Singular minimisers in the calculus of variations : a degenerate form of cavitation
Singular perturbation for the Dirichlet boundary control of elliptic problems
A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small...
Singular perturbation for the Dirichlet boundary control of elliptic problems
A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small...
Singular perturbations in optimal control problem with application to nonlinear structural analysis
This paper concerns an optimal control problem of elliptic singular perturbations in variational inequalities (with controls appearing in coefficients, right hand sides and convex sets of states as well). The existence of an optimal control is verified. Applications to the optimal control of an elasto-plastic plate with a small rigidity and with an obstacle are presented. For elasto-plastic plates with a moving part of the boundary a primal finite element model is applied and a convergence result...
Singular points of order of Clarke regular and arbitrary functions
Let be a separable Banach space and a locally Lipschitz real function on . For , let be the set of points , at which the Clarke subdifferential is at least -dimensional. It is well-known that if is convex or semiconvex (semiconcave), then can be covered by countably many Lipschitz surfaces of codimension . We show that this result holds even for each Clarke regular function (and so also for each approximately convex function). Motivated by a resent result of A.D. Ioffe, we prove...
Singular Quadratic Functionals.
Singular quadratic functionals and transformation of linear Hamiltonian systems
Singular sets of convex bodies and surfaces with generalized curvatures.
Singular trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory.
Singularities of optimal averaged profit for stationary strategies.
Singularities of the stationary domain for polydynamical systems
Sixty years of cybernetics: a comparison of approaches to solving the control problem
The H2 control problem consists of stabilizing a control system while minimizing the H2 norm of its transfer function. Several solutions to this problem are available. For systems in state space form, an optimal regulator can be obtained by solving two algebraic Riccati equations. For systems described by transfer functions, either Wiener-Hopf optimization or projection results can be applied. The optimal regulator is then obtained using operations with proper stable rational matrices: inner-outer...
Size minimizing surfaces
We prove a new existence theorem pertaining to the Plateau problem in -dimensional Euclidean space. We compare the approach of E.R. Reifenberg with that of H. Federer and W.H. Fleming. A relevant technical step consists in showing that compact rectifiable surfaces are approximatable in Hausdorff measure and in Hausdorff distance by locally acyclic surfaces having the same boundary.
Size-minimizing rectifiable currents.
Slice convergence : stabilité et optimisation dans les espaces non réflexifs
Il est démontré par Mentagui [ESAIM : COCV 9 (2003) 297-315] que, dans le cas des espaces de Banach généraux, la convergence d’Attouch-Wets est stable par une classe d’opérations classiques de l’analyse convexe, lorsque les limites des suites d’ensembles et de fonctions satisfont certaines conditions de qualification naturelles. Ceci tombe en défaut avec la slice convergence. Dans cet article, nous établissons des conditions de qualification uniformes assurant la stabilité de la slice convergence...
Slice convergence: stabilité et optimisation dans les espaces non réflexifs
Il est démontré par Mentagui [ESAIM: COCV9 (2003) 297-315] que, dans le cas des espaces de Banach généraux, la convergence d'Attouch-Wets est stable par une classe d'opérations classiques de l'analyse convexe, lorsque les limites des suites d'ensembles et de fonctions satisfont certaines conditions de qualification naturelles. Ceci tombe en défaut avec la slice convergence. Dans cet article, nous établissons des conditions de qualification uniformes assurant la stabilité de la slice convergence...
Slicing of generalized surfaces with curvature measures and diameter's estimate
We prove generalizations of Meusnier's theorem and Fenchel's inequality for a class of generalized surfaces with curvature measures. Moreover, we apply them to obtain a diameter estimate.
Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations.
Smooth bifurcation for a Signorini problem on a rectangle
We study a parameter depending semilinear elliptic PDE on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. We describe smooth branches of smooth nontrivial solutions bifurcating from the trivial solution branch in eigenvalues of the linearized problem. In particular, the contact sets of these nontrivial solutions are intervals which change smoothly along the branch. The main tools of the proof...
Smooth optimal synthesis for infinite horizon variational problems
We study Hamiltonian systems which generate extremal flows of regular variational problems on smooth manifolds and demonstrate that negativity of the generalized curvature of such a system implies the existence of a global smooth optimal synthesis for the infinite horizon problem. We also show that in the Euclidean case negativity of the generalized curvature is a consequence of the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification for...