lineare Gleichungen mit Matrizen, deren Einträge Polynome im Ableitungsoperator d/dt sind. Bei Nutzung der Laplace-Transformation handelt es sich um Polynome in s. Algebraisch bilden diese einen Euklidischen Ring. Durch Überführung der Matrizen in die Hermitesche Normalform werden m Basisgrößen definiert. Die Verläufe oder Trajektorien der Basisgrößen lassen sich frei vorgegeben. Damit werden die Trajektorien sämtlicher übrigen Signale, insbesondere die der erforderlichen Eingangssignale, festgelegt und können ohne Integration berechnet werden. Ein linksteilerfremdes (auch steuerbar genanntes) Modell ist dabei nicht zwingend erforderlich. Damit eignen sich die Basisgrößen besonders zur Planung von Trajektorien. Genauer untersucht wird die Planung mit Polynomen in der Zeit als Ansatzfunktionen und die Planung von Trajektorien, die ein quadratisches Kostenfunktional minimieren. In der technischen Praxis werden die Systeme stets von den geplanten Trajektorien abweichen. Insbesondere bei instabilen Regelstrecken ist deshalb ein stabilisierender Folgeregler unentbehrlich. Die Struktur der Folgeregelung wird eingeführt und es wird deutlich gemacht, dass jede Methode zum Entwurf linearer Regler angewendet werden kann. Die Nullstellenzuweisung durch dynamische Ausgangsrückführung mit Reglern vorgegebener möglichst geringer dynamischer Ordnung wird detailliert untersucht und eine neue Lösungsmöglichkeit aufgezeigt. Durch Nutzung der modifizierten z-Transformation lässt sich die Theorie auf ein hybrides System, bestehend aus einer zeitkontinuierlichen Regelstrecke und einer zeitdiskreten digitalen Steuerung und Regelung, ausdehnen. Dabei werden die Verläufe der Signale zwischen den Abtastzeitpunkten in die Planung einbezogen. Zum Schluss werden die linearen Beobachter im Licht der polynomialen Matrizendarstellung neu untersucht. Es wird gezeigt, dass die polynomiale Matrizendarstellung einen theoretischen Rahmen bietet, in dem sich sämtliche linearen Beobachter mit einer Methode entwerfen lassen. - (Die Dissertation ist veröffentlicht in der Reihe Fortschritt-Berichte VDI, Reihe 8 - Mess-, Steuerungs- und Regelungstechnik, Band 1164 im VDI Verlag GmbH, Düsseldorf, ISBN 978-3-18-516408-8)
In this thesis linear time invariant lumped systems (LTI-systems) with m>1 inputs and p > 1 outputs (MIMO-systems) are investigated. These systems can be represented by linear equations with matrices, whose entries are polynomials in the differential operator d/dt. If Laplace-transform is employed, the polynomials are in s. Algebraically polynomials form a Euclidean ring. The conversion of the matrices to the Hermite form leads to defining m basic variables. The trajectories of the basis variables may be chosen arbitrarily. With that choice the trajectories of all remaining variables and especially the input variables are determined and can be calculated without integration. A left coprime (also called controllable) model is not required. Hence basis variables are particularly useful for planning trajectories. Special attention is paid to planning trajectories with polynomials in time as basic functions and planning trajectories which minimise a quadratic functional of costs. In engineering practice the systems will always differ from the planed trajectories. Especially with unstable plants a stabilising tracking controller is compulsory. The structure of the tracking control is introduced. It becomes apparent that every linear theory for the design of closed loop controllers is suitable. Pole assignment by dynamic output feedback with low order controllers of a fixed structure is looked at in more detail. A new approach to this problem is presented. Using the modified z-transform the theory is extended to hybrid systems consisting of a digital or discrete time controller and a plant in continuous time. Thereby the course of the signals between the sampling moments is taken into account. Finally linear observers are reinvestigated using the polynomial matrix representation. It is shown that the polynomial matrix representation provides a theoretical framework in which all linear observers can be designed
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Prado, Marcia Lissandra Machado. "Controle robusto por alocação de polos via analise intervalar modal." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260560.

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Orientador: Paulo Augusto Valente Ferreira
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-06T08:04:01Z (GMT). No. of bitstreams: 1 Prado_MarciaLissandraMachado_D.pdf: 1397184 bytes, checksum: 5c23769b43bb76b58c39a5fb95adaaee (MD5) Previous issue date: 2006
Resumo: Uma abordagem baseada em análise intervalar para o projeto de controladores por realimentação de estados robusta é proposta. Demonstra-se que quando especificações para alocação de pólos são representadas por conjuntos espectrais de polinômios intervalares, o problema do projeto por realimentação de estados robusta pode ser completamente formulado e resolvido no contexto de conceitos e métodos de análise intervalar. Representações poliédricas convexas de uma classe de controladores por realimentação de estados robusta satisfazendo a uma equação de Ackerman intervalar são derivadas. Um procedimento de projeto baseado em programação não-linear que objetiva a maximização da não-fragilidade do controlador robusto resultante é introduzido. Para sistemas multivariáveis é proposta uma abordagem por alocação de pólos utilizando a equação de Sylvester intervalar e técnicas de resolução baseadas em intervalos modais. Exemplos numéricos ilustram o projeto de controladores por realimentação de estados obtidos a partir da abordagem por análise intervalar proposta
Abstract: An interval analysis approach for the design of robust state feedback controllers is proposed. It is shown that when regional pole placement specifications are represented as spectral sets of interval polynomials, the robust state feedback design problem can be entirely formulated and solved in the context of the concepts and methods of interval analysis. Explicit convex polyhedral representations of a class of robust state feedback controllers satisfying an interval Ackerman¿s equation are derived. A design procedure based on nonlinear programming which aims at maximizing the non-fragility of the resulting robust controller is introduced. In the case multivariable systems is proposed an approach based on pole placement which employs an interval Sylvester equation and modal intervals techniques. Numerical examples illustrate the design of robust state feedback controllers through the interval analysis approaches proposed.
Doutorado
Automação
Doutor em Engenharia Elétrica
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Books on the topic "Système polynomiaux invariants"

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Zabrodin, Anton. Quantum spin chains and classical integrable systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0013.

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This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0th time of the hierarchy. This implies a remarkable relation between the quantum spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, a system of algebraic equations can be obtained for the spectrum of the spin chain Hamiltonians.
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Invitation to Nonlinear Algebra. American Mathematical Society, 2021.

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Book chapters on the topic "Système polynomiaux invariants"

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Mover, Sergio, Alessandro Cimatti, Alberto Griggio, Ahmed Irfan, and Stefano Tonetta. "Implicit Semi-Algebraic Abstraction for Polynomial Dynamical Systems." In Computer Aided Verification, 529–51. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81685-8_25.

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AbstractSemi-algebraic abstraction is an approach to the safety verification problem for polynomial dynamical systems where the state space is partitioned according to the sign of a set of polynomials. Similarly to predicate abstraction for discrete systems, the number of abstract states is exponential in the number of polynomials. Hence, semi-algebraic abstraction is expensive to explicitly compute and then analyze (e.g., to prove a safety property or extract invariants).In this paper, we propose an implicit encoding of the semi-algebraic abstraction, which avoids the explicit enumeration of the abstract states: the safety verification problem for dynamical systems is reduced to a corresponding problem for infinite-state transition systems, allowing us to reuse existing model-checking tools based on Satisfiability Modulo Theory (SMT). The main challenge we solve is to express the semi-algebraic abstraction as a first-order logic formula that is linear in the number of predicates, instead of exponential, thus letting the model checker lazily explore the exponential number of abstract states with symbolic techniques. We implemented the approach and validated experimentally its potential to prove safety for polynomial dynamical systems.
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Rodríguez-Carbonell, Enric, and Ashish Tiwari. "Generating Polynomial Invariants for Hybrid Systems." In Hybrid Systems: Computation and Control, 590–605. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-31954-2_38.

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Artés, Joan C., Jaume Llibre, Dana Schlomiuk, and Nicolae Vulpe. "Invariants in mathematical classification problems." In Geometric Configurations of Singularities of Planar Polynomial Differential Systems, 91–98. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-50570-7_4.

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Chesi, Graziano, Andrea Garulli, Alberto Tesi, and Antonio Vicino. "Robustness with Time-invariant Uncertainty." In Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems, 99–132. London: Springer London, 2009. http://dx.doi.org/10.1007/978-1-84882-781-3_4.

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Artés, Joan C., Jaume Llibre, Dana Schlomiuk, and Nicolae Vulpe. "Invariant theory of planar polynomial vector fields." In Geometric Configurations of Singularities of Planar Polynomial Differential Systems, 99–132. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-50570-7_5.

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Kofnov, Andrey, Marcel Moosbrugger, Miroslav Stankovič, Ezio Bartocci, and Efstathia Bura. "Moment-Based Invariants for Probabilistic Loops with Non-polynomial Assignments." In Quantitative Evaluation of Systems, 3–25. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16336-4_1.

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Sogokon, Andrew, Khalil Ghorbal, Paul B. Jackson, and André Platzer. "A Method for Invariant Generation for Polynomial Continuous Systems." In Lecture Notes in Computer Science, 268–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-49122-5_13.

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Hacinliyan, Avadis Simon, Orhan Ozgur Aybar, and Ilknur Kusbeyzi Aybar. "Invariants, Attractors and Bifurcation in Two Dimensional Maps with Polynomial Interaction." In Chaos and Complex Systems, 349–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33914-1_47.

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Caminata, Alessio, and Elisa Gorla. "Solving Multivariate Polynomial Systems and an Invariant from Commutative Algebra." In Arithmetic of Finite Fields, 3–36. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68869-1_1.

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Schilli, Christian, Eva Zerz, and Viktor Levandovskyy. "Controlled and Conditioned Invariance for Polynomial and Rational Feedback Systems." In Algebraic and Symbolic Computation Methods in Dynamical Systems, 259–93. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38356-5_10.

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Conference papers on the topic "Système polynomiaux invariants"

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Goubault, Eric, Jacques-Henri Jourdan, Sylvie Putot, and Sriram Sankaranarayanan. "Finding non-polynomial positive invariants and lyapunov functions for polynomial systems through Darboux polynomials." In 2014 American Control Conference - ACC 2014. IEEE, 2014. http://dx.doi.org/10.1109/acc.2014.6859330.

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Mohsenizadeh, Navid, Swaroop Darbha, and Shankar P. Bhattacharyya. "Synthesis of Digital PID Controllers for Discrete-Time Systems With Guaranteed Non-Overshooting Transient Response." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-6196.

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In this paper, we present a new method of synthesizing digital PID controllers for discrete-time, Linear Time Invariant (LTI) Systems satisfying a class of transient response specifications. The problem of synthesizing a controller to achieve desirable transient specifications, such as requiring the transient response to be within an allowable range of overshoot, can be carried out as a problem of guaranteeing the impulse response of an appropriate closed loop error transfer function to be non-negative. An earlier result by the authors provides necessary and sufficient conditions for the impulse response of a discrete-time transfer function to be non-negative in terms of the requirement of a sequence of polynomials to be sign-invariant on the interval [1, ∞). An application of this result to the error transfer function yields a sequence of polynomials which are required to be sign-invariant on [1, ∞) but whose coefficients are polynomial functions of the controller gains k1, k2 and k3.
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Emami, Tooran, and John M. Watkins. "Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay." In ASME 2008 Dynamic Systems and Control Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/dscc2008-2205.

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A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.
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Spires, J. M., and S. C. Sinha. "Response of Linear Time-Periodic Systems Subjected to Stochastic Excitations: A Chebyshev Polynomial Approach." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0336.

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Abstract In many situations engineering systems modeled by a system of linear second order differential equations with periodic damping and stiffness matrices are subjected to stochastic excitations. It has been shown that the fundamental solution matrix for such systems can be efficiently computed using a Chebyshev polynomial series solution technique. Further, it has been shown that the Liapunov-Floquet transformation matrix can be computed, and the original time-periodic system can be put into a time invariant form. In this paper, these techniques are applied in finding the transient mean square response and transient autocorrelation response of periodic systems subjected to stochastic forcing vectors. Two formulations are presented. In the first formulation, the mean square response of the original system is computed directly. In the second formulation, the original system is transformed to a time-invariant form. The autocorrelation response is found by determining the response of the time-invariant system. Both formulations utilize the convolution integral to form an expression for the response. This expression can be evaluated numerically, symbolically, or through Chebyshev polynomial expansion. Results for some time-invariant and periodic systems are included, as illustrative examples.
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Liu, Jiang, Naijun Zhan, and Hengjun Zhao. "Computing semi-algebraic invariants for polynomial dynamical systems." In the ninth ACM international conference. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/2038642.2038659.

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Ben Sassi, Mohamed Amin, Antoine Girard, and Sriram Sankaranarayanan. "Iterative computation of polyhedral invariants sets for polynomial dynamical systems." In 2014 IEEE 53rd Annual Conference on Decision and Control (CDC). IEEE, 2014. http://dx.doi.org/10.1109/cdc.2014.7040384.

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O’Connor, Sam, Mark Plecnik, Aravind Baskar, and James Joo. "Complete Solutions for the Approximate Synthesis of Spherical Four-Bar Function Generators." In ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/detc2023-116895.

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Abstract Kinematic synthesis to meet an approximate motion specification naturally forms a constrained optimization problem. In this work, we conduct global design searches by direct computation of all critical points through stationarity conditions. The idea is not new, but performed at scale is only possible through modern polynomial homotopy continuation solvers. Such a complete computation finds all minima, including the global, serving as a powerful design exploration technique. We form equality constrained objective functions that pertain to the synthesis of spherical four-bar linkages for approximate function generation. For each problem considered, Lagrangian stationarity conditions set up a square system of polynomials. We consider the most general case where all mechanism dimensions may vary, and a more specific case that enables the placement of ground pivots. The former optimization problem is shown to permit an estimated maximum of 268 sets of critical points, and the latter permits 61 sets. Critical points are classified as saddles or minima through a post-process eigenanalysis of the projected Hessian. Approximate motion is specified as discretized points from a desired input-output angle function. The coefficients of the stationarity polynomials can be expressed as summations of symmetric matrices indexed by the discretization points. We take the sums themselves to parameterize these polynomials rather than constituent terms (the discrete data). In this way, the algebraic structure of the synthesis equations remains invariant to the number of discretization points chosen. The results of our computational work were used to design a mechanism that coordinates the unfolding of wings for a deployable aircraft.
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Xue, Bai, Qiuye Wang, Naijun Zhan, and Martin Fränzle. "Robust invariant sets generation for state-constrained perturbed polynomial systems." In HSCC '19: 22nd ACM International Conference on Hybrid Systems: Computation and Control. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3302504.3311810.

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Sharma, Ashu, and Subhash C. Sinha. "On Computation of Approximate Lyapunov-Perron Transformations." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97702.

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Abstract Many dynamical systems can be modeled by a set of linear/nonlinear ordinary differential equations with quasi-periodic coefficients. Application of Lyapunov-Perron (L-P) transformations to such systems produce dynamically equivalent systems in which the linear parts are time-invariant. In this work, a technique for the computation of approximate L-P transformations is suggested. First, a quasi-periodic system is replaced by a periodic system with a ‘suitable’ large principal period to which Floquet theory can be applied. Then, the state transition matrix (STM) of the periodic system is computed in the symbolic form using shifted Chebyshev polynomials and Picard iteration method. Finally, since the STM can be expressed in terms of a periodic matrix and a time-invariant matrix (Lyapunov-Floquet theorem), this factorization is utilized to compute approximate L-P transformations. A two-frequency quasi-periodic system is investigated using the proposed method and approximate L-P transformations are generated for stable, unstable and critical cases. These transformations are also inverted by defining the adjoint system to the periodic system. Unlike perturbation and averaging, the proposed technique is not restricted by the existence of a generating solution and a small parameter. Approximate L-P transformations can be utilized to design controllers using time-invariant methods and may also serve as a powerful tool in bifurcation studies of nonlinear quasi-periodic systems.
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Vu, Thi Xuan. "Computing Critical Points for Algebraic Systems Defined by Hyperoctahedral Invariant Polynomials." In ISSAC '22: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3476446.3536181.

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