Search results for "Control and Optimization"
showing 10 items of 448 documents
Normalizability, Synchronicity, and Relative Exactness for Vector Fields in C2
2004
In this paper, we study the necessary and su.cient condition under which an orbitally normalizable vector field of saddle or saddle-node type in C2 is analytically conjugate to its formal normal form (i.e., normalizable) by a transformation fixing the leaves of the foliation locally. First, we express this condition in terms of the relative exactness of a certain 1-form derived from comparing the time-form of the vector field with the time-form of the normal form. Then we show that this condition is equivalent to a synchronicity condition: the vanishing of the integral of this 1-form along certain asymptotic cycles de.ned by the vector field. This can be seen as a generalization of the clas…
The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two
1997
In previous papers, we gave in dimension 2 and 3 a classification of generic synthesis of analytic systems\(\dot v(t) = X(v(t)) + u(t)Y(v(t))\) with a terminal submanifoldN of codimension one when the trajectories are not tangent toN. We complete here this classification in all generic cases in dimension 3, giving a topological classification and a model in each case. We prove also that in dimensionn≥3, out of a subvariety ofN of codimension there, we have described all the local synthesis.
Ecuaciones en derivadas parciales gobernadas por operadores acretivos
2010
Una teoria que ha resultado ser de gran utilidad en el estudio de muchas ecuaciones en derivadas parciales no lineales es la teoria de semigrupos no lineales generados por operadores acretivos en espacios de Banach. Dicha teoria se basa fundamentalmente en el Teorema de Crandall-Ligget y en las aportaciones de Ph. Benilan. En este articulo, despues de hacer una exposicion esquematica de esta teoria general, veremos como la hemos aplicado a algunas ecuaciones en derivadas parciales no lineales que aparecen en diversos campos de la Ciencia.
CQ *-algebras of measurable operators
2022
Abstract We study, from a quite general point of view, a CQ*-algebra (X, 𝖀0) possessing a sufficient family of bounded positive tracial sesquilinear forms. Non-commutative L 2-spaces are shown to constitute examples of a class of CQ*-algebras and any abstract CQ*-algebra (X, 𝖀0) possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a direct sum of non-commutative L 2-spaces.
Partial differential equations governed by accretive operators
2012
The theory of nonlinear semigroups in Banach spaces generated by accretive operators has been very useful in the study of many nonlinear partial differential equations Such a theory is fundamentally based in the Crandall-Liggett Theorem and in the contributions of Ph. Benilan. In this paper, after outlining some of the main points of this theory, we present some of the applications to some nonlinear partial differential equations that appear in different fields of Science.
Stability and Finiteness Properties of Medial Axis and Skeleton
2004
The medial axis is a geometric object associated with any bounded open set in \Bbb R^n which has various applications in computer science. We study it from a mathematical point of view. We give some results about its geometrical structure when the open set is subanalytic and we prove that it is stable under C2-perturbations when the open set is bounded by a hypersurface with positive local feature size.
Some common fixed point results for weakly compatible mappings in cone metric type space
2013
In this paper we consider cone metric type spaces which are introduced as a generalization of symmetric and metric spaces by Khamsi and Hussain in 2010. Then we prove several common fixed point for weakly compatible mappings in cone metric type spaces. All results are proved in the settings of a solid cone, without the assumption of continuity of the mappings.
Existence for shape optimization problems in arbitrary dimension
2002
We discuss some existence results for optimal design problems governed by second order elliptic equations with the homogeneous Neumann boundary conditions or with the interior transmission conditions. We show that our continuity hypotheses for the unknown boundaries yield the compactness of the associated characteristic functions, which, in turn, guarantees convergence of any minimizing sequences for the first problem. In the second case, weaker assumptions of measurability type are shown to be sufficient for the existence of the optimal material distribution. We impose no restriction on the dimension of the underlying Euclidean space.
Shakedown optimum design of reinforced concrete framed structures
1994
Structures subjected to variable repeated loads can undergo the shakedown or adaptation phenomenon,-which prevents them from collapse but may cause lack of serviceability, for the plastic deformations developed, although finite, as shakedown occurrence postulates, may exceed some maximum values imposed by external ductility criteria. This paper is devoted to the optimal design of reinforced concrete structures, subjected to variable and repeated loads. For such structures the knowledge of the actual values taken by the plastic deformations, at shakedown occurrence, is a crucial issue. An approximate assessment of such plastic deformations is needed, which is herein provided in the shape of …
OPTIMUM DESIGN OF REINFORCED CONCRETE STRUCTURES UNDER VARIABLE LOADINGS
1987
Abstract This paper presents a method for optimal design of reinforced concrete (RC) structures, subjected to quasi-static variable loads and accounting for cross-sections limited ductility requirements. It consists of a very simple refinement procedure to be applied in the classical Optimal Shakedown Design, (OSD), which leads to a strengthened structure satisfying the requisite that the actual plastic relative rotations, developed at a specified set of critical sections as a result of a variable repeated loading program, do not exceed given upper limits. This strengthened design is a safe but not strictly optimal design and is obtained using the simple rule that the steel reinforcement ar…